Question

(3 3/4*3/5-7 1/2:27+1 2/9):(3 1/61-1 1/4)

Answer 1

Ответ:

(3 3/4*3/5-7 1/2:27+1 2/9):(3 1/6-1 1/4) = 8/9

1) 3 3/4 • 3/5 = 15/4 • 3/5 = 3/4 • 3/1 = 6/4 = 3/2 = 1 1/2 = 1,5

2) 7 1/2 : 27 = 15/2 • 1/27 = 5/2 • 1/9 = 5/18

3) 1,5 - 5/18 = 1 1/2 - 5/18 = 1 9/18 - 5/18 = 1 4/18 = 1 2/9

4) 1 2/9 + 1 2/9 = 2 4/9

5) 3 1/6 - 1 1/4 = 3 2/12 - 1 3/12 = 1 11/12

6) 2 4/9 : 1 11/12 = 22/9 • 12/33 = 2/3 • 4/3 = 8/9

Answer 2

To solve the expression, let's break it down step by step:

Step 1: Simplify the expression within the first set of parentheses: 3 3/4 * 3/5 - 7 1/2 ÷ 27 + 1 2/9

To simplify this, we need to convert the mixed numbers to improper fractions.

3 3/4 = (4 * 3 + 3)/4 = 15/4 7 1/2 = (2 * 7 + 1)/2 = 15/2 1 2/9 = (9 * 1 + 2)/9 = 11/9

Now we can rewrite the expression: (15/4 * 3/5 - 15/2 ÷ 27 + 11/9) ÷ (3 1/61 - 1 1/4)

Step 2: Simplify the expression within the second set of parentheses: 3 1/61 = (61 * 3 + 1)/61 = 184/61 1 1/4 = (4 * 1 + 1)/4 = 5/4

Now we can rewrite the expression: (15/4 * 3/5 - 15/2 ÷ 27 + 11/9) ÷ (184/61 - 5/4)

Step 3: Perform the multiplication and division operations within the first set of parentheses: 15/4 * 3/5 = (15 * 3)/(4 * 5) = 45/20 = 9/4 15/2 ÷ 27 = (15/2)/(27/1) = (15/2) * (1/27) = 15/54 = 5/18

Now the expression becomes: (9/4 - 5/18 + 11/9) ÷ (184/61 - 5/4)

Step 4: Perform the addition and subtraction operations within the first set of parentheses: 9/4 - 5/18 = (81/36 - 10/36) = 71/36

Now the expression becomes: (71/36 + 11/9) ÷ (184/61 - 5/4)

Step 5: Perform the addition and subtraction operations within the second set of parentheses: 184/61 - 5/4 = (736/244 - 305/244) = 431/244

Now the expression becomes: (71/36 + 11/9) ÷ (431/244)

Step 6: Perform the division operation: (71/36 + 11/9) ÷ (431/244) = [(71/36 + 44/36)] / (431/244) = 115/36 ÷ (431/244)

To divide by a fraction, we multiply by its reciprocal: 115/36 ÷ (431/244) = 115/36 * (244/431) = (115 * 244) / (36 * 431) = 28060/15516 = 1420/779

Therefore, the simplified value of the expression is 1420/779.