Question

(3 2/5-1 3/4)* 3 1/3+ 3/7 : 3 3/7+ 1/2 (4 7/9- 2 5/6):1 5/9+4/9*6 3/16+1/8

Answer 1

Ответ:

Пошаговое объяснение:

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

1) 3 2/5 - 1 3/4 = 3 8/20 - 1 15/20 = 1 13/20

2) 1 13/20 * 3 1/3 = 33/20 * 10/3 = 11/2 = 5 1/2

3) 3/7 : 3 3/7 = 3/7 * 7/24 = 1/8

4) 5 1/2 + 1/8 = 5 4/8 + 1/8 = 5 5/8

5) 5 5/8 + 1/2 = 5 5/8 + 4/8 = 5 9/8 = 6 1/8

(4 7/9- 2 5/6):1 5/9+4/9*6 3/16+1/8 = 4 1/8

1) 4 7/9 - 2 5/6 = 4 14/18 - 2 15/18 = 1 17/18

2) 1 17/18 : 1 5/9 = 35/18 * 9/14 = 35/28 = 1 7/28 = 1 1/4

3) 4/9 * 6 3/16 = 4/9 * 99/16 = 11/4 = 2 3/4

4) 1 1/4 + 2 3/4 = 3 4/4 = 4

5) 4 + 1/8 = 4 1/8

Answer 2

To simplify the given expression, let's take it step by step:

Step 1: Perform the operations inside the parentheses first. (3 2/5 - 1 3/4) * 3 1/3 + 3/7 : 3 3/7 + 1/2 * (4 7/9 - 2 5/6) : 1 5/9 + 4/9 * 6 3/16 + 1/8

Step 2: Simplify each operation.

1. (3 2/5 - 1 3/4) = 3.4 - 1.75 = 1.65
2. (4 7/9 - 2 5/6) = 4.777... - 2.833... ≈ 1.944... (rounded to three decimal places)
3. 3 1/3 = 10/3
4. 3 3/7 = 24/7
5. 1 5/9 = 14/9
6. 6 3/16 = 99/16

Step 3: Now we have: 1.65 * 10/3 + 3/7 : 24/7 + 1/2 * 1.944... : 14/9 + 4/9 * 99/16 + 1/8

Step 4: Perform the multiplications and divisions from left to right. 1.65 * 10/3 = 5.5 3/7 : 24/7 = 3/7 * 7/24 = 1/8 1/2 * 1.944... ≈ 0.972... (rounded to three decimal places) 4/9 * 99/16 = 11/4 5.5 + 1/8 + 0.972... : 14/9 + 11/4 + 1/8

Step 5: Convert all fractions to a common denominator (72) to combine them. 1/8 = 9/72 14/9 = 112/72

Now we have: 5.5 + 9/72 + 0.972... : 112/72 + 11/4 + 9/72

Step 6: Add and subtract the fractions: 0.972... ≈ 35/36 (rounded to three decimal places)

5.5 + 35/36 : 112/72 + 11/4 + 9/72

Step 7: Convert the whole numbers to fractions with a common denominator (72). 5.5 = 396/72 11/4 = 198/72

Now we have: 396/72 + 35/36 : 112/72 + 198/72 + 9/72

Step 8: Combine the fractions: 396/72 + 35/36 = (396*2 + 35)/72 = 827/72

Now we have: 827/72 : 112/72 + 198/72 + 9/72

Step 9: Perform the division: 827/72 : 112/72 = 827/72 * 72/112 = 827/112

Now we have: 827/112 + 198/72 + 9/72

Step 10: Combine the fractions: 827/112 + 198/72 + 9/72 = 827/112 + (198 + 9)/72 = 827/112 + 207/72

Step 11: Convert the whole number to a fraction with a common denominator (112). 207/72 = 161/112

Now we have: 827/112 + 161/112

Step 12: Combine the fractions: 827/112 + 161/112 = (827 + 161)/112 = 988/112

Step 13: Reduce the fraction to its simplest form (if possible): 988/112 = 247/28

The simplified result of the expression is 247/28.