Question

3/4 : 2/3, 1/3 : (3/4+2/3), (1/3+1/2):(3/7-2/5) 8 12/15+ 5 8/10, 4/15+4/8+4/7+31/56, 1/9+3/16+3/9-2/9 3/8 :7/16, 4/31:7/8

Answer 1

3/4+2/3=1 5/12

3/5-1/3=4/15

3/4-2/3=1/12

3/4+2/14=1/2

1/4-1/6=1/12

3/5+1/3=14/15

4/5+3/4=1 11/20

7/10-1/4= 9/20

Answer 2

To simplify the given expressions, let's perform the calculations step by step:

1. 3/4 : 2/3 To divide fractions, we multiply the first fraction by the reciprocal of the second fraction: (3/4) ÷ (2/3) = (3/4) * (3/2) = 9/8

2. 1/3 : (3/4 + 2/3) To divide by a complex fraction, we multiply by the reciprocal of the entire complex fraction: (1/3) ÷ ((3/4) + (2/3)) = (1/3) * (1 / ((3/4) + (2/3)))

To add the fractions in the denominator, we need a common denominator, which is 12. So: (1/3) ÷ ((3/4) + (2/3)) = (1/3) * (1 / ((9/12) + (8/12))) = (1/3) * (1 / (17/12))

Now, to divide by a fraction, we multiply by its reciprocal: (1/3) ÷ ((3/4) + (2/3)) = (1/3) * (12/17) = 4/17

3. (1/3 + 1/2) : (3/7 - 2/5) Again, we need a common denominator to perform the calculations: (1/3 + 1/2) : (3/7 - 2/5) = ((5/15) + (7/15)) : ((15/35) - (14/35)) = (12/15) : (1/35)

To divide by a fraction, we multiply by its reciprocal: (1/3 + 1/2) : (3/7 - 2/5) = (12/15) * (35/1) = 12 * 35 = 420

4. 8 12/15 + 5 8/10 To add mixed numbers, first convert them to improper fractions: 8 12/15 = (8 * 15 + 12) / 15 = 132/15 5 8/10 = (5 * 10 + 8) / 10 = 58/10

Now, add the improper fractions: 8 12/15 + 5 8/10 = 132/15 + 58/10

To add fractions, we need a common denominator, which is 30. So: 8 12/15 + 5 8/10 = (132/15) + (174/30)

Now, add the fractions: 8 12/15 + 5 8/10 = (132/15) + (174/30) = (264/30) + (174/30) = 438/30

Reduce the fraction to its simplest form: 8 12/15 + 5 8/10 = 438/30 = 73/5

5. 4/15 + 4/8 + 4/7 + 31/56 To add fractions, we need a common denominator, which is 840. So: 4/15 + 4/8 + 4/7 + 31/56 = (224/840) + (420/840) + (480/840) + (465/840)

Now, add the fractions: 4/15 + 4/8 + 4/7 + 31/56 = (224/840) + (420/840) + (480/840) + (465/840) = 1589/840

6. 1/9 + 3/16 + 3/9 - 2/9 To add and subtract fractions, we need a common denominator, which is 144. So: 1/9 + 3/16 + 3/9 - 2/9 = (16/144) + (27/144) + (48/144) - (32/144)

Now, add and subtract the fractions: 1/9 + 3/16 + 3/9 - 2/9 = (16/144) + (27/144) + (48/144) - (32/144) = 59/144

7. 3/8 : 7/16 To divide fractions, we multiply the first fraction by the reciprocal of the second fraction: (3/8) ÷ (7/16) = (3/8) * (16/7) = 48/56 = 12/14 = 6/7

8. 4/31 : 7/8 To divide fractions, we multiply the first fraction by the reciprocal of the second fraction: (4/31) ÷ (7/8) = (4/31) * (8/7) = 32/217

So, the simplified expressions are:

1. 3/4 : 2/3 = 9/8
2. 1/3 : (3/4 + 2/3) = 4/17
3. (1/3 + 1/2) : (3/7 - 2/5) = 420
4. 8 12/15 + 5 8/10 = 73/5
5. 4/15 + 4/8 + 4/7 + 31/56 = 1589/840
6. 1/9 + 3/16 + 3/9 - 2/9 = 59/144
7. 3/8 : 7/16 = 6/7
8. 4/31 : 7/8 = 32/217