Question

5 4/45-4 1/6):5 8/15×34 2/7+0,3:0,01+2/7---------------------------------4 2/3+0,75)×9/13​

Answer 1

((5 4/45 - 4 1/6) : 5 8/15) /((4 2/3 + 0,75) * 3 9/13) * 34 2/7 + (0,3 : 0,01)/70 + 2/7
1) 5 4/45 - 4 1/6 = 229/45 - 25/6 = (229 * 2)/90 - (25 * 15)/90 = (458 - 375)/90 = 83/90;
2) 83/90 : 5 8/15 = 83/90 : 83/15 = 83/90 * 15/83 = 15/90 = 1/6;
3) 4 2/3 + 0,75 = 14/3 + 75/100 = 14/3 + 3/4 = (14 * 4 + 3 * 3)/12 = (56 + 9)/12 = 65/12;
4) 65/12 * 3 9/13 = 65/12 * 48/13 = 20;
5) 1/6 : 20 = 1/120;
6) 0,3 : 0,01 = 30;
7) 30 : 70 = 3/7;
8) 1/120 * 34 2/7 = 1/120 + 240/7 = 2/7;
9) 2/7 + 3/7 + 2/7 = 7/7 = 1.

Answer 2

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

Step 1: Perform the operations inside the parentheses. 5 4/45 - 4 1/6 = 5 + 4/45 - 4 - 1/6 = 5 - 4 - 1/6 + 4/45 = 1 - 1/6 + 4/45 (converted 5 to 1 to make the fractions similar)

Step 2: Find a common denominator for 1 and 6 and add the fractions. Common denominator for 1 and 6 is 6. 1 - 1/6 = 6/6 - 1/6 = 5/6

Step 3: Find a common denominator for 5/6 and 4/45 and add the fractions. Common denominator for 6 and 45 is 90. (5/6) + (4/45) = (75/90) + (8/90) = 83/90

Step 4: Perform the next operation inside the parentheses. 5 8/15 × 34 2/7 = 5 + 8/15 × 34 + 2/7 = 5 + 8/15 × 34 + 2/7 = 5 + (272/15) + (30/7)

Step 5: Find a common denominator for 15 and 7 and add the fractions. Common denominator for 15 and 7 is 105. (272/15) + (30/7) = (1824/105) + (450/105) = 2274/105

Step 6: Perform the next operation inside the parentheses. 0.3 ÷ 0.01 = 0.3 / 0.01 = 30

Step 7: Perform the next operation inside the parentheses. 4 2/3 + 0.75 = 4 + 2/3 + 0.75 = 4 + 8/12 + 9/12 = 4 + 17/12

Step 8: Perform the next operation: (4 + 17/12) × 9/13 Convert 4 to a fraction with the same denominator as 12: 4 = 48/12 (48/12 + 17/12) × 9/13 = (65/12) × 9/13 = 585/156

Step 9: Perform the final operation: (83/90) × (2274/105) + 30 ÷ 2/7 × (585/156) First, perform the multiplications and divisions: (83/90) × (2274/105) ≈ 1.89212121 (rounded to 8 decimal places)

Now, convert 30 to a fraction with 7 as the denominator: 30 = 210/7

Now, perform the final operation: 1.89212121 + 210/7 × (585/156) Convert 210 to a fraction with the same denominator as 156: 210 = 27360/130 1.89212121 + 27360/130 × (585/156) = 1.89212121 + 16037500/20280 ≈ 1.89212121 + 791.39112903

The final result is approximately: 1.89212121 + 791.39112903 ≈ 793.28325024.