Вопросы и задания, страница 184 - гдз по математике 5 класс учебник Бунимович, Дорофеев

Глава 10. Десятичные дроби и действия с ними. 40. Сложение и вычитание десятичных дробей - страница 184.

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App\Models\Task {#1030 // resources/views/models/task/default.blade.php
  #connection: "mysql"
  #table: "tasks"
  #primaryKey: "id"
  #keyType: "int"
  +incrementing: true
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  #attributes: array:24 [
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    "field_display_title" => "Вопросы и задания"
    "field_outside_task" => null
    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1036
      #items: []
      #escapeWhenCastingToString: false
    }
    "field_metatags_title" => null
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    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1034
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      #escapeWhenCastingToString: false
    }
    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1078
      #items: array:1 [
        0 => App\Models\Branch {#1035
          #connection: "mysql"
          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
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          #attributes: array:24 [
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            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Десятичные дроби и действия с ними"
            "field_branch_order" => "10"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1038
              #items: array:1 [
                0 => App\Models\Term {#1037
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
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                  #attributes: array:7 [
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                    "updated_at" => null
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                      "field_genitive_case" => "Главы"
                      "field_nominative_case" => "Глава"
                      "field_prepositional_case" => "Главе"
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                  #original: array:7 [
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                    "field_cases" => array:6 [
                      "field_accusative_case" => "Главу"
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                      "field_genitive_case" => "Главы"
                      "field_nominative_case" => "Глава"
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                    ]
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                  ]
                  #changes: []
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            "book" => Illuminate\Database\Eloquent\Collection {#1039
              #items: array:1 [
                0 => App\Models\Book {#1040
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                    "field_subject" => Illuminate\Database\Eloquent\Collection {#1041
                      #items: array:1 [
                        0 => App\Models\Term {#1042
                          #connection: "mysql"
                          #table: "terms"
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                          +incrementing: false
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                          #attributes: array:10 [ …10]
                          #original: array:10 [ …10]
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                        }
                      ]
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                    "field_class" => Illuminate\Database\Eloquent\Collection {#1043
                      #items: array:1 [
                        0 => App\Models\Term {#1044
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
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                          #attributes: array:6 [ …6]
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                          #changes: []
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                          +timestamps: true
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                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045
                      #items: array:1 [
                        0 => App\Models\Term {#1046
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
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                          #escapeWhenCastingToString: false
                          #attributes: array:6 [ …6]
                          #original: array:6 [ …6]
                          #changes: []
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                          #attributeCastCache: []
                          #dateFormat: null
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                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1047
                      #items: array:6 [
                        0 => App\Models\Term {#1048
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:12 [ …12]
                          #original: array:12 [ …12]
                          #changes: []
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                          #dateFormat: null
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                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                        1 => App\Models\Term {#1049
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
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                          #attributes: array:12 [ …12]
                          #original: array:12 [ …12]
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                          #touches: []
                          +timestamps: true
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                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                        2 => App\Models\Term {#1050
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
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                          #escapeWhenCastingToString: false
                          #attributes: array:12 [ …12]
                          #original: array:12 [ …12]
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                          #dateFormat: null
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                          #dispatchesEvents: []
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                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                           …4
                        }
                        3 => App\Models\Term {#1051 …30}
                        4 => App\Models\Term {#1052 …30}
                        5 => App\Models\Term {#1053 …30}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1054
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1055
                      #items: array:1 [
                        0 => App\Models\Term {#1056 …30}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1057
                      #items: array:1 [
                        0 => App\Models\Term {#1058 …30}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1059
                      #items: array:1 [
                        0 => App\Models\Term {#1060 …30}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1061
                      #items: array:1 [
                        0 => App\Models\Term {#1062 …30}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1063
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1064
                      #items: array:1 [
                        0 => App\Models\Term {#1065 …30}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1066
                      #items: array:1 [
                        0 => App\Models\Term {#1067 …30}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_publication_number" => null
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1068
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                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1069
                      #items: []
                      #escapeWhenCastingToString: false
                    }
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                    "field_cover_description" => "с компасом"
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                    "field_part" => ""
                    "field_part_writing" => ""
                    "field_second_foreign_language" => null
                    "field_for_whom" => "Учебное пособие"
                    "field_allowed" => null
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                    "field_link_to_source" => null
                    "field_tasks_count" => "941"
                    "field_priority" => "10"
                    "field_default_folder" => "/matematika_05/bunimovich-u23/"
                    "field_isbn" => "978-5-09-105798-0"
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                      0 => "/media/matematika_05/bunimovich-u23/covers/cover1.webp?ts=1737321399"
                    ]
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                      0 => ""
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                      0 => array:4 [
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                        "alt" => ""
                        "width" => "1200"
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                      ]
                    ]
                    "field_popular_book" => null
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1070
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                      #escapeWhenCastingToString: false
                    }
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                      #escapeWhenCastingToString: false
                    }
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1072
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_url" => "/5-klass/matematika/bunimovich-uchebnik"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1073
                      #items: array:1 [
                        0 => App\Models\Term {#1074 …30}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_metatags_title" => null
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                  #original: array:50 [
                    "id" => 59
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                    "field_subject" => Illuminate\Database\Eloquent\Collection {#1041}
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                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045}
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1047}
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1054}
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        0 => App\Models\Branch {#1127
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              #items: array:1 [
                0 => App\Models\Term {#1128
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                    "field_cases" => array:6 [
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                      "field_genitive_case" => "Главы"
                      "field_nominative_case" => "Глава"
                      "field_prepositional_case" => "Главе"
                    ]
                    "field_page_check_not_needed" => null
                    "field_short_name" => null
                  ]
                  #original: array:7 [
                    "id" => 29
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Глава"
                    "field_cases" => array:6 [
                      "field_accusative_case" => "Главу"
                      "field_creative_case" => "Главой"
                      "field_dative_case" => "Главе"
                      "field_genitive_case" => "Главы"
                      "field_nominative_case" => "Глава"
                      "field_prepositional_case" => "Главе"
                    ]
                    "field_page_check_not_needed" => null
                    "field_short_name" => null
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "175"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1167
              #items: array:1 [
                0 => App\Models\Book {#1130
                  #connection: "mysql"
                  #table: "books"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:50 [
                    "id" => 59
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_tree_default_status" => "tasks"
                    "field_pages_status" => null
                    "field_subject" => Illuminate\Database\Eloquent\Collection {#1132
                      #items: array:1 [
                        0 => App\Models\Term {#1129
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:10 [
                            "id" => 6484
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Математика"
                            "field_abbreviated_name" => null
                            "field_cases" => array:6 [
                              "field_accusative_case" => "математику"
                              "field_creative_case" => "математикой"
                              "field_dative_case" => "математике"
                              "field_genitive_case" => "математики"
                              "field_nominative_case" => "математика"
                              "field_prepositional_case" => "математике"
                            ]
                            "field_foreign_lang_name" => null
                            "field_short_name" => null
                            "field_subject_type" => "technical_subject"
                            "field_translit" => "matematika"
                          ]
                          #original: array:10 [
                            "id" => 6484
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Математика"
                            "field_abbreviated_name" => null
                            "field_cases" => array:6 [
                              "field_accusative_case" => "математику"
                              "field_creative_case" => "математикой"
                              "field_dative_case" => "математике"
                              "field_genitive_case" => "математики"
                              "field_nominative_case" => "математика"
                              "field_prepositional_case" => "математике"
                            ]
                            "field_foreign_lang_name" => null
                            "field_short_name" => null
                            "field_subject_type" => "technical_subject"
                            "field_translit" => "matematika"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1133
                      #items: array:1 [
                        0 => App\Models\Term {#1134
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 5445
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "5"
                            "field_cases" => array:6 [
                              "field_accusative_case" => "пятый"
                              "field_creative_case" => "пятым"
                              "field_dative_case" => "пятому"
                              "field_genitive_case" => "пятого"
                              "field_nominative_case" => "пятый"
                              "field_prepositional_case" => "пятом"
                            ]
                            "field_translit" => "pjatyj"
                          ]
                          #original: array:6 [
                            "id" => 5445
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "5"
                            "field_cases" => array:6 [
                              "field_accusative_case" => "пятый"
                              "field_creative_case" => "пятым"
                              "field_dative_case" => "пятому"
                              "field_genitive_case" => "пятого"
                              "field_nominative_case" => "пятый"
                              "field_prepositional_case" => "пятом"
                            ]
                            "field_translit" => "pjatyj"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1135
                      #items: array:1 [
                        0 => App\Models\Term {#1136
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 5153
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Просвещение"
                            "field_cases" => null
                            "field_translit" => "prosveschenie"
                          ]
                          #original: array:6 [
                            "id" => 5153
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Просвещение"
                            "field_cases" => null
                            "field_translit" => "prosveschenie"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1137
                      #items: array:6 [
                        0 => App\Models\Term {#1138
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:12 [
                            "id" => 3941
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Бунимович"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Евгений"
                            "field_patronymic" => "Абрамович"
                            "field_surname_rp" => null
                          ]
                          #original: array:12 [
                            "id" => 3941
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Бунимович"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Евгений"
                            "field_patronymic" => "Абрамович"
                            "field_surname_rp" => null
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                        1 => App\Models\Term {#1139
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:12 [
                            "id" => 4283
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Дорофеев"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Георгий"
                            "field_patronymic" => "Владимирович"
                            "field_surname_rp" => null
                          ]
                          #original: array:12 [
                            "id" => 4283
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Дорофеев"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Георгий"
                            "field_patronymic" => "Владимирович"
                            "field_surname_rp" => null
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                        2 => App\Models\Term {#1140
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:12 [
                            "id" => 5879
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Суворова"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Светлана"
                            "field_patronymic" => "Борисовна"
                            "field_surname_rp" => null
                          ]
                          #original: array:12 [
                            "id" => 5879
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Суворова"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Светлана"
                            "field_patronymic" => "Борисовна"
                            "field_surname_rp" => null
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                        3 => App\Models\Term {#1141
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:12 [
                            "id" => 4848
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Кузнецова"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Людмила"
                            "field_patronymic" => "Викторовна"
                            "field_surname_rp" => null
                          ]
                          #original: array:12 [
                            "id" => 4848
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Кузнецова"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Людмила"
                            "field_patronymic" => "Викторовна"
                            "field_surname_rp" => null
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                        4 => App\Models\Term {#1142
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:12 [
                            "id" => 5198
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Минаева"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Светлана"
                            "field_patronymic" => "Станиславовна"
                            "field_surname_rp" => null
                          ]
                          #original: array:12 [
                            "id" => 5198
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Минаева"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Светлана"
                            "field_patronymic" => "Станиславовна"
                            "field_surname_rp" => null
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                        5 => App\Models\Term {#1143
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:12 [
                            "id" => 5622
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Рослова"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Лариса"
                            "field_patronymic" => "Олеговна"
                            "field_surname_rp" => null
                          ]
                          #original: array:12 [
                            "id" => 5622
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Рослова"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Лариса"
                            "field_patronymic" => "Олеговна"
                            "field_surname_rp" => null
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1144
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1145
                      #items: array:1 [
                        0 => App\Models\Term {#1146
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:10 [
                            "id" => 6671
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Учебник"
                            "field_book_type_foreign" => null
                            "field_cases" => array:6 [
                              "field_accusative_case" => "учебник"
                              "field_creative_case" => "учебником"
                              "field_dative_case" => "учебнику"
                              "field_genitive_case" => "учебника"
                              "field_nominative_case" => "учебник"
                              "field_prepositional_case" => "учебнике"
                            ]
                            "field_plural_form" => null
                            "field_short_name" => null
                            "field_short_name_foreign" => null
                            "field_translit" => "uchebnik"
                          ]
                          #original: array:10 [
                            "id" => 6671
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Учебник"
                            "field_book_type_foreign" => null
                            "field_cases" => array:6 [
                              "field_accusative_case" => "учебник"
                              "field_creative_case" => "учебником"
                              "field_dative_case" => "учебнику"
                              "field_genitive_case" => "учебника"
                              "field_nominative_case" => "учебник"
                              "field_prepositional_case" => "учебнике"
                            ]
                            "field_plural_form" => null
                            "field_short_name" => null
                            "field_short_name_foreign" => null
                            "field_translit" => "uchebnik"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1147
                      #items: array:1 [
                        0 => App\Models\Term {#1148
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 9
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Россия"
                            "field_cases" => array:6 [
                              "field_accusative_case" => null
                              "field_creative_case" => null
                              "field_dative_case" => null
                              "field_genitive_case" => null
                              "field_nominative_case" => null
                              "field_prepositional_case" => null
                            ]
                            "field_translit" => "rossiya"
                          ]
                          #original: array:6 [
                            "id" => 9
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Россия"
                            "field_cases" => array:6 [
                              "field_accusative_case" => null
                              "field_creative_case" => null
                              "field_dative_case" => null
                              "field_genitive_case" => null
                              "field_nominative_case" => null
                              "field_prepositional_case" => null
                            ]
                            "field_translit" => "rossiya"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1149
                      #items: array:1 [
                        0 => App\Models\Term {#1150
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 15
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Москва"
                            "field_cases" => array:6 [
                              "field_accusative_case" => null
                              "field_creative_case" => null
                              "field_dative_case" => null
                              "field_genitive_case" => null
                              "field_nominative_case" => null
                              "field_prepositional_case" => null
                            ]
                            "field_translit" => "moskva"
                          ]
                          #original: array:6 [
                            "id" => 15
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Москва"
                            "field_cases" => array:6 [
                              "field_accusative_case" => null
                              "field_creative_case" => null
                              "field_dative_case" => null
                              "field_genitive_case" => null
                              "field_nominative_case" => null
                              "field_prepositional_case" => null
                            ]
                            "field_translit" => "moskva"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1151
                      #items: array:1 [
                        0 => App\Models\Term {#1152
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:8 [
                            "id" => 4795
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "сферы"
                            "field_cases" => null
                            "field_foreign_lang_series" => null
                            "field_transcription_eng" => null
                            "field_translit" => "sfery"
                          ]
                          #original: array:8 [
                            "id" => 4795
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "сферы"
                            "field_cases" => null
                            "field_foreign_lang_series" => null
                            "field_transcription_eng" => null
                            "field_translit" => "sfery"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1153
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1154
                      #items: array:1 [
                        0 => App\Models\Term {#1155
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 38
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "базовый"
                            "field_cases" => array:6 [
                              "field_accusative_case" => "базовый"
                              "field_creative_case" => "базовым"
                              "field_dative_case" => "базовому"
                              "field_genitive_case" => "базового"
                              "field_nominative_case" => "базовый"
                              "field_prepositional_case" => "базовом"
                            ]
                            "field_translit" => "bazovyy"
                          ]
                          #original: array:6 [
                            "id" => 38
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "базовый"
                            "field_cases" => array:6 [
                              "field_accusative_case" => "базовый"
                              "field_creative_case" => "базовым"
                              "field_dative_case" => "базовому"
                              "field_genitive_case" => "базового"
                              "field_nominative_case" => "базовый"
                              "field_prepositional_case" => "базовом"
                            ]
                            "field_translit" => "bazovyy"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1156
                      #items: array:1 [
                        0 => App\Models\Term {#1157
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:10 [
                            "id" => 25
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "ФГОС (новый)"
                            "field_cases" => array:6 [
                              "field_accusative_case" => null
                              "field_creative_case" => null
                              "field_dative_case" => null
                              "field_genitive_case" => null
                              "field_nominative_case" => null
                              "field_prepositional_case" => null
                            ]
                            "field_color" => "красный"
                            "field_end_year" => "2027"
                            "field_start_year" => "2023"
                            "field_translit" => "fgos"
                            "field_type" => "новый"
                          ]
                          #original: array:10 [
                            "id" => 25
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "ФГОС (новый)"
                            "field_cases" => array:6 [
                              "field_accusative_case" => null
                              "field_creative_case" => null
                              "field_dative_case" => null
                              "field_genitive_case" => null
                              "field_nominative_case" => null
                              "field_prepositional_case" => null
                            ]
                            "field_color" => "красный"
                            "field_end_year" => "2027"
                            "field_start_year" => "2023"
                            "field_translit" => "fgos"
                            "field_type" => "новый"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_publication_number" => null
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1158
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1159
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => "с компасом"
                    "field_publication_year" => "2023"
                    "field_publication_year_until" => null
                    "field_part" => ""
                    "field_part_writing" => ""
                    "field_second_foreign_language" => null
                    "field_for_whom" => "Учебное пособие"
                    "field_allowed" => null
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "941"
                    "field_priority" => "10"
                    "field_default_folder" => "/matematika_05/bunimovich-u23/"
                    "field_isbn" => "978-5-09-105798-0"
                    "field_cover" => array:1 [
                      0 => "/media/matematika_05/bunimovich-u23/covers/cover1.webp?ts=1737321399"
                    ]
                    "field_cover_alts" => array:1 [
                      0 => ""
                    ]
                    "field_covers" => array:1 [
                      0 => array:4 [
                        "path" => "/media/matematika_05/bunimovich-u23/covers/cover1.webp?ts=1737321399"
                        "alt" => ""
                        "width" => "1200"
                        "height" => "1604"
                      ]
                    ]
                    "field_popular_book" => null
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1160
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1161
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1162
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_url" => "/5-klass/matematika/bunimovich-uchebnik"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1163
                      #items: array:1 [
                        0 => App\Models\Term {#1164
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 50
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "оранжевый"
                            "field_cases" => array:6 [
                              "field_accusative_case" => "оранжевый"
                              "field_creative_case" => "оранжевым"
                              "field_dative_case" => "оранжевому"
                              "field_genitive_case" => "оранжевого"
                              "field_nominative_case" => "оранжевый"
                              "field_prepositional_case" => "оранжевом"
                            ]
                            "field_translit" => "oranzhevyy"
                          ]
                          #original: array:6 [
                            "id" => 50
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "оранжевый"
                            "field_cases" => array:6 [
                              "field_accusative_case" => "оранжевый"
                              "field_creative_case" => "оранжевым"
                              "field_dative_case" => "оранжевому"
                              "field_genitive_case" => "оранжевого"
                              "field_nominative_case" => "оранжевый"
                              "field_prepositional_case" => "оранжевом"
                            ]
                            "field_translit" => "oranzhevyy"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "breadcrumbs" => array:3 [
                      "class" => 376
                      "subject" => 544
                      "class_subject" => 398
                    ]
                  ]
                  #original: array:50 [
                    "id" => 59
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_tree_default_status" => "tasks"
                    "field_pages_status" => null
                    "field_subject" => Illuminate\Database\Eloquent\Collection {#1132}
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1133}
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1135}
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1137}
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1144}
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1145}
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1147}
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1149}
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1151}
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1153}
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1154}
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1156}
                    "field_publication_number" => null
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1158}
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1159}
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => "с компасом"
                    "field_publication_year" => "2023"
                    "field_publication_year_until" => null
                    "field_part" => ""
                    "field_part_writing" => ""
                    "field_second_foreign_language" => null
                    "field_for_whom" => "Учебное пособие"
                    "field_allowed" => null
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "941"
                    "field_priority" => "10"
                    "field_default_folder" => "/matematika_05/bunimovich-u23/"
                    "field_isbn" => "978-5-09-105798-0"
                    "field_cover" => array:1 [
                      0 => "/media/matematika_05/bunimovich-u23/covers/cover1.webp?ts=1737321399"
                    ]
                    "field_cover_alts" => array:1 [
                      0 => ""
                    ]
                    "field_covers" => array:1 [
                      0 => array:4 [
                        "path" => "/media/matematika_05/bunimovich-u23/covers/cover1.webp?ts=1737321399"
                        "alt" => ""
                        "width" => "1200"
                        "height" => "1604"
                      ]
                    ]
                    "field_popular_book" => null
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1160}
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1161}
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1162}
                    "field_url" => "/5-klass/matematika/bunimovich-uchebnik"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1163}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "breadcrumbs" => array:3 [
                      "class" => 376
                      "subject" => 544
                      "class_subject" => 398
                    ]
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1165
              #items: []
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 534117
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Десятичные дроби и действия с ними"
            "field_branch_order" => "10"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1131}
            "field_page_start" => "175"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1167}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1165}
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
        1 => App\Models\Branch {#1166
          #connection: "mysql"
          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:24 [
            "id" => 534121
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "40. Сложение и вычитание десятичных дробей"
            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1168
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "184"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1169
              #items: array:1 [
                0 => App\Models\Book {#1130}
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            "text" => "<p><strong>Сложение десятичных дробей</strong></p><p>Чтобы сложить десятичные дроби, нужно выполнить следующие шаги: <br>1. Уравнять количество знаков после запятой в слагаемых. В нашем примере у числа $16,8$ один знак после запятой, а у числа $9,12$ — два. Поэтому к числу $16,8$ дописываем справа один ноль, чтобы получить $16,80$. Значение дроби от этого не изменится. <br>2. Записать дроби друг под другом (в столбик) так, чтобы запятая находилась строго под запятой, а соответствующие разряды оказались друг под другом. <br>3. Выполнить сложение так, как складывают натуральные числа, не обращая внимания на запятые. <br>4. В полученной сумме поставить запятую под запятыми в исходных дробях.</p><p>Выполним сложение чисел $16,8$ и $9,12$: <br> <span style="font-family: monospace; font-size: 1.1em; line-height: 1.5;"> 16,80<br> + <u style="text-decoration-style: single; text-decoration-color: black;"> 9,12</u><br> 25,92 </span> <br> Объяснение вычисления: <br>• Складываем сотые доли: $0 + 2 = 2$. <br>• Складываем десятые доли: $8 + 1 = 9$. <br>• Складываем единицы: $6 + 9 = 15$. Пишем $5$ в разряд единиц, а $1$ десяток запоминаем и переносим в разряд десятков. <br>• Складываем десятки: $1 + 0 + 1$ (который запомнили) = $2$. <br>• Ставим запятую в результате под запятыми.</p><p>Ответ: $16,8 + 9,12 = 25,92$.</p><p><strong>Вычитание десятичных дробей</strong></p><p>Чтобы найти разность десятичных дробей, нужно: <br>1. Уравнять количество знаков после запятой в уменьшаемом и вычитаемом. Так же, как и при сложении, представим $16,8$ в виде $16,80$. <br>2. Записать вычитаемое под уменьшаемым (в столбик) так, чтобы запятая находилась строго под запятой. <br>3. Выполнить вычитание так, как вычитают натуральные числа, не обращая внимания на запятые. <br>4. В полученной разности поставить запятую под запятыми в уменьшаемом и вычитаемом.</p><p>Выполним вычитание из числа $16,8$ числа $9,12$: <br> <span style="font-family: monospace; font-size: 1.1em; line-height: 1.5;"> 16,80<br> - <u style="text-decoration-style: single; text-decoration-color: black;"> 9,12</u><br> 7,68 </span> <br> Объяснение вычисления: <br>• Вычитаем сотые доли: из $0$ вычесть $2$ нельзя. Занимаем единицу из старшего разряда (десятых). $10 - 2 = 8$. <br>• Вычитаем десятые доли: в разряде десятых было $8$, но мы заняли единицу, поэтому осталось $7$. Теперь $7 - 1 = 6$. <br>• Вычитаем единицы: из $6$ вычесть $9$ нельзя. Занимаем единицу из старшего разряда (десятков). $16 - 9 = 7$. <br>• Вычитаем десятки: в разряде десятков была $1$, но мы ее заняли, поэтому остался $0$. <br>• Ставим запятую в результате под запятыми.</p><p>Ответ: $16,8 - 9,12 = 7,68$.</p>"
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            "text" => "<p><strong>Сложение десятичных дробей</strong></p><p>Чтобы сложить десятичные дроби, нужно выполнить следующие шаги: <br>1. Уравнять количество знаков после запятой в слагаемых. В нашем примере у числа $16,8$ один знак после запятой, а у числа $9,12$ — два. Поэтому к числу $16,8$ дописываем справа один ноль, чтобы получить $16,80$. Значение дроби от этого не изменится. <br>2. Записать дроби друг под другом (в столбик) так, чтобы запятая находилась строго под запятой, а соответствующие разряды оказались друг под другом. <br>3. Выполнить сложение так, как складывают натуральные числа, не обращая внимания на запятые. <br>4. В полученной сумме поставить запятую под запятыми в исходных дробях.</p><p>Выполним сложение чисел $16,8$ и $9,12$: <br> <span style="font-family: monospace; font-size: 1.1em; line-height: 1.5;"> 16,80<br> + <u style="text-decoration-style: single; text-decoration-color: black;"> 9,12</u><br> 25,92 </span> <br> Объяснение вычисления: <br>• Складываем сотые доли: $0 + 2 = 2$. <br>• Складываем десятые доли: $8 + 1 = 9$. <br>• Складываем единицы: $6 + 9 = 15$. Пишем $5$ в разряд единиц, а $1$ десяток запоминаем и переносим в разряд десятков. <br>• Складываем десятки: $1 + 0 + 1$ (который запомнили) = $2$. <br>• Ставим запятую в результате под запятыми.</p><p>Ответ: $16,8 + 9,12 = 25,92$.</p><p><strong>Вычитание десятичных дробей</strong></p><p>Чтобы найти разность десятичных дробей, нужно: <br>1. Уравнять количество знаков после запятой в уменьшаемом и вычитаемом. Так же, как и при сложении, представим $16,8$ в виде $16,80$. <br>2. Записать вычитаемое под уменьшаемым (в столбик) так, чтобы запятая находилась строго под запятой. <br>3. Выполнить вычитание так, как вычитают натуральные числа, не обращая внимания на запятые. <br>4. В полученной разности поставить запятую под запятыми в уменьшаемом и вычитаемом.</p><p>Выполним вычитание из числа $16,8$ числа $9,12$: <br> <span style="font-family: monospace; font-size: 1.1em; line-height: 1.5;"> 16,80<br> - <u style="text-decoration-style: single; text-decoration-color: black;"> 9,12</u><br> 7,68 </span> <br> Объяснение вычисления: <br>• Вычитаем сотые доли: из $0$ вычесть $2$ нельзя. Занимаем единицу из старшего разряда (десятых). $10 - 2 = 8$. <br>• Вычитаем десятые доли: в разряде десятых было $8$, но мы заняли единицу, поэтому осталось $7$. Теперь $7 - 1 = 6$. <br>• Вычитаем единицы: из $6$ вычесть $9$ нельзя. Занимаем единицу из старшего разряда (десятков). $16 - 9 = 7$. <br>• Вычитаем десятки: в разряде десятков была $1$, но мы ее заняли, поэтому остался $0$. <br>• Ставим запятую в результате под запятыми.</p><p>Ответ: $16,8 - 9,12 = 7,68$.</p>"
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Вопросы и задания (с. 184)

Просмотр Редак-ть Редак-ть (переопр)

Условие. Вопросы и задания (с. 184)

Редак-ть Редакция

скриншот условия

ВОПРОСЫ И ЗАДАНИЯ

На примере вычисления суммы и разности чисел 16,8 и 9,12 объясните, как складывают и как вычитают десятичные дроби.

Решение. Вопросы и задания (с. 184)

Редак-ть Редакция

Решение 2. Вопросы и задания (с. 184)

Редак-ть Редакция

Сложение десятичных дробей

Чтобы сложить десятичные дроби, нужно выполнить следующие шаги:
1. Уравнять количество знаков после запятой в слагаемых. В нашем примере у числа $16,8$ один знак после запятой, а у числа $9,12$ — два. Поэтому к числу $16,8$ дописываем справа один ноль, чтобы получить $16,80$. Значение дроби от этого не изменится.
2. Записать дроби друг под другом (в столбик) так, чтобы запятая находилась строго под запятой, а соответствующие разряды оказались друг под другом.
3. Выполнить сложение так, как складывают натуральные числа, не обращая внимания на запятые.
4. В полученной сумме поставить запятую под запятыми в исходных дробях.

Выполним сложение чисел $16,8$ и $9,12$:
16,80
+ 9,12
25,92
Объяснение вычисления:
• Складываем сотые доли: $0 + 2 = 2$.
• Складываем десятые доли: $8 + 1 = 9$.
• Складываем единицы: $6 + 9 = 15$. Пишем $5$ в разряд единиц, а $1$ десяток запоминаем и переносим в разряд десятков.
• Складываем десятки: $1 + 0 + 1$ (который запомнили) = $2$.
• Ставим запятую в результате под запятыми.

Ответ: $16,8 + 9,12 = 25,92$.

Вычитание десятичных дробей

Чтобы найти разность десятичных дробей, нужно:
1. Уравнять количество знаков после запятой в уменьшаемом и вычитаемом. Так же, как и при сложении, представим $16,8$ в виде $16,80$.
2. Записать вычитаемое под уменьшаемым (в столбик) так, чтобы запятая находилась строго под запятой.
3. Выполнить вычитание так, как вычитают натуральные числа, не обращая внимания на запятые.
4. В полученной разности поставить запятую под запятыми в уменьшаемом и вычитаемом.

Выполним вычитание из числа $16,8$ числа $9,12$:
16,80
- 9,12
7,68
Объяснение вычисления:
• Вычитаем сотые доли: из $0$ вычесть $2$ нельзя. Занимаем единицу из старшего разряда (десятых). $10 - 2 = 8$.
• Вычитаем десятые доли: в разряде десятых было $8$, но мы заняли единицу, поэтому осталось $7$. Теперь $7 - 1 = 6$.
• Вычитаем единицы: из $6$ вычесть $9$ нельзя. Занимаем единицу из старшего разряда (десятков). $16 - 9 = 7$.
• Вычитаем десятки: в разряде десятков была $1$, но мы ее заняли, поэтому остался $0$.
• Ставим запятую в результате под запятыми.

Ответ: $16,8 - 9,12 = 7,68$.