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Номер 3, страница 42 - гдз по алгебре 7 класс учебник Дорофеев, Суворова
Авторы: Дорофеев Г. В., Суворова С. Б., Бунимович Е. А., Кузнецова Л. В., Минаева С. С., Рослова Л. О.
Тип: Учебник
Издательство: Просвещение
Год издания: 2019 - 2022
Цвет обложки: белый, голубой, оранжевый с галочкой
ISBN: 978-5-09-074650-2
Рекомендовано Министерством образования и науки Российской Федерации
Популярные ГДЗ в 7 классе
Глава 1. Дроби и проценты. Чему вы научились. Проверьте себя (тест) - номер 3, страница 42.
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" => 441935 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "42" "field_page_end" => null "field_url" => "/7-klass/algebra/dorofeev-uchebnik/ps1-3" "field_display_title" => "3" "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" => 441558 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Дроби и проценты" "field_branch_order" => "1" "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 [ …6] "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 [ …6] "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" => "5" "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" => 386 "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 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #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 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1071 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1072 #items: [] #escapeWhenCastingToString: false } "field_standart_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:10 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_publication_number" => "9" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "с галочкой" "field_publication_year" => "2019" "field_publication_year_until" => "2022" "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для общеобразовательных организаций" "field_allowed" => "Рекомендовано Министерством образования и науки Российской Федерации" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1403" "field_priority" => "10" "field_default_folder" => "/algebra_07/dorofeev/" "field_isbn" => "978-5-09-074650-2" "field_cover" => array:1 [ 0 => "/media/algebra_07/dorofeev/covers/cover1.webp?ts=1736282735" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_07/dorofeev/covers/cover1.webp?ts=1736282735" "alt" => "" "width" => "682" "height" => "910" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1077 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1078 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1079 #items: [] #escapeWhenCastingToString: false } "field_url" => "/7-klass/algebra/dorofeev-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1080 #items: array:3 [ 0 => App\Models\Term {#1081 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Term {#1082 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 2 => 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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => "<!--Текст в низу страницы--> <h2>Решебник к учебнику Дорофеева - верный помощник </h2> <p> Алгебра - не самый любимый предмет у школьников. Многие не могут разобраться в сложной программе, испытывают проблемы всякий раз, как приходится решать уравнения. Если не помочь им понять суть тематического материала, то ребята так и не приобретут необходимых навыков, а их успеваемость значительно снизится. Допускать подобного нельзя, ведь умение ориентироваться в столь сложной науке может пригодиться ученикам во взрослой жизни. Отличным помощником для подростков станет «<strong>ГДЗ по Алгебре 7 класс Учебник Дорофеев, Суворова, Бунимович (Просвещение)</strong>». </p> <p> В этом году вполне возможны трудности при изучении следующих тем: <ol> <li>Проценты и статистические характеристики.</li> <li>Зависимости, формулы и пропорции.</li> <li>Буквенные выражения, действия с ними.</li> <li>Корни уравнений.</li> <li>Координатные прямые и плоскости.</li> <li>Графики, комбинаторные задачи.</li> </ol> <p> Отсутствие теории в учебниках мешает учащимся самостоятельно разобраться в параграфах. Если во время урока они пропустят объяснения учителя или не поймут их, то просить о помощи семиклассникам приходится родителей. Но многие ли мамы и папы помнят, как находить квадрат суммы/разности или каким способом разложить многочлен на множители? Поэтому лучше воспользоваться решебником, в котором авторы приводят подробную информацию по всему текущему курсу. </p> <h2> ГДЗ по алгебре - не просто шпаргалка </h2> <p> Даже отличникам не хочется часами просиживать над выполнением домашних заданий, что уж говорить о детях, которые с трудом отличают формулы от уравнений? Поиск более легких путей заставляет учеников порой прибегать к списыванию. Но это не лучший выход из ситуации, так как он не принесет ребятам нужных навыков. Поэтому не стоит относиться к <strong>ГДЗ по Алгебре за 7 класс Дорофеев</strong>, как к шпаргалке. Это полноценное учебное пособие, которое может принести учащимся много пользы. </p> <p> Авторы снабдили свое издание: <ol> <li>верными ответами ко всем номерам;</li> <li>детально расписанными решениями;</li> <li>наглядными примерами;</li> <li>дополнительными пояснениями.</li> </ol> <p> Школьникам необходимо научиться правильно использовать предоставленную информацию, чтобы не попасть в еще большие неприятности. Только понимание алгоритмов позволит легко ориентироваться в сложных задачах и не допускать промахов при сдаче контрольных работ. В решебнике есть все необходимое, чтобы семиклассники полноценно усвоили непростой материал. </p> <h2> Онлайн-сборник пригодится в 7 классе </h2> <p> Если подростки не понимают, как подступиться к решению какой-нибудь задачи, то они могут долго сидеть над тетрадями, пытаясь найти правильный ответ. Но тратить несколько часов на выполнение д/з по одному предмету - плохой показатель. <strong>Решебник 7 класс к учебнику Дорофеева Г. В. (Просвещение)</strong>» позволит даже самые сложные упражнения сделать за несколько минут. </p> <p> Использование справочника даёт возможность: <ul> <li>быстро выполнить домашние задания;</li> <li>исправить все найденные ошибки;</li> <li>тщательно разобраться в каждой теме;</li> <li>запомнить нужные алгоритмы.</li> </ul> <p> Работать с пособием очень просто. Онлайн-формат позволяет открыть его в любой удобный момент, заниматься даже по пути в школу или повторить сведения перед уроком на перемене. Авторы решебника рекомендуют всегда просматривать теоретическую информацию, после чего приступать к самостоятельному выполнению заданий. Когда все будет сделано, можно сверять получившиеся результаты с ответами из ГДЗ. 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Многие не могут разобраться в сложной программе, испытывают проблемы всякий раз, как приходится решать уравнения. Если не помочь им понять суть тематического материала, то ребята так и не приобретут необходимых навыков, а их успеваемость значительно снизится. Допускать подобного нельзя, ведь умение ориентироваться в столь сложной науке может пригодиться ученикам во взрослой жизни. Отличным помощником для подростков станет «<strong>ГДЗ по Алгебре 7 класс Учебник Дорофеев, Суворова, Бунимович (Просвещение)</strong>». </p> <p> В этом году вполне возможны трудности при изучении следующих тем: <ol> <li>Проценты и статистические характеристики.</li> <li>Зависимости, формулы и пропорции.</li> <li>Буквенные выражения, действия с ними.</li> <li>Корни уравнений.</li> <li>Координатные прямые и плоскости.</li> <li>Графики, комбинаторные задачи.</li> </ol> <p> Отсутствие теории в учебниках мешает учащимся самостоятельно разобраться в параграфах. Если во время урока они пропустят объяснения учителя или не поймут их, то просить о помощи семиклассникам приходится родителей. Но многие ли мамы и папы помнят, как находить квадрат суммы/разности или каким способом разложить многочлен на множители? Поэтому лучше воспользоваться решебником, в котором авторы приводят подробную информацию по всему текущему курсу. </p> <h2> ГДЗ по алгебре - не просто шпаргалка </h2> <p> Даже отличникам не хочется часами просиживать над выполнением домашних заданий, что уж говорить о детях, которые с трудом отличают формулы от уравнений? Поиск более легких путей заставляет учеников порой прибегать к списыванию. Но это не лучший выход из ситуации, так как он не принесет ребятам нужных навыков. Поэтому не стоит относиться к <strong>ГДЗ по Алгебре за 7 класс Дорофеев</strong>, как к шпаргалке. Это полноценное учебное пособие, которое может принести учащимся много пользы. </p> <p> Авторы снабдили свое издание: <ol> <li>верными ответами ко всем номерам;</li> <li>детально расписанными решениями;</li> <li>наглядными примерами;</li> <li>дополнительными пояснениями.</li> </ol> <p> Школьникам необходимо научиться правильно использовать предоставленную информацию, чтобы не попасть в еще большие неприятности. Только понимание алгоритмов позволит легко ориентироваться в сложных задачах и не допускать промахов при сдаче контрольных работ. В решебнике есть все необходимое, чтобы семиклассники полноценно усвоили непростой материал. </p> <h2> Онлайн-сборник пригодится в 7 классе </h2> <p> Если подростки не понимают, как подступиться к решению какой-нибудь задачи, то они могут долго сидеть над тетрадями, пытаясь найти правильный ответ. Но тратить несколько часов на выполнение д/з по одному предмету - плохой показатель. <strong>Решебник 7 класс к учебнику Дорофеева Г. В. (Просвещение)</strong>» позволит даже самые сложные упражнения сделать за несколько минут. </p> <p> Использование справочника даёт возможность: <ul> <li>быстро выполнить домашние задания;</li> <li>исправить все найденные ошибки;</li> <li>тщательно разобраться в каждой теме;</li> <li>запомнить нужные алгоритмы.</li> </ul> <p> Работать с пособием очень просто. Онлайн-формат позволяет открыть его в любой удобный момент, заниматься даже по пути в школу или повторить сведения перед уроком на перемене. Авторы решебника рекомендуют всегда просматривать теоретическую информацию, после чего приступать к самостоятельному выполнению заданий. Когда все будет сделано, можно сверять получившиеся результаты с ответами из ГДЗ. 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"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 {#1140} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1149} ] #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:6 [ 0 => App\Models\Element {#1100 #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" => 510344 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1092 #items: array:1 [ 0 => App\Models\Edition {#1101 #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" => 1298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1097 …2} "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" => "vadim" …8 ] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "441935" "type" => "task" ] "text" => "<p><strong>3</strong> Найдите значение выражения $\frac{0.3 \cdot 0.25}{0.45}$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "3-1.jpg" "alt" => null "width" => "1082" "height" => 157 "path" => "/media/algebra_07/dorofeev/0-ps1/3-1.webp?ts=1736353665" ] ] ] #original: array:7 [ "id" => 510344 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1092} "task" => array:2 [ "refs" => "441935" "type" => "task" ] "text" => "<p><strong>3</strong> Найдите значение выражения $\frac{0.3 \cdot 0.25}{0.45}$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "3-1.jpg" "alt" => null "width" => "1082" "height" => 157 "path" => "/media/algebra_07/dorofeev/0-ps1/3-1.webp?ts=1736353665" ] ] ] #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 {#1124 #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" => 511832 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1153 #items: array:1 [ 0 => App\Models\Edition {#1122 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "441935" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "3-1.png" "alt" => null "width" => "720" "height" => 2004 "path" => "/media/algebra_07/dorofeev/1-ps1/3-1.webp?ts=1736355125" ] ] ] #original: array:6 [ "id" => 511832 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1153} "task" => array:2 [ "refs" => "441935" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "3-1.png" "alt" => null "width" => "720" "height" => 2004 "path" => "/media/algebra_07/dorofeev/1-ps1/3-1.webp?ts=1736355125" ] ] ] #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\Element {#1094 #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" => 510412 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1034 #items: array:1 [ 0 => App\Models\Edition {#1093 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "441935" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "3-1.png" "alt" => null "width" => "349" "height" => 162 "path" => "/media/algebra_07/dorofeev/2-ps1/3-1.webp?ts=1736353497" ] ] ] #original: array:6 [ "id" => 510412 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1034} "task" => array:2 [ "refs" => "441935" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "3-1.png" "alt" => null "width" => "349" "height" => 162 "path" => "/media/algebra_07/dorofeev/2-ps1/3-1.webp?ts=1736353497" ] ] ] #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\Element {#1107 #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" => 509956 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1098 #items: array:1 [ 0 => App\Models\Edition {#1108 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "441935" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "3-1.jpg" "alt" => null "width" => "565" "height" => 142 "path" => "/media/algebra_07/dorofeev/4-ps1/3-1.webp?ts=1736353145" ] ] ] #original: array:6 [ "id" => 509956 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1098} "task" => array:2 [ "refs" => "441935" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "3-1.jpg" "alt" => null "width" => "565" "height" => 142 "path" => "/media/algebra_07/dorofeev/4-ps1/3-1.webp?ts=1736353145" ] ] ] #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\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" => 510876 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1125 #items: array:1 [ 0 => App\Models\Edition {#1041 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "441935" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "3-1.png" "alt" => null "width" => "970" "height" => 385 "path" => "/media/algebra_07/dorofeev/5-ps1/3-1.webp?ts=1736353732" ] ] ] #original: array:6 [ "id" => 510876 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1125} "task" => array:2 [ "refs" => "441935" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "3-1.png" "alt" => null "width" => "970" "height" => 385 "path" => "/media/algebra_07/dorofeev/5-ps1/3-1.webp?ts=1736353732" ] ] ] #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\Element {#1146 #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" => 1383329 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1161 #items: array:1 [ 0 => App\Models\Edition {#1144 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "441935" "type" => "task" ] "text" => "<p>Для решения данной задачи представим все десятичные дроби в виде обыкновенных дробей. Это упростит вычисления и сокращение.</p><p>1. Преобразуем десятичные дроби в обыкновенные:</p><ul><li>$0.3 = \frac{3}{10}$</li> <li>$0.25 = \frac{25}{100} = \frac{1}{4}$</li> <li>$0.45 = \frac{45}{100} = \frac{9}{20}$</li></ul><p>2. Подставим полученные обыкновенные дроби в исходное выражение:</p><p>$\frac{0.3 \cdot 0.25}{0.45} = \frac{\frac{3}{10} \cdot \frac{1}{4}}{\frac{9}{20}}$</p><p>3. Сначала выполним операцию умножения в числителе:</p><p>$\frac{3}{10} \cdot \frac{1}{4} = \frac{3 \cdot 1}{10 \cdot 4} = \frac{3}{40}$</p><p>4. Теперь наше выражение выглядит как деление двух дробей:</p><p>$\frac{\frac{3}{40}}{\frac{9}{20}}$</p><p>Чтобы разделить одну дробь на другую, нужно первую дробь умножить на дробь, обратную второй:</p><p>$\frac{3}{40} \div \frac{9}{20} = \frac{3}{40} \cdot \frac{20}{9}$</p><p>5. Выполним умножение, предварительно сократив числители и знаменатели:</p><p>$\frac{3}{40} \cdot \frac{20}{9} = \frac{3 \cdot 20}{40 \cdot 9} = \frac{3 \cdot 20}{2 \cdot 20 \cdot 3 \cdot 3}$</p><p>Сокращаем общие множители (3 и 20):</p><p>$\frac{\cancel{3} \cdot \cancel{20}}{2 \cdot \cancel{20} \cdot \cancel{3} \cdot 3} = \frac{1}{2 \cdot 3} = \frac{1}{6}$</p><p>Ответ: $\frac{1}{6}$</p>" ] #original: array:6 [ "id" => 1383329 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1161} "task" => array:2 [ "refs" => "441935" "type" => "task" ] "text" => "<p>Для решения данной задачи представим все десятичные дроби в виде обыкновенных дробей. Это упростит вычисления и сокращение.</p><p>1. Преобразуем десятичные дроби в обыкновенные:</p><ul><li>$0.3 = \frac{3}{10}$</li> <li>$0.25 = \frac{25}{100} = \frac{1}{4}$</li> <li>$0.45 = \frac{45}{100} = \frac{9}{20}$</li></ul><p>2. Подставим полученные обыкновенные дроби в исходное выражение:</p><p>$\frac{0.3 \cdot 0.25}{0.45} = \frac{\frac{3}{10} \cdot \frac{1}{4}}{\frac{9}{20}}$</p><p>3. Сначала выполним операцию умножения в числителе:</p><p>$\frac{3}{10} \cdot \frac{1}{4} = \frac{3 \cdot 1}{10 \cdot 4} = \frac{3}{40}$</p><p>4. Теперь наше выражение выглядит как деление двух дробей:</p><p>$\frac{\frac{3}{40}}{\frac{9}{20}}$</p><p>Чтобы разделить одну дробь на другую, нужно первую дробь умножить на дробь, обратную второй:</p><p>$\frac{3}{40} \div \frac{9}{20} = \frac{3}{40} \cdot \frac{20}{9}$</p><p>5. Выполним умножение, предварительно сократив числители и знаменатели:</p><p>$\frac{3}{40} \cdot \frac{20}{9} = \frac{3 \cdot 20}{40 \cdot 9} = \frac{3 \cdot 20}{2 \cdot 20 \cdot 3 \cdot 3}$</p><p>Сокращаем общие множители (3 и 20):</p><p>$\frac{\cancel{3} \cdot \cancel{20}}{2 \cdot \cancel{20} \cdot \cancel{3} \cdot 3} = \frac{1}{2 \cdot 3} = \frac{1}{6}$</p><p>Ответ: $\frac{1}{6}$</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" => "441936" "type" => "task" ] "previous" => array:2 [ "refs" => "441934" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1110 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1563 #items: array:1 [ 0 => App\Models\BookPage {#1032 #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" => 890993 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "42" "field_url" => "/7-klass/algebra/dorofeev-uchebnik/page-42" "field_display_title" => "42" "field_folder" => "1" "field_image_name" => "42" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1023 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1026 #items: array:1 [ 0 => App\Models\Book {#1118 #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 [ …50] #original: array:50 [ …50] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #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 {#1184 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1185 #items: array:1 [ 0 => App\Models\Element {#1186 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "890994" "type" => "book_page" ] "previous" => array:2 [ "refs" => "890992" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1194 #items: array:16 [ 0 => App\Models\Task {#1195 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Task {#1302 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 2 => App\Models\Task {#1321 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 3 => App\Models\Task {#1340 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 4 => App\Models\Task {#1359 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 5 => App\Models\Task {#1378 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 6 => App\Models\Task {#1395 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 7 => App\Models\Task {#1410 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 8 => App\Models\Task {#1427 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 9 => App\Models\Task {#1444 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 10 => App\Models\Task {#1461 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 11 => App\Models\Task {#1478 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 12 => App\Models\Task {#1495 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 13 => App\Models\Task {#1510 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 14 => App\Models\Task {#1527 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 15 => App\Models\Task {#1544 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 890993 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "42" "field_url" => "/7-klass/algebra/dorofeev-uchebnik/page-42" "field_display_title" => "42" "field_folder" => "1" "field_image_name" => "42" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1023} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1026} "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 {#1184} "content" => Illuminate\Database\Eloquent\Collection {#1185} "next" => array:2 [ "refs" => "890994" "type" => "book_page" ] "previous" => array:2 [ "refs" => "890992" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1194} ] #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" => 441935 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "42" "field_page_end" => null "field_url" => "/7-klass/algebra/dorofeev-uchebnik/ps1-3" "field_display_title" => "3" "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 {#1120} "content" => Illuminate\Database\Eloquent\Collection {#1038} "next" => array:2 [ "refs" => "441936" "type" => "task" ] "previous" => array:2 [ "refs" => "441934" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1110} "page" => array:2 [ "refs" => "890993" "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 => "*" ] }
№3 (с. 42)
Условие. №3 (с. 42)
скриншот условия
3 Найдите значение выражения $\frac{0.3 \cdot 0.25}{0.45}$.
Решение 1. №3 (с. 42)
Решение 2. №3 (с. 42)
Решение 4. №3 (с. 42)
Решение 5. №3 (с. 42)
Решение 6. №3 (с. 42)
Для решения данной задачи представим все десятичные дроби в виде обыкновенных дробей. Это упростит вычисления и сокращение.
1. Преобразуем десятичные дроби в обыкновенные:
- $0.3 = \frac{3}{10}$
- $0.25 = \frac{25}{100} = \frac{1}{4}$
- $0.45 = \frac{45}{100} = \frac{9}{20}$
2. Подставим полученные обыкновенные дроби в исходное выражение:
$\frac{0.3 \cdot 0.25}{0.45} = \frac{\frac{3}{10} \cdot \frac{1}{4}}{\frac{9}{20}}$
3. Сначала выполним операцию умножения в числителе:
$\frac{3}{10} \cdot \frac{1}{4} = \frac{3 \cdot 1}{10 \cdot 4} = \frac{3}{40}$
4. Теперь наше выражение выглядит как деление двух дробей:
$\frac{\frac{3}{40}}{\frac{9}{20}}$
Чтобы разделить одну дробь на другую, нужно первую дробь умножить на дробь, обратную второй:
$\frac{3}{40} \div \frac{9}{20} = \frac{3}{40} \cdot \frac{20}{9}$
5. Выполним умножение, предварительно сократив числители и знаменатели:
$\frac{3}{40} \cdot \frac{20}{9} = \frac{3 \cdot 20}{40 \cdot 9} = \frac{3 \cdot 20}{2 \cdot 20 \cdot 3 \cdot 3}$
Сокращаем общие множители (3 и 20):
$\frac{\cancel{3} \cdot \cancel{20}}{2 \cdot \cancel{20} \cdot \cancel{3} \cdot 3} = \frac{1}{2 \cdot 3} = \frac{1}{6}$
Ответ: $\frac{1}{6}$
Другие задания:
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