Question

Выполните действия : 1) (2/7+5/21)÷1 4/7; 2) (8/11+3/22)÷5/11; 3) 1 7/12÷(3/8+5/12); 4) 17/36÷(7/12-5/9); 5) (3/14+5/7)÷3 5/7; 6) 19/24÷(3/16+5/24). помогите пожалуйста решить. Спасибо большое заранее. покажите как решаются.

Answer 1

Ответ:

1) 1/3

2) 1.9

3) 14/19

4) 17

5) 1/4

6) 2

Пошаговое объяснение:

Пример 1.

Чтобы складывать дроби, нужно привести их к одному знаменателю. В данном случае числом, наименьшим кратным и для 7, и для 21 будет число 21. Тогда 2/7 = 6/21 (и числитель, и знаменатель умножаем на частное от 21 и 7, то есть на 3). Тогда получается 2/7 + 5/21 = 6/21 + 5/21 = 11/21.

Далее преобразовываем выражение 1*4/7. Чтобы сделать из этой смешанной дроби обыкновенную дробь, нужно первое чило умножить на знаменатель и прибавить числитель: 1*4/7 = (1*7 + 4)/7 = 11/7. Получается 11/21 ÷ 11/7.

Чтобы разделить дробь на дробь, нужно во второй дроби поменять местами числитель и знаменатель и перемножить с первой дробью: 11/21 ÷ 11/7 = 11/21 * 7/11 = 11*7 / 21*11. Сокращаем 11 и 7, получаем 1*1 / 3*1 = 1/3

Пример 2.

8/11 = 16/22

16/22 + 3/22 = 19/22

19/22 ÷ 5/11 = 19/22 * 11/5 = 19*11 / 22*5 = 19*1 / 2*5 = 19/10 = 1.9

Пример 3.

Общее кратное для 8 и 12 = 24.

3/8 = 9/24, а 5/12 = 10/24.

9/24 + 10/24 = 19/24.

7/12 ÷ 19/24 = 7/12 * 24/19 = 7*24 / 12*19 = 7*2 / 1*19 = 14/19

Пример 4.

Общее кратное для 12 и 9 = 36

7/12 = 21/36, а 5/9 = 20/36

21/36 - 20/36 = 1/36

17/36 ÷ 1/36 = 17/36 * 36/1 = 17*36 / 36 = 17

Пример 5.

5/7 = 10/14

3/14 + 10/14 = 13/14

3*5/7 = (3*7 + 5)/7 = 26/7

13/14 ÷ 26/7 = 13/14 * 7/26 = 13*7 / 14*26 = 1*1 / 2*2 = 1/4

Пример 6.

Общее кратное для 16 и 24 = 48

3/16 = 9/48, а 5/24 = 10/48

9/48 + 10/48 = 19/48

19/24 ÷ 19/48 = 19/24 * 48/19 = 19*48 / 24*19 = 1*2 / 1*1 = 2/1 = 2

Answer 2

Problem 1: (2/7 + 5/21) ÷ (1 + 4/7)

To solve this problem, we need to simplify the expression step by step.

Step 1: Simplify the numerator of the fraction inside the parentheses. - 2/7 + 5/21 = (6/21 + 5/21) = 11/21

Step 2: Simplify the denominator of the fraction inside the parentheses. - 1 + 4/7 = (7/7 + 4/7) = 11/7

Step 3: Divide the numerator by the denominator. - (11/21) ÷ (11/7) = (11/21) * (7/11) = 1/3

Therefore, the solution to problem 1 is 1/3.

Problem 2: (8/11 + 3/22) ÷ (5/11)

To solve this problem, we need to simplify the expression step by step.

Step 1: Simplify the numerator of the fraction inside the parentheses. - 8/11 + 3/22 = (16/22 + 3/22) = 19/22

Step 2: Divide the numerator by the denominator. - (19/22) ÷ (5/11) = (19/22) * (11/5) = 209/110

Therefore, the solution to problem 2 is 209/110.

Problem 3: 1 + 7/12 ÷ (3/8 + 5/12)

To solve this problem, we need to simplify the expression step by step.

Step 1: Simplify the denominator of the fraction inside the parentheses. - 3/8 + 5/12 = (9/24 + 10/24) = 19/24

Step 2: Divide the numerator by the denominator. - 7/12 ÷ (19/24) = (7/12) * (24/19) = 14/19

Step 3: Add the result to 1. - 1 + 14/19 = (19/19 + 14/19) = 33/19

Therefore, the solution to problem 3 is 33/19.

Problem 4: 17/36 ÷ (7/12 - 5/9)

To solve this problem, we need to simplify the expression step by step.

Step 1: Simplify the denominator of the fraction inside the parentheses. - 7/12 - 5/9 = (21/36 - 20/36) = 1/36

Step 2: Divide the numerator by the denominator. - 17/36 ÷ (1/36) = (17/36) * (36/1) = 17/1 = 17

Therefore, the solution to problem 4 is 17.

Problem 5: (3/14 + 5/7) ÷ (3 + 5/7)

To solve this problem, we need to simplify the expression step by step.

Step 1: Simplify the numerator of the fraction inside the parentheses. - 3/14 + 5/7 = (9/42 + 30/42) = 39/42

Step 2: Simplify the denominator of the fraction inside the parentheses. - 3 + 5/7 = (21/7 + 5/7) = 26/7

Step 3: Divide the numerator by the denominator. - (39/42) ÷ (26/7) = (39/42) * (7/26) = 13/26

Therefore, the solution to problem 5 is 13/26.

Problem 6: 19/24 ÷ (3/16 + 5/24)

To solve this problem, we need to simplify the expression step by step.

Step 1: Simplify the denominator of the fraction inside the parentheses. - 3/16 + 5/24 = (9/48 + 10/48) = 19/48

Step 2: Divide the numerator by the denominator. - 19/24 ÷ (19/48) = (19/24) * (48/19) = 48/24 = 2

Therefore, the solution to problem 6 is 2.

I hope this helps! Let me know if you have any further questions.