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Страница 68 - 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
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Cтраница 68
App\Models\BookPage {#1003 // resources/views/models/book_page/default.blade.php #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" => 949362 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "68" "field_url" => "/5-klass/matematika/bunimovich-uchebnik/page-68" "field_display_title" => "68" "field_folder" => "1" "field_image_name" => "68" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1008 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1044 #items: array:1 [ 0 => App\Models\Book {#1006 #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 {#1009 #items: array:1 [ 0 => App\Models\Term {#1007 #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 {#1010 #items: array:1 [ 0 => App\Models\Term {#1011 #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 {#1012 #items: array:1 [ 0 => App\Models\Term {#1013 #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 {#1014 #items: array:6 [ 0 => App\Models\Term {#1015 #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 {#1016 #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 {#1017 #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 {#1018 #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 {#1019 #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 {#1020 #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 {#1021 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1022 #items: array:1 [ 0 => App\Models\Term {#1023 #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 {#1024 #items: array:1 [ 0 => App\Models\Term {#1025 #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 {#1026 #items: array:1 [ 0 => App\Models\Term {#1027 #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 {#1028 #items: array:1 [ 0 => App\Models\Term {#1029 #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 {#1030 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1031 #items: array:1 [ 0 => App\Models\Term {#1032 #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 {#1033 #items: array:1 [ 0 => App\Models\Term {#1034 #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 {#1035 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1036 #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 {#1037 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1038 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_url" => "/5-klass/matematika/bunimovich-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1040 #items: array:1 [ 0 => App\Models\Term {#1041 #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 {#1009} "field_class" => Illuminate\Database\Eloquent\Collection {#1010} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1012} "field_author" => Illuminate\Database\Eloquent\Collection {#1014} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1021} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1022} "field_country" => Illuminate\Database\Eloquent\Collection {#1024} "field_city" => Illuminate\Database\Eloquent\Collection {#1026} "field_series" => Illuminate\Database\Eloquent\Collection {#1028} "field_umk" => Illuminate\Database\Eloquent\Collection {#1030} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1031} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1033} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1035} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1036} "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 {#1037} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1038} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1039} "field_url" => "/5-klass/matematika/bunimovich-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1040} "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 } "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 {#1042 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1053 #items: array:1 [ 0 => App\Models\Element {#1052 #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" => 1124644 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1062 #items: array:1 [ 0 => App\Models\Edition {#1054 #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 {#1056 #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_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 {#1057 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1058 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1059 #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 {#1056} "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 {#1057} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1058} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1059} "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 } "book_page" => array:2 [ "refs" => "949362" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "68-1.jpg" "alt" => null "width" => "2313" "height" => 3093 "path" => "/media/matematika_05/bunimovich-u23/0-1/68-1.webp?ts=1744804771" ] ] ] #original: array:6 [ "id" => 1124644 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1062} "book_page" => array:2 [ "refs" => "949362" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "68-1.jpg" "alt" => null "width" => "2313" "height" => 3093 "path" => "/media/matematika_05/bunimovich-u23/0-1/68-1.webp?ts=1744804771" ] ] ] #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" => Illuminate\Database\Eloquent\Collection {#4114 #items: array:1 [ 0 => App\Models\BookPage {#4109 #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" => 949363 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_url" => "/5-klass/matematika/bunimovich-uchebnik/page-69" "field_display_title" => "69" "field_folder" => "1" "field_image_name" => "69" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#4112 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#4115 #items: array:1 [ 0 => App\Models\Book {#1006} ] #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 {#4113 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#4129 #items: array:1 [ 0 => App\Models\Element {#4128 #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" => 1124645 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#4130 #items: array:1 [ 0 => App\Models\Edition {#1054} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "949363" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "69-1.jpg" "alt" => null "width" => "2320" "height" => 3098 "path" => "/media/matematika_05/bunimovich-u23/0-1/69-1.webp?ts=1744804771" ] ] ] #original: array:6 [ "id" => 1124645 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#4130} "book_page" => array:2 [ "refs" => "949363" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "69-1.jpg" "alt" => null "width" => "2320" "height" => 3098 "path" => "/media/matematika_05/bunimovich-u23/0-1/69-1.webp?ts=1744804771" ] ] ] #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" => "949364" "type" => "book_page" ] "previous" => array:2 [ "refs" => "949362" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#4133 #items: array:1 [ 0 => App\Models\Task {#4132 #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" => 534397 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/5-klass/matematika/bunimovich-uchebnik/vop-14" "field_display_title" => "Вопросы и задания" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#4134 #items: [] #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 {#4135 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#4145 #items: array:1 [ 0 => App\Models\Branch {#4144 #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" => 534082 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Использование свойств действий при вычислениях" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#4149 #items: array:1 [ 0 => App\Models\Term {#4146 #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" => "67" "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 {#4148 #items: array:1 [ 0 => App\Models\Book {#1006} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#4147 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 534082 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Использование свойств действий при вычислениях" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#4149} "field_page_start" => "67" "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 {#4148} "branch_parent" => Illuminate\Database\Eloquent\Collection {#4147} ] #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 {#4185 #items: array:2 [ 0 => App\Models\Branch {#4193 #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" => 534082 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Использование свойств действий при вычислениях" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#4194 #items: array:1 [ 0 => App\Models\Term {#4146} ] #escapeWhenCastingToString: false } "field_page_start" => "67" "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 {#4195 #items: array:1 [ 0 => App\Models\Book {#1006} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#4196 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 534082 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Использование свойств действий при вычислениях" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#4194} "field_page_start" => "67" "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 {#4195} "branch_parent" => Illuminate\Database\Eloquent\Collection {#4196} ] #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 {#4197 #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" => 534083 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "14. Свойства сложения и умножения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#4198 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "68" "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 {#4199 #items: array:1 [ 0 => App\Models\Book {#1006} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#4200 #items: array:1 [ 0 => App\Models\Branch {#4144} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 534083 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "14. Свойства сложения и умножения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#4198} "field_page_start" => "68" "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 {#4199} "branch_parent" => Illuminate\Database\Eloquent\Collection {#4200} ] #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 {#4137 #items: array:2 [ 0 => App\Models\Element {#4176 #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" => 646965 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#4175 #items: array:1 [ 0 => App\Models\Edition {#1054} ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "534397" "type" => "task" ] "text" => "<p><strong>ВОПРОСЫ И ЗАДАНИЯ</strong></p><p><strong>Запишите с помощью букв переместительное и сочетательное свойства сложения и умножения.</strong></p><p><strong>Вычислите сумму</strong></p><p>$ (13 + 48) + (17 + 12) $, сгруппировав слагаемые иначе.</p><p><strong>Измените группировку множителей в произведении</strong></p><p>$ 2 \cdot (3 \cdot 5) \cdot 6 $ и вычислите результат.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "14-1.jpg" "alt" => null "width" => "758" "height" => 812 "path" => "/media/matematika_05/bunimovich-u23/0-vop/14-1.webp?ts=1737374578" ] ] ] #original: array:7 [ "id" => 646965 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#4175} "task" => array:2 [ "refs" => "534397" "type" => "task" ] "text" => "<p><strong>ВОПРОСЫ И ЗАДАНИЯ</strong></p><p><strong>Запишите с помощью букв переместительное и сочетательное свойства сложения и умножения.</strong></p><p><strong>Вычислите сумму</strong></p><p>$ (13 + 48) + (17 + 12) $, сгруппировав слагаемые иначе.</p><p><strong>Измените группировку множителей в произведении</strong></p><p>$ 2 \cdot (3 \cdot 5) \cdot 6 $ и вычислите результат.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "14-1.jpg" "alt" => null "width" => "758" "height" => 812 "path" => "/media/matematika_05/bunimovich-u23/0-vop/14-1.webp?ts=1737374578" ] ] ] #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 {#4173 #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" => 1469377 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#4164 #items: array:1 [ 0 => App\Models\Edition {#4174 #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 {#4172 #items: array:1 [ 0 => App\Models\Term {#4171 …30} ] #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 {#4170 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#4168 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#4169 #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 {#4172} "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 {#4170} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#4168} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#4169} "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" => "534397" "type" => "task" ] "text" => "<p><strong>Запишите с помощью букв переместительное и сочетательное свойства сложения и умножения.</strong></p><p>Для любых чисел $a$, $b$ и $c$ справедливы следующие равенства:<br> <em>Переместительное свойство сложения (коммутативность):</em><br> $a + b = b + a$<br> От перестановки мест слагаемых сумма не меняется.<br><br> <em>Сочетательное свойство сложения (ассоциативность):</em><br> $(a + b) + c = a + (b + c)$<br> Чтобы к сумме двух чисел прибавить третье число, можно к первому числу прибавить сумму второго и третьего чисел.<br><br> <em>Переместительное свойство умножения (коммутативность):</em><br> $a \cdot b = b \cdot a$<br> От перестановки мест множителей произведение не меняется.<br><br> <em>Сочетательное свойство умножения (ассоциативность):</em><br> $(a \cdot b) \cdot c = a \cdot (b \cdot c)$<br> Чтобы произведение двух чисел умножить на третье число, можно первое число умножить на произведение второго и третьего чисел.<br> Ответ: $a + b = b + a$; $(a + b) + c = a + (b + c)$; $a \cdot b = b \cdot a$; $(a \cdot b) \cdot c = a \cdot (b \cdot c)$.</p><p><strong>Вычислите сумму (13 + 48) + (17 + 12), сгруппировав слагаемые иначе.</strong></p><p>Чтобы упростить вычисление, воспользуемся переместительным и сочетательным свойствами сложения. Сгруппируем слагаемые так, чтобы в сумме получались "круглые" числа. <br> $(13 + 48) + (17 + 12) = 13 + 48 + 17 + 12 = (13 + 17) + (48 + 12)$ <br> Сначала вычислим сумму в каждой из новых скобок: <br> $13 + 17 = 30$ <br> $48 + 12 = 60$ <br> Теперь сложим полученные результаты: <br> $30 + 60 = 90$ <br> Ответ: 90.</p><p><strong>Измените группировку множителей в произведении 2 · (3 · 5) · 6 и вычислите результат.</strong></p><p>Используя сочетательное свойство умножения, можно изменить порядок вычислений для удобства. <br> $2 \cdot (3 \cdot 5) \cdot 6 = 2 \cdot 3 \cdot 5 \cdot 6$ <br> Сгруппируем множители по-другому, например, так, чтобы получить в произведении 10, на которое легко умножать: <br> $(2 \cdot 5) \cdot (3 \cdot 6)$ <br> Вычислим произведение в каждой из новых скобок: <br> $2 \cdot 5 = 10$ <br> $3 \cdot 6 = 18$ <br> Теперь перемножим полученные результаты: <br> $10 \cdot 18 = 180$ <br> Ответ: 180.</p>" ] #original: array:6 [ "id" => 1469377 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#4164} "task" => array:2 [ "refs" => "534397" "type" => "task" ] "text" => "<p><strong>Запишите с помощью букв переместительное и сочетательное свойства сложения и умножения.</strong></p><p>Для любых чисел $a$, $b$ и $c$ справедливы следующие равенства:<br> <em>Переместительное свойство сложения (коммутативность):</em><br> $a + b = b + a$<br> От перестановки мест слагаемых сумма не меняется.<br><br> <em>Сочетательное свойство сложения (ассоциативность):</em><br> $(a + b) + c = a + (b + c)$<br> Чтобы к сумме двух чисел прибавить третье число, можно к первому числу прибавить сумму второго и третьего чисел.<br><br> <em>Переместительное свойство умножения (коммутативность):</em><br> $a \cdot b = b \cdot a$<br> От перестановки мест множителей произведение не меняется.<br><br> <em>Сочетательное свойство умножения (ассоциативность):</em><br> $(a \cdot b) \cdot c = a \cdot (b \cdot c)$<br> Чтобы произведение двух чисел умножить на третье число, можно первое число умножить на произведение второго и третьего чисел.<br> Ответ: $a + b = b + a$; $(a + b) + c = a + (b + c)$; $a \cdot b = b \cdot a$; $(a \cdot b) \cdot c = a \cdot (b \cdot c)$.</p><p><strong>Вычислите сумму (13 + 48) + (17 + 12), сгруппировав слагаемые иначе.</strong></p><p>Чтобы упростить вычисление, воспользуемся переместительным и сочетательным свойствами сложения. Сгруппируем слагаемые так, чтобы в сумме получались "круглые" числа. <br> $(13 + 48) + (17 + 12) = 13 + 48 + 17 + 12 = (13 + 17) + (48 + 12)$ <br> Сначала вычислим сумму в каждой из новых скобок: <br> $13 + 17 = 30$ <br> $48 + 12 = 60$ <br> Теперь сложим полученные результаты: <br> $30 + 60 = 90$ <br> Ответ: 90.</p><p><strong>Измените группировку множителей в произведении 2 · (3 · 5) · 6 и вычислите результат.</strong></p><p>Используя сочетательное свойство умножения, можно изменить порядок вычислений для удобства. <br> $2 \cdot (3 \cdot 5) \cdot 6 = 2 \cdot 3 \cdot 5 \cdot 6$ <br> Сгруппируем множители по-другому, например, так, чтобы получить в произведении 10, на которое легко умножать: <br> $(2 \cdot 5) \cdot (3 \cdot 6)$ <br> Вычислим произведение в каждой из новых скобок: <br> $2 \cdot 5 = 10$ <br> $3 \cdot 6 = 18$ <br> Теперь перемножим полученные результаты: <br> $10 \cdot 18 = 180$ <br> Ответ: 180.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] 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"field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#4135} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#4145} "parent_branches" => Illuminate\Database\Eloquent\Collection {#4185} "content" => Illuminate\Database\Eloquent\Collection {#4137} "next" => array:2 [ "refs" => "534398" "type" => "task" ] "previous" => array:2 [ "refs" => "534396" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#4179} "page" => array:2 [ "refs" => "949363" "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 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 949363 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_url" => "/5-klass/matematika/bunimovich-uchebnik/page-69" "field_display_title" => "69" "field_folder" => "1" "field_image_name" => "69" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#4112} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#4115} "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 {#4113} "content" => Illuminate\Database\Eloquent\Collection {#4129} "next" => array:2 [ "refs" => "949364" "type" => "book_page" ] "previous" => array:2 [ "refs" => "949362" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#4133} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "previous" => Illuminate\Database\Eloquent\Collection {#4105 #items: array:1 [ 0 => App\Models\BookPage {#4104 #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" => 949361 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "67" "field_url" => "/5-klass/matematika/bunimovich-uchebnik/page-67" "field_display_title" => "67" "field_folder" => "1" "field_image_name" => "67" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#4106 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#4107 #items: array:1 [ 0 => App\Models\Book {#1006} ] #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 {#4108 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#4118 #items: array:1 [ 0 => App\Models\Element {#4117 #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" => 1124643 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#4119 #items: array:1 [ 0 => App\Models\Edition {#1054} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "949361" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "67-1.jpg" "alt" => null "width" => "2321" "height" => 3099 "path" => "/media/matematika_05/bunimovich-u23/0-1/67-1.webp?ts=1744804771" ] ] ] #original: array:6 [ "id" => 1124643 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#4119} "book_page" => array:2 [ "refs" => "949361" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "67-1.jpg" "alt" => null "width" => "2321" "height" => 3099 "path" => "/media/matematika_05/bunimovich-u23/0-1/67-1.webp?ts=1744804771" ] ] ] #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" => "949362" "type" => "book_page" ] "previous" => array:2 [ "refs" => "949360" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#4110 #items: [] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 949361 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "67" "field_url" => "/5-klass/matematika/bunimovich-uchebnik/page-67" "field_display_title" => "67" "field_folder" => "1" "field_image_name" => "67" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#4106} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#4107} "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 {#4108} "content" => Illuminate\Database\Eloquent\Collection {#4118} "next" => array:2 [ "refs" => "949362" "type" => "book_page" ] "previous" => array:2 [ "refs" => "949360" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#4110} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "tasks" => Illuminate\Database\Eloquent\Collection {#1045 #items: [] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 949362 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "68" "field_url" => "/5-klass/matematika/bunimovich-uchebnik/page-68" "field_display_title" => "68" "field_folder" => "1" "field_image_name" => "68" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1008} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1044} "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 {#1042} "content" => Illuminate\Database\Eloquent\Collection {#1053} "next" => array:2 [ "refs" => "949363" "type" => "book_page" ] "previous" => array:2 [ "refs" => "949361" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1045} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
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