Question

А) (7/15 + 7 / 30 + 4 / 5): (2 - 1/3 - 1/2) Б) 17: (3/ 5 + 1 / 4 )+ (7/ 8 - 1 / 4 )х( 4/5)

Answer 1

Ответ:

Пошаговое объяснение:

а)7/15 + 7 / 30 + 4 / 5=14/30+7/30+24/30=45/30

2 - 1/3 - 1/2=2-2/6-3/6=1/6

45/30:1/6=45/30*6=45/5=9

б)3/ 5 + 1 / 4=12/20+5/20=17/20

17:17/20=17*20/17=20

7/8-1/4=7/8-2/8=5/8

5/8*4/5=1/2

20+1/2=20 1/2

Answer 2

Let's solve each expression step by step:

А) (7/15 + 7/30 + 4/5) / (2 - 1/3 - 1/2)

Step 1: Find common denominators for fractions in the numerator. The common denominator for 15, 30, and 5 is 30.

Step 2: Convert each fraction in the numerator to have a denominator of 30. (7/15) * (2/2) = 14/30 (7/30) * (1/1) = 7/30 (4/5) * (6/6) = 24/30

Now, the expression becomes: (14/30 + 7/30 + 24/30) / (2 - 1/3 - 1/2)

Step 3: Combine the fractions in the numerator. (14/30 + 7/30 + 24/30) = 45/30

The expression now becomes: 45/30 / (2 - 1/3 - 1/2)

Step 4: Find common denominators for the fractions in the denominator. The common denominator for 1, 3, and 2 is 6.

Step 5: Convert each fraction in the denominator to have a denominator of 6. (2/1) * (3/3) = 6/3 (1/3) * (2/2) = 2/6 (1/2) * (3/3) = 3/6

Now, the expression becomes: 45/30 / (6/3 - 2/6 - 3/6)

Step 6: Combine the fractions in the denominator. (6/3 - 2/6 - 3/6) = (6/3 - 5/6) = (12/6 - 5/6) = 7/6

The final expression is: (45/30) / (7/6)

Step 7: Divide the fractions. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. (45/30) / (7/6) = (45/30) * (6/7)

Step 8: Simplify the result. (45/30) * (6/7) = (3/2) * (6/7) = 18/14 = 9/7

So, the result of expression А is 9/7.

Б) 17 / (3/5 + 1/4) + (7/8 - 1/4) * (4/5)

Step 1: Find common denominators for fractions in the brackets. The common denominator for 5 and 4 is 20.

Step 2: Convert each fraction in the brackets to have a denominator of 20. (3/5) * (4/4) = 12/20 (1/4) * (5/5) = 5/20

Now, the expression becomes: 17 / (12/20 + 5/20) + (7/8 - 5/20) * (4/5)

Step 3: Combine the fractions in the brackets. (12/20 + 5/20) = 17/20 (7/8 - 5/20) = (35/40 - 5/20) = 30/40 = 3/4

The expression now becomes: 17 / (17/20) + (3/4) * (4/5)

Step 4: Divide the fractions in the first term. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. 17 / (17/20) = 17 * (20/17) = 20

Step 5: Multiply the fractions in the second term. (3/4) * (4/5) = 12/20 = 3/5

The final expression is: 20 + 3/5

Step 6: Convert the whole number 20 to a fraction with a denominator of 5. 20 = 20/1

Now, the expression becomes: 20/1 + 3/5

Step 7: Find a common denominator for both fractions (1 and 5 have a common denominator of 5). 20/1 + 3/5 = 100/5 + 3/5

Step 8: Combine the fractions. 100/5 + 3/5 = 103/5

So, the result of expression Б is 103/5.