Practice worksheet for converting between improper fractions and mixed numbers.

Let’s solve each problem step by step.

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Part A: Convert improper fractions to mixed numbers

An improper fraction has a numerator bigger than the denominator. To turn it into a mixed number, divide the top by the bottom. The answer is the whole number, and the remainder becomes the new numerator over the same denominator.

1) 9 ÷ 5 = 1 with remainder 4 → 1 4/5

2) 53 ÷ 12 = 4 (because 12×4=48), remainder 5 → 4 5/12

3) 10 ÷ 3 = 3 (3×3=9), remainder 1 → 3 1/3

4) 8 ÷ 7 = 1 (7×1=7), remainder 1 → 1 1/7

5) 65 ÷ 11 = 5 (11×5=55), remainder 10 → 5 10/11

6) 31 ÷ 4 = 7 (4×7=28), remainder 3 → 7 3/4

7) 29 ÷ 6 = 4 (6×4=24), remainder 5 → 4 5/6

8) 74 ÷ 9 = 8 (9×8=72), remainder 2 → 8 2/9

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Part B: Convert mixed numbers to improper fractions

A mixed number has a whole number and a fraction. To make it an improper fraction:

Multiply the whole number by the denominator, then add the numerator. Put that result over the original denominator.

1) 9 3/10 → (9 × 10) + 3 = 90 + 3 = 93 → 93/10

2) 7 1/2 → (7 × 2) + 1 = 14 + 1 = 15 → 15/2

3) 1 1/6 → (1 × 6) + 1 = 6 + 1 = 7 → 7/6

4) 2 6/11 → (2 × 11) + 6 = 22 + 6 = 28 → 28/11

5) 4 5/8 → (4 × 8) + 5 = 32 + 5 = 37 → 37/8

6) 1 3/5 → (1 × 5) + 3 = 5 + 3 = 8 → 8/5

7) 6 2/7 → (6 × 7) + 2 = 42 + 2 = 44 → 44/7

8) 5 8/9 → (5 × 9) + 8 = 45 + 8 = 53 → 53/9

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Final Answer:

Part A:
1) 1 4/5
2) 4 5/12
3) 3 1/3
4) 1 1/7
5) 5 10/11
6) 7 3/4
7) 4 5/6
8) 8 2/9

Part B:
1) 93/10
2) 15/2
3) 7/6
4) 28/11
5) 37/8
6) 8/5
7) 44/7
8) 53/9