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

1)42/11
2)10/19
3)19/34
4)17/36
5)4
6)1/24

Answer 2

1) (2/7 + 5/21) ÷ (1 + 4/7)

To solve this expression, we need to perform the addition and division operations in the correct order of operations.

First, let's simplify the addition inside the parentheses: 2/7 + 5/21 = (6/21 + 5/21) = 11/21

Now, let's simplify the division: (11/21) ÷ (1 + 4/7)

To simplify the division, we need to convert the mixed number 1 + 4/7 into an improper fraction: 1 + 4/7 = (7/7 + 4/7) = 11/7

Now, we can rewrite the expression as: (11/21) ÷ (11/7)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction: (11/21) ÷ (11/7) = (11/21) * (7/11)

Now, we can cancel out the common factors of 11: (11/21) * (7/11) = (1/3) * (1/1) = 1/3

Therefore, the solution to the expression (2/7 + 5/21) ÷ (1 + 4/7) is 1/3.

2) (8/11 + 3/22) ÷ (5/11)

To solve this expression, we need to perform the addition and division operations in the correct order of operations.

First, let's simplify the addition inside the parentheses: 8/11 + 3/22 = (16/22 + 3/22) = 19/22

Now, let's simplify the division: (19/22) ÷ (5/11)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction: (19/22) ÷ (5/11) = (19/22) * (11/5)

Now, we can cancel out the common factors: (19/22) * (11/5) = (19/2) * (1/1) = 19/2 = 9 1/2

Therefore, the solution to the expression (8/11 + 3/22) ÷ (5/11) is 9 1/2.

3) 1 + 7/12 ÷ (3/8 + 5/12)

To solve this expression, we need to perform the addition and division operations in the correct order of operations.

First, let's simplify the addition inside the parentheses: 3/8 + 5/12 = (9/24 + 10/24) = 19/24

Now, let's simplify the division: 7/12 ÷ 19/24

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction: 7/12 ÷ 19/24 = (7/12) * (24/19)

Now, we can cancel out the common factors: (7/12) * (24/19) = (7/1) * (2/1) = 14/19

Finally, let's add 1 to the result: 1 + 14/19 = (19/19) + (14/19) = 33/19 = 1 14/19

Therefore, the solution to the expression 1 + 7/12 ÷ (3/8 + 5/12) is 1 14/19.

4) 17/36 ÷ (7/12 - 5/9)

To solve this expression, we need to perform the subtraction and division operations in the correct order of operations.

First, let's simplify the subtraction inside the parentheses: 7/12 - 5/9

To subtract fractions, we need a common denominator. The least common multiple of 12 and 9 is 36. Let's convert the fractions: 7/12 - 5/9 = (21/36) - (20/36) = 1/36

Now, let's simplify the division: 17/36 ÷ 1/36

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction: 17/36 ÷ 1/36 = (17/36) * (36/1) = 17/1 = 17

Therefore, the solution to the expression 17/36 ÷ (7/12 - 5/9) is 17.

5) (3/14 + 5/7) ÷ (3 + 5/7)

To solve this expression, we need to perform the addition and division operations in the correct order of operations.

First, let's simplify the addition inside the parentheses: 3/14 + 5/7 = (3/14 + 10/14) = 13/14

Now, let's simplify the division: (13/14) ÷ (3 + 5/7)

To simplify the division, we need to convert the mixed number 3 + 5/7 into an improper fraction: 3 + 5/7 = (21/7 + 5/7) = 26/7

Now, we can rewrite the expression as: (13/14) ÷ (26/7)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction: (13/14) ÷ (26/7) = (13/14) * (7/26)

Now, we can cancel out the common factors: (13/14) * (7/26) = (1/2) * (1/1) = 1/2

Therefore, the solution to the expression (3/14 + 5/7) ÷ (3 + 5/7) is 1/2.

6) 19/24 ÷ (3/16 + 5/24)

To solve this expression, we need to perform the addition and division operations in the correct order of operations.

First, let's simplify the addition inside the parentheses: 3/16 + 5/24 = (9/48 + 10/48) = 19/48

Now, let's simplify the division: 19/24 ÷ 19/48

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction: 19/24 ÷ 19/48 = (19/24) * (48/19)

Now, we can cancel out the common factors: (19/24) * (48/19) = (1/2) * (2/1) = 1/1 = 1

Therefore, the solution to the expression 19/24 ÷ (3/16 + 5/24) is 1.