gdz.top
Номер 530, страница 156 - гдз по математике 5 класс учебник Бунимович, Дорофеев
Авторы: Бунимович Е. А., Дорофеев Г. В., Суворова С. Б., Кузнецова Л. В., Минаева С. С., Рослова Л. О.
Тип: Учебник
Серия: сферы
Издательство: Просвещение
Год издания: 2023 - 2026
Уровень обучения: базовый
Цвет обложки: оранжевый с компасом
ISBN: 978-5-09-105798-0
Популярные ГДЗ в 5 классе
Учебник
рабочая тетрадь
Учебник
Учебник
Учебник
Тренировочные упражнения в формате ОГЭ (ГИА)
Рабочая тетрадь
Рабочая тетрадь
Тренировочные упражнения в формате ОГЭ (ГИА)
сборник грамматических упражнений
Учебник
Мой тренажёр
контрольные задания
контрольные задания
Грамматический тренажёр
Практические работы
Проверочные работы
Контурные карты
Учебник
Учебник
рабочая тетрадь
Глава 9. Действия с дробями. 33. Сложение и вычитание смешанных дробей - номер 530, страница 156.
App\Models\Task {#1030 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 534779 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "156" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-530" "field_display_title" => "530" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #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" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #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 "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #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" => 534110 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Действия с дробями" "field_branch_order" => "9" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1047 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: 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 ] #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" => "149" "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 {#1086 #items: array:1 [ 0 => App\Models\Book {#1049 #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 {#1051 #items: array:1 [ 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: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 {#1052 #items: array:1 [ 0 => App\Models\Term {#1053 #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 {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 #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 {#1056 #items: array:6 [ 0 => App\Models\Term {#1057 #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 {#1058 #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 {#1059 #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 {#1060 #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 {#1061 #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 {#1062 #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 {#1063 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:1 [ 0 => App\Models\Term {#1065 #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 {#1066 #items: array:1 [ 0 => App\Models\Term {#1067 #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 {#1068 #items: array:1 [ 0 => App\Models\Term {#1069 #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 {#1070 #items: array:1 [ 0 => App\Models\Term {#1071 #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 {#1072 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1073 #items: array:1 [ 0 => App\Models\Term {#1074 #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 {#1075 #items: array:1 [ 0 => App\Models\Term {#1076 #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 …1 ] "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 {#1077 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1078 #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 {#1079 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1080 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1081 #items: [] #escapeWhenCastingToString: false } "field_url" => "/5-klass/matematika/bunimovich-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1082 #items: array:1 [ 0 => App\Models\Term {#1083 #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 [ …6] "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 [ …6] "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 {#1051} "field_class" => Illuminate\Database\Eloquent\Collection {#1052} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054} "field_author" => Illuminate\Database\Eloquent\Collection {#1056} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1063} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1064} "field_country" => Illuminate\Database\Eloquent\Collection {#1066} "field_city" => Illuminate\Database\Eloquent\Collection {#1068} "field_series" => Illuminate\Database\Eloquent\Collection {#1070} "field_umk" => Illuminate\Database\Eloquent\Collection {#1072} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1073} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1075} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1077} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1078} "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 {#1079} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1080} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1081} "field_url" => "/5-klass/matematika/bunimovich-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1082} "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 {#1084 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 534110 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Действия с дробями" "field_branch_order" => "9" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050} "field_page_start" => "149" "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 {#1086} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1084} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1121 #items: array:2 [ 0 => App\Models\Branch {#1129 #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" => 534110 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Действия с дробями" "field_branch_order" => "9" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Term {#1047} ] #escapeWhenCastingToString: false } "field_page_start" => "149" "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 {#1131 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1132 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 534110 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Действия с дробями" "field_branch_order" => "9" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1130} "field_page_start" => "149" "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 {#1131} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1132} ] #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 {#1133 #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" => 534112 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "33. Сложение и вычитание смешанных дробей" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1134 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "154" "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 {#1135 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1136 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 534112 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "33. Сложение и вычитание смешанных дробей" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1134} "field_page_start" => "154" "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 {#1135} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1136} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:2 [ 0 => App\Models\Element {#1112 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 646598 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1102 #items: array:1 [ 0 => App\Models\Edition {#1111 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1542 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1110 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "margarita" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1107 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1108 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1106 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 1542 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1110} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "margarita" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1107} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1108} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1106} "field_content_source" => 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 } "task" => array:2 [ "refs" => "534779" "type" => "task" ] "text" => "<p><strong>530</strong> Выполните сложение и представьте результат в виде смешанной дроби:</p><p><strong>а)</strong> $\frac{3}{8} + \frac{7}{8}$;</p><p><strong>б)</strong> $\frac{5}{12} + \frac{2}{3}$;</p><p><strong>В)</strong> $\frac{3}{4} + \frac{4}{5}$;</p><p><strong>Г)</strong> $\frac{4}{15} + \frac{17}{20}$;</p><p><strong>Д)</strong> $\frac{15}{12} + \frac{11}{18}$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "530-1.jpg" "alt" => null "width" => "2003" "height" => 338 "path" => "/media/matematika_05/bunimovich-u23/0-00/530-1.webp?ts=1737374363" ] ] ] #original: array:7 [ "id" => 646598 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1102} "task" => array:2 [ "refs" => "534779" "type" => "task" ] "text" => "<p><strong>530</strong> Выполните сложение и представьте результат в виде смешанной дроби:</p><p><strong>а)</strong> $\frac{3}{8} + \frac{7}{8}$;</p><p><strong>б)</strong> $\frac{5}{12} + \frac{2}{3}$;</p><p><strong>В)</strong> $\frac{3}{4} + \frac{4}{5}$;</p><p><strong>Г)</strong> $\frac{4}{15} + \frac{17}{20}$;</p><p><strong>Д)</strong> $\frac{15}{12} + \frac{11}{18}$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "530-1.jpg" "alt" => null "width" => "2003" "height" => 338 "path" => "/media/matematika_05/bunimovich-u23/0-00/530-1.webp?ts=1737374363" ] ] ] #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\Element {#1104 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1469010 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1096 #items: array:1 [ 0 => App\Models\Edition {#1105 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5408 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1100 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "vadim" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1101 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1098 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1099 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5408 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1100} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "vadim" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1101} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1098} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1099} "field_content_source" => 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 } "task" => array:2 [ "refs" => "534779" "type" => "task" ] "text" => "<p><strong>а)</strong></p><p>Для сложения дробей $ \frac{3}{8} $ и $ \frac{7}{8} $, у которых одинаковые знаменатели, нужно сложить их числители, а знаменатель оставить прежним:</p><p>$ \frac{3}{8} + \frac{7}{8} = \frac{3+7}{8} = \frac{10}{8} $</p><p>Получилась неправильная дробь $ \frac{10}{8} $. Чтобы представить ее в виде смешанной дроби, нужно разделить числитель на знаменатель с остатком:</p><p>$ 10 \div 8 = 1 $ (остаток $ 2 $)</p><p>Целая часть смешанной дроби равна $ 1 $, числитель дробной части равен остатку $ 2 $, а знаменатель остается прежним — $ 8 $. Получаем $ 1\frac{2}{8} $.</p><p>Дробную часть $ \frac{2}{8} $ можно сократить, разделив числитель и знаменатель на их наибольший общий делитель, равный 2:</p><p>$ \frac{2}{8} = \frac{2 \div 2}{8 \div 2} = \frac{1}{4} $</p><p>Таким образом, окончательный результат: $ 1\frac{1}{4} $.</p><p><strong>Ответ:</strong> $ 1\frac{1}{4} $</p><p><strong>б)</strong></p><p>Чтобы сложить дроби $ \frac{5}{12} $ и $ \frac{2}{3} $ с разными знаменателями, нужно привести их к общему знаменателю. Наименьший общий знаменатель для 12 и 3 — это 12.</p><p>Первая дробь $ \frac{5}{12} $ уже имеет нужный знаменатель.</p><p>Для второй дроби $ \frac{2}{3} $ найдем дополнительный множитель: $ 12 \div 3 = 4 $. Умножим числитель и знаменатель на 4:</p><p>$ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} $</p><p>Теперь сложим дроби с одинаковыми знаменателями:</p><p>$ \frac{5}{12} + \frac{8}{12} = \frac{5+8}{12} = \frac{13}{12} $</p><p>Преобразуем неправильную дробь $ \frac{13}{12} $ в смешанную. Разделим 13 на 12 с остатком:</p><p>$ 13 \div 12 = 1 $ (остаток $ 1 $)</p><p>Результат: $ 1\frac{1}{12} $.</p><p><strong>Ответ:</strong> $ 1\frac{1}{12} $</p><p><strong>в)</strong></p><p>Для сложения дробей $ \frac{3}{4} $ и $ \frac{4}{5} $ найдем наименьший общий знаменатель для 4 и 5. Так как числа 4 и 5 взаимно простые, их наименьший общий знаменатель равен их произведению: $ 4 \times 5 = 20 $.</p><p>Приведем каждую дробь к знаменателю 20.</p><p>Для дроби $ \frac{3}{4} $ дополнительный множитель $ 20 \div 4 = 5 $:</p><p>$ \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20} $</p><p>Для дроби $ \frac{4}{5} $ дополнительный множитель $ 20 \div 5 = 4 $:</p><p>$ \frac{4}{5} = \frac{4 \times 4}{5 \times 4} = \frac{16}{20} $</p><p>Сложим полученные дроби:</p><p>$ \frac{15}{20} + \frac{16}{20} = \frac{15+16}{20} = \frac{31}{20} $</p><p>Преобразуем неправильную дробь $ \frac{31}{20} $ в смешанную. Разделим 31 на 20 с остатком:</p><p>$ 31 \div 20 = 1 $ (остаток $ 11 $)</p><p>Результат: $ 1\frac{11}{20} $.</p><p><strong>Ответ:</strong> $ 1\frac{11}{20} $</p><p><strong>г)</strong></p><p>Чтобы сложить дроби $ \frac{4}{15} $ и $ \frac{17}{20} $, найдем наименьший общий знаменатель (НОК) для 15 и 20.</p><p>Разложим знаменатели на простые множители: $ 15 = 3 \times 5 $; $ 20 = 2 \times 2 \times 5 = 2^2 \times 5 $.</p><p>НОК(15, 20) = $ 2^2 \times 3 \times 5 = 60 $. Общий знаменатель — 60.</p><p>Приведем дроби к знаменателю 60.</p><p>Дополнительный множитель для $ \frac{4}{15} $ равен $ 60 \div 15 = 4 $:</p><p>$ \frac{4}{15} = \frac{4 \times 4}{15 \times 4} = \frac{16}{60} $</p><p>Дополнительный множитель для $ \frac{17}{20} $ равен $ 60 \div 20 = 3 $:</p><p>$ \frac{17}{20} = \frac{17 \times 3}{20 \times 3} = \frac{51}{60} $</p><p>Сложим полученные дроби:</p><p>$ \frac{16}{60} + \frac{51}{60} = \frac{16+51}{60} = \frac{67}{60} $</p><p>Преобразуем неправильную дробь $ \frac{67}{60} $ в смешанную. Разделим 67 на 60 с остатком:</p><p>$ 67 \div 60 = 1 $ (остаток $ 7 $)</p><p>Результат: $ 1\frac{7}{60} $.</p><p><strong>Ответ:</strong> $ 1\frac{7}{60} $</p><p><strong>д)</strong></p><p>Чтобы сложить дроби $ \frac{15}{12} $ и $ \frac{11}{18} $, найдем наименьший общий знаменатель (НОК) для 12 и 18.</p><p>Разложим знаменатели на простые множители: $ 12 = 2 \times 2 \times 3 = 2^2 \times 3 $; $ 18 = 2 \times 3 \times 3 = 2 \times 3^2 $.</p><p>НОК(12, 18) = $ 2^2 \times 3^2 = 4 \times 9 = 36 $. Общий знаменатель — 36.</p><p>Приведем дроби к знаменателю 36.</p><p>Дополнительный множитель для $ \frac{15}{12} $ равен $ 36 \div 12 = 3 $:</p><p>$ \frac{15}{12} = \frac{15 \times 3}{12 \times 3} = \frac{45}{36} $</p><p>Дополнительный множитель для $ \frac{11}{18} $ равен $ 36 \div 18 = 2 $:</p><p>$ \frac{11}{18} = \frac{11 \times 2}{18 \times 2} = \frac{22}{36} $</p><p>Сложим полученные дроби:</p><p>$ \frac{45}{36} + \frac{22}{36} = \frac{45+22}{36} = \frac{67}{36} $</p><p>Преобразуем неправильную дробь $ \frac{67}{36} $ в смешанную. Разделим 67 на 36 с остатком:</p><p>$ 67 \div 36 = 1 $ (остаток $ 31 $)</p><p>Результат: $ 1\frac{31}{36} $.</p><p><strong>Ответ:</strong> $ 1\frac{31}{36} $</p>" ] #original: array:6 [ "id" => 1469010 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1096} "task" => array:2 [ "refs" => "534779" "type" => "task" ] "text" => "<p><strong>а)</strong></p><p>Для сложения дробей $ \frac{3}{8} $ и $ \frac{7}{8} $, у которых одинаковые знаменатели, нужно сложить их числители, а знаменатель оставить прежним:</p><p>$ \frac{3}{8} + \frac{7}{8} = \frac{3+7}{8} = \frac{10}{8} $</p><p>Получилась неправильная дробь $ \frac{10}{8} $. Чтобы представить ее в виде смешанной дроби, нужно разделить числитель на знаменатель с остатком:</p><p>$ 10 \div 8 = 1 $ (остаток $ 2 $)</p><p>Целая часть смешанной дроби равна $ 1 $, числитель дробной части равен остатку $ 2 $, а знаменатель остается прежним — $ 8 $. Получаем $ 1\frac{2}{8} $.</p><p>Дробную часть $ \frac{2}{8} $ можно сократить, разделив числитель и знаменатель на их наибольший общий делитель, равный 2:</p><p>$ \frac{2}{8} = \frac{2 \div 2}{8 \div 2} = \frac{1}{4} $</p><p>Таким образом, окончательный результат: $ 1\frac{1}{4} $.</p><p><strong>Ответ:</strong> $ 1\frac{1}{4} $</p><p><strong>б)</strong></p><p>Чтобы сложить дроби $ \frac{5}{12} $ и $ \frac{2}{3} $ с разными знаменателями, нужно привести их к общему знаменателю. Наименьший общий знаменатель для 12 и 3 — это 12.</p><p>Первая дробь $ \frac{5}{12} $ уже имеет нужный знаменатель.</p><p>Для второй дроби $ \frac{2}{3} $ найдем дополнительный множитель: $ 12 \div 3 = 4 $. Умножим числитель и знаменатель на 4:</p><p>$ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} $</p><p>Теперь сложим дроби с одинаковыми знаменателями:</p><p>$ \frac{5}{12} + \frac{8}{12} = \frac{5+8}{12} = \frac{13}{12} $</p><p>Преобразуем неправильную дробь $ \frac{13}{12} $ в смешанную. Разделим 13 на 12 с остатком:</p><p>$ 13 \div 12 = 1 $ (остаток $ 1 $)</p><p>Результат: $ 1\frac{1}{12} $.</p><p><strong>Ответ:</strong> $ 1\frac{1}{12} $</p><p><strong>в)</strong></p><p>Для сложения дробей $ \frac{3}{4} $ и $ \frac{4}{5} $ найдем наименьший общий знаменатель для 4 и 5. Так как числа 4 и 5 взаимно простые, их наименьший общий знаменатель равен их произведению: $ 4 \times 5 = 20 $.</p><p>Приведем каждую дробь к знаменателю 20.</p><p>Для дроби $ \frac{3}{4} $ дополнительный множитель $ 20 \div 4 = 5 $:</p><p>$ \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20} $</p><p>Для дроби $ \frac{4}{5} $ дополнительный множитель $ 20 \div 5 = 4 $:</p><p>$ \frac{4}{5} = \frac{4 \times 4}{5 \times 4} = \frac{16}{20} $</p><p>Сложим полученные дроби:</p><p>$ \frac{15}{20} + \frac{16}{20} = \frac{15+16}{20} = \frac{31}{20} $</p><p>Преобразуем неправильную дробь $ \frac{31}{20} $ в смешанную. Разделим 31 на 20 с остатком:</p><p>$ 31 \div 20 = 1 $ (остаток $ 11 $)</p><p>Результат: $ 1\frac{11}{20} $.</p><p><strong>Ответ:</strong> $ 1\frac{11}{20} $</p><p><strong>г)</strong></p><p>Чтобы сложить дроби $ \frac{4}{15} $ и $ \frac{17}{20} $, найдем наименьший общий знаменатель (НОК) для 15 и 20.</p><p>Разложим знаменатели на простые множители: $ 15 = 3 \times 5 $; $ 20 = 2 \times 2 \times 5 = 2^2 \times 5 $.</p><p>НОК(15, 20) = $ 2^2 \times 3 \times 5 = 60 $. Общий знаменатель — 60.</p><p>Приведем дроби к знаменателю 60.</p><p>Дополнительный множитель для $ \frac{4}{15} $ равен $ 60 \div 15 = 4 $:</p><p>$ \frac{4}{15} = \frac{4 \times 4}{15 \times 4} = \frac{16}{60} $</p><p>Дополнительный множитель для $ \frac{17}{20} $ равен $ 60 \div 20 = 3 $:</p><p>$ \frac{17}{20} = \frac{17 \times 3}{20 \times 3} = \frac{51}{60} $</p><p>Сложим полученные дроби:</p><p>$ \frac{16}{60} + \frac{51}{60} = \frac{16+51}{60} = \frac{67}{60} $</p><p>Преобразуем неправильную дробь $ \frac{67}{60} $ в смешанную. Разделим 67 на 60 с остатком:</p><p>$ 67 \div 60 = 1 $ (остаток $ 7 $)</p><p>Результат: $ 1\frac{7}{60} $.</p><p><strong>Ответ:</strong> $ 1\frac{7}{60} $</p><p><strong>д)</strong></p><p>Чтобы сложить дроби $ \frac{15}{12} $ и $ \frac{11}{18} $, найдем наименьший общий знаменатель (НОК) для 12 и 18.</p><p>Разложим знаменатели на простые множители: $ 12 = 2 \times 2 \times 3 = 2^2 \times 3 $; $ 18 = 2 \times 3 \times 3 = 2 \times 3^2 $.</p><p>НОК(12, 18) = $ 2^2 \times 3^2 = 4 \times 9 = 36 $. Общий знаменатель — 36.</p><p>Приведем дроби к знаменателю 36.</p><p>Дополнительный множитель для $ \frac{15}{12} $ равен $ 36 \div 12 = 3 $:</p><p>$ \frac{15}{12} = \frac{15 \times 3}{12 \times 3} = \frac{45}{36} $</p><p>Дополнительный множитель для $ \frac{11}{18} $ равен $ 36 \div 18 = 2 $:</p><p>$ \frac{11}{18} = \frac{11 \times 2}{18 \times 2} = \frac{22}{36} $</p><p>Сложим полученные дроби:</p><p>$ \frac{45}{36} + \frac{22}{36} = \frac{45+22}{36} = \frac{67}{36} $</p><p>Преобразуем неправильную дробь $ \frac{67}{36} $ в смешанную. Разделим 67 на 36 с остатком:</p><p>$ 67 \div 36 = 1 $ (остаток $ 31 $)</p><p>Результат: $ 1\frac{31}{36} $.</p><p><strong>Ответ:</strong> $ 1\frac{31}{36} $</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "534780" "type" => "task" ] "previous" => array:2 [ "refs" => "534778" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1115 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1040 #items: array:1 [ 0 => App\Models\BookPage {#1117 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 949450 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "156" "field_url" => "/5-klass/matematika/bunimovich-uchebnik/page-156" "field_display_title" => "156" "field_folder" => "1" "field_image_name" => "156" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1097 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1095 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1041 #items: array:1 [ 0 => App\Models\Element {#1043 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1124732 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1034 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1124732 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1034 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "949451" "type" => "book_page" ] "previous" => array:2 [ "refs" => "949449" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1195 #items: array:7 [ 0 => App\Models\Task {#1209 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 534773 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "156" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-524" "field_display_title" => "524" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1210 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1211 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1212 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1213 …2} "content" => Illuminate\Database\Eloquent\Collection {#1215 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1221 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 534773 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "156" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-524" "field_display_title" => "524" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1210 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1211 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1212 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1213 …2} "content" => Illuminate\Database\Eloquent\Collection {#1215 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1221 …2} "page" => array:2 [ …2] ] #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\Task {#1216 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 534774 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "156" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-525" "field_display_title" => "525" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1214 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1223 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1219 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1217 …2} "content" => Illuminate\Database\Eloquent\Collection {#1218 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1233 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 534774 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "156" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-525" "field_display_title" => "525" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1214 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1223 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1219 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1217 …2} "content" => Illuminate\Database\Eloquent\Collection {#1218 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1233 …2} "page" => array:2 [ …2] ] #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\Task {#1228 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 534775 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "156" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-526" "field_display_title" => "526" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1220 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1235 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1231 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1229 …2} "content" => Illuminate\Database\Eloquent\Collection {#1230 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1245 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 534775 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "156" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-526" "field_display_title" => "526" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1220 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1235 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1231 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1229 …2} "content" => Illuminate\Database\Eloquent\Collection {#1230 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1245 …2} "page" => array:2 [ …2] ] #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\Task {#1240 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 534776 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "156" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-527" "field_display_title" => "527" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1232 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1247 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1243 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1241 …2} "content" => Illuminate\Database\Eloquent\Collection {#1242 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1257 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 534776 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "156" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-527" "field_display_title" => "527" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1232 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1247 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1243 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1241 …2} "content" => Illuminate\Database\Eloquent\Collection {#1242 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1257 …2} "page" => array:2 [ …2] ] #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\Task {#1252 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 534777 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "156" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-528" "field_display_title" => "528" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1244 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1259 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1255 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1253 …2} "content" => Illuminate\Database\Eloquent\Collection {#1254 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1269 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 534777 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "156" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-528" "field_display_title" => "528" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1244 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1259 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1255 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1253 …2} "content" => Illuminate\Database\Eloquent\Collection {#1254 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1269 …2} "page" => array:2 [ …2] ] #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\Task {#1264 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 534778 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "156" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-529" "field_display_title" => "529" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1256 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1271 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1267 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1265 …2} "content" => Illuminate\Database\Eloquent\Collection {#1266 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1281 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 534778 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "156" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-529" "field_display_title" => "529" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1256 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1271 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1267 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1265 …2} "content" => Illuminate\Database\Eloquent\Collection {#1266 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1281 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 6 => App\Models\Task {#1276 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 534779 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "156" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-530" "field_display_title" => "530" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1268 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1283 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1279 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1277 …2} "content" => Illuminate\Database\Eloquent\Collection {#1280 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1278 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 534779 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "156" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-530" "field_display_title" => "530" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1268 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1283 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1279 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1277 …2} "content" => Illuminate\Database\Eloquent\Collection {#1280 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1278 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 949450 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "156" "field_url" => "/5-klass/matematika/bunimovich-uchebnik/page-156" "field_display_title" => "156" "field_folder" => "1" "field_image_name" => "156" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1097} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1090} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1095} "content" => Illuminate\Database\Eloquent\Collection {#1041} "next" => array:2 [ "refs" => "949451" "type" => "book_page" ] "previous" => array:2 [ "refs" => "949449" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1195} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 534779 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "156" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/00-530" "field_display_title" => "530" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1121} "content" => Illuminate\Database\Eloquent\Collection {#1038} "next" => array:2 [ "refs" => "534780" "type" => "task" ] "previous" => array:2 [ "refs" => "534778" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1115} "page" => array:2 [ "refs" => "949450" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№530 (с. 156)
Условие. №530 (с. 156)
скриншот условия
530 Выполните сложение и представьте результат в виде смешанной дроби:
а) $\frac{3}{8} + \frac{7}{8}$;
б) $\frac{5}{12} + \frac{2}{3}$;
В) $\frac{3}{4} + \frac{4}{5}$;
Г) $\frac{4}{15} + \frac{17}{20}$;
Д) $\frac{15}{12} + \frac{11}{18}$.
Решение 2. №530 (с. 156)
а)
Для сложения дробей $ \frac{3}{8} $ и $ \frac{7}{8} $, у которых одинаковые знаменатели, нужно сложить их числители, а знаменатель оставить прежним:
$ \frac{3}{8} + \frac{7}{8} = \frac{3+7}{8} = \frac{10}{8} $
Получилась неправильная дробь $ \frac{10}{8} $. Чтобы представить ее в виде смешанной дроби, нужно разделить числитель на знаменатель с остатком:
$ 10 \div 8 = 1 $ (остаток $ 2 $)
Целая часть смешанной дроби равна $ 1 $, числитель дробной части равен остатку $ 2 $, а знаменатель остается прежним — $ 8 $. Получаем $ 1\frac{2}{8} $.
Дробную часть $ \frac{2}{8} $ можно сократить, разделив числитель и знаменатель на их наибольший общий делитель, равный 2:
$ \frac{2}{8} = \frac{2 \div 2}{8 \div 2} = \frac{1}{4} $
Таким образом, окончательный результат: $ 1\frac{1}{4} $.
Ответ: $ 1\frac{1}{4} $
б)
Чтобы сложить дроби $ \frac{5}{12} $ и $ \frac{2}{3} $ с разными знаменателями, нужно привести их к общему знаменателю. Наименьший общий знаменатель для 12 и 3 — это 12.
Первая дробь $ \frac{5}{12} $ уже имеет нужный знаменатель.
Для второй дроби $ \frac{2}{3} $ найдем дополнительный множитель: $ 12 \div 3 = 4 $. Умножим числитель и знаменатель на 4:
$ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} $
Теперь сложим дроби с одинаковыми знаменателями:
$ \frac{5}{12} + \frac{8}{12} = \frac{5+8}{12} = \frac{13}{12} $
Преобразуем неправильную дробь $ \frac{13}{12} $ в смешанную. Разделим 13 на 12 с остатком:
$ 13 \div 12 = 1 $ (остаток $ 1 $)
Результат: $ 1\frac{1}{12} $.
Ответ: $ 1\frac{1}{12} $
в)
Для сложения дробей $ \frac{3}{4} $ и $ \frac{4}{5} $ найдем наименьший общий знаменатель для 4 и 5. Так как числа 4 и 5 взаимно простые, их наименьший общий знаменатель равен их произведению: $ 4 \times 5 = 20 $.
Приведем каждую дробь к знаменателю 20.
Для дроби $ \frac{3}{4} $ дополнительный множитель $ 20 \div 4 = 5 $:
$ \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20} $
Для дроби $ \frac{4}{5} $ дополнительный множитель $ 20 \div 5 = 4 $:
$ \frac{4}{5} = \frac{4 \times 4}{5 \times 4} = \frac{16}{20} $
Сложим полученные дроби:
$ \frac{15}{20} + \frac{16}{20} = \frac{15+16}{20} = \frac{31}{20} $
Преобразуем неправильную дробь $ \frac{31}{20} $ в смешанную. Разделим 31 на 20 с остатком:
$ 31 \div 20 = 1 $ (остаток $ 11 $)
Результат: $ 1\frac{11}{20} $.
Ответ: $ 1\frac{11}{20} $
г)
Чтобы сложить дроби $ \frac{4}{15} $ и $ \frac{17}{20} $, найдем наименьший общий знаменатель (НОК) для 15 и 20.
Разложим знаменатели на простые множители: $ 15 = 3 \times 5 $; $ 20 = 2 \times 2 \times 5 = 2^2 \times 5 $.
НОК(15, 20) = $ 2^2 \times 3 \times 5 = 60 $. Общий знаменатель — 60.
Приведем дроби к знаменателю 60.
Дополнительный множитель для $ \frac{4}{15} $ равен $ 60 \div 15 = 4 $:
$ \frac{4}{15} = \frac{4 \times 4}{15 \times 4} = \frac{16}{60} $
Дополнительный множитель для $ \frac{17}{20} $ равен $ 60 \div 20 = 3 $:
$ \frac{17}{20} = \frac{17 \times 3}{20 \times 3} = \frac{51}{60} $
Сложим полученные дроби:
$ \frac{16}{60} + \frac{51}{60} = \frac{16+51}{60} = \frac{67}{60} $
Преобразуем неправильную дробь $ \frac{67}{60} $ в смешанную. Разделим 67 на 60 с остатком:
$ 67 \div 60 = 1 $ (остаток $ 7 $)
Результат: $ 1\frac{7}{60} $.
Ответ: $ 1\frac{7}{60} $
д)
Чтобы сложить дроби $ \frac{15}{12} $ и $ \frac{11}{18} $, найдем наименьший общий знаменатель (НОК) для 12 и 18.
Разложим знаменатели на простые множители: $ 12 = 2 \times 2 \times 3 = 2^2 \times 3 $; $ 18 = 2 \times 3 \times 3 = 2 \times 3^2 $.
НОК(12, 18) = $ 2^2 \times 3^2 = 4 \times 9 = 36 $. Общий знаменатель — 36.
Приведем дроби к знаменателю 36.
Дополнительный множитель для $ \frac{15}{12} $ равен $ 36 \div 12 = 3 $:
$ \frac{15}{12} = \frac{15 \times 3}{12 \times 3} = \frac{45}{36} $
Дополнительный множитель для $ \frac{11}{18} $ равен $ 36 \div 18 = 2 $:
$ \frac{11}{18} = \frac{11 \times 2}{18 \times 2} = \frac{22}{36} $
Сложим полученные дроби:
$ \frac{45}{36} + \frac{22}{36} = \frac{45+22}{36} = \frac{67}{36} $
Преобразуем неправильную дробь $ \frac{67}{36} $ в смешанную. Разделим 67 на 36 с остатком:
$ 67 \div 36 = 1 $ (остаток $ 31 $)
Результат: $ 1\frac{31}{36} $.
Ответ: $ 1\frac{31}{36} $
Другие задания:
Помогло решение? Оставьте отзыв в комментариях ниже.
Присоединяйтесь к Телеграм-группе @top_gdz
ПрисоединитьсяМы подготовили для вас ответ c подробным объяснением домашего задания по математике за 5 класс, для упражнения номер 530 расположенного на странице 156 к учебнику серии сферы 2023 года издания для учащихся школ и гимназий.
Теперь на нашем сайте ГДЗ.ТОП вы всегда легко и бесплатно найдёте условие с правильным ответом на вопрос «Как решить ДЗ» и «Как сделать» задание по математике к упражнению №530 (с. 156), авторов: Бунимович (Евгений Абрамович), Дорофеев (Георгий Владимирович), Суворова (Светлана Борисовна), Кузнецова (Людмила Викторовна), Минаева (Светлана Станиславовна), Рослова (Лариса Олеговна), ФГОС (новый, красный) базовый уровень обучения учебного пособия издательства Просвещение.