Math worksheet for converting mixed numbers and improper fractions, with practice problems and an extension activity.

Let’s solve each part step by step.

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Section A: Change mixed numbers to improper fractions, and improper fractions to mixed numbers.

We’ll go one by one.

1) 9/5 → This is an improper fraction. Divide 9 by 5:
5 goes into 9 once (5×1=5), remainder 4.
So, 9/5 = 1 4/5

2) 14/3 → Divide 14 by 3:
3×4=12, remainder 2 → 14/3 = 4 2/3

3) 16/5 → 5×3=15, remainder 1 → 16/5 = 3 1/5

4) 27/7 → 7×3=21, remainder 6 → 27/7 = 3 6/7

5) 4 2/9 → Mixed number to improper:
Multiply whole number by denominator: 4×9=36, add numerator: 36+2=38 → 38/9

6) 7 1/8 → 7×8=56 +1 =57 → 57/8

7) 3 2/11 → 3×11=33 +2=35 → 35/11

8) 2 3/20 → 2×20=40 +3=43 → 43/20

9) 8 7/12 → 8×12=96 +7=103 → 103/12

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Section B: Simplify your answers where possible.

This means convert between mixed/improper AND simplify the fraction part if needed.

1) 1 3/9 → First, simplify 3/9 = 1/3 → So answer is 1 1/3

2) 6 2/12 → Simplify 2/12 = 1/6 → 6 1/6

3) 8 3/15 → Simplify 3/15 = 1/5 → 8 1/5

4) 10 12/26 → Simplify 12/26: divide top and bottom by 2 → 6/13 → 10 6/13

5) 14/4 → Improper fraction. 14÷4 = 3 with remainder 2 → 3 2/4 → simplify 2/4 = 1/2 → 3 1/2

6) 24/15 → 24÷15 = 1 with remainder 9 → 1 9/15 → simplify 9/15 = 3/5 → 1 3/5

7) 32/12 → 32÷12 = 2 with remainder 8 → 2 8/12 → simplify 8/12 = 2/3 → 2 2/3

8) 81/18 → 81÷18 = 4 with remainder 9 → 4 9/18 → simplify 9/18 = 1/2 → 4 1/2

9) 112/35 → 112÷35 = 3 with remainder 7 → 3 7/35 → simplify 7/35 = 1/5 → 3 1/5

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Extension: Write decimals and percentages as mixed numbers and improper fractions. Simplify.

Remember:
- Decimal → write as fraction over 10, 100, etc., then simplify.
- Percent → write over 100, then simplify.

1) 2.08
→ As fraction: 208/100
→ Simplify: divide numerator and denominator by 4 → 52/25
→ Improper fraction: 52/25
→ Mixed number: 52 ÷ 25 = 2 with remainder 2 → 2 2/25

2) 160%
→ 160/100 = 16/10 = 8/5 (simplified)
→ Improper fraction: 8/5
→ Mixed number: 8÷5 = 1 rem 3 → 1 3/5

3) 112.5%
→ 112.5 / 100 = 1125 / 1000 (multiply top and bottom by 10 to remove decimal)
→ Simplify: divide numerator and denominator by 125 → 9/8
→ Improper fraction: 9/8
→ Mixed number: 9÷8 = 1 rem 1 → 1 1/8

Wait — let me double-check 112.5%:

112.5% = 112.5 / 100 = 1.125
As fraction: 1125/1000
Divide numerator and denominator by 125:
1125 ÷ 125 = 9
1000 ÷ 125 = 8
So yes, 9/8 or 1 1/8

But wait — 112.5% is more than 100%, so it should be greater than 1. Correct.

Actually, let me check again:
112.5% = 112.5 / 100 = 1.125
1.125 = 1 + 0.125 = 1 + 1/8 = 1 1/8 → correct.

Improper fraction: 9/8 → correct.

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Now, compiling all final answers clearly.

Final Answer:

Section A:
1) 1 4/5
2) 4 2/3
3) 3 1/5
4) 3 6/7
5) 38/9
6) 57/8
7) 35/11
8) 43/20
9) 103/12

Section B:
1) 1 1/3
2) 6 1/6
3) 8 1/5
4) 10 6/13
5) 3 1/2
6) 1 3/5
7) 2 2/3
8) 4 1/2
9) 3 1/5

Extension Table:

| | Mixed Number | Improper Fraction |
|----------|--------------|-------------------|
| 2.08 | 2 2/25 | 52/25 |
| 160% | 1 3/5 | 8/5 |
| 112.5% | 1 1/8 | 9/8 |