Multiplication and Division of Fractions worksheet with 12 problems for practice.

Let’s solve each problem one by one, step by step. We’ll use simple rules:

- For multiplication: Multiply numerators together, multiply denominators together. Then simplify if needed.
- For division: Flip the second fraction (that’s called “reciprocal”), then multiply.

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Problem 1: 2/6 × 15/13

Step 1: Multiply numerators → 2 × 15 = 30
Step 2: Multiply denominators → 6 × 13 = 78
→ So we have 30/78

Step 3: Simplify. Both divisible by 6?
30 ÷ 6 = 5
78 ÷ 6 = 13
✔ Final: 5/13

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Problem 2: 10/24 ÷ 36/40

Step 1: Flip the second fraction → 40/36
Now it’s: 10/24 × 40/36

Step 2: Multiply numerators → 10 × 40 = 400
Multiply denominators → 24 × 36 = 864
→ 400/864

Step 3: Simplify. Let’s divide numerator and denominator by 16:
400 ÷ 16 = 25
864 ÷ 16 = 54
✔ Final: 25/54

*(Check: 16×25=400, 16×54=864 — yes!)*

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Problem 3: 9/10 × 21/63

Step 1: Multiply numerators → 9 × 21 = 189
Multiply denominators → 10 × 63 = 630
→ 189/630

Step 2: Simplify. Both divisible by 63?
189 ÷ 63 = 3
630 ÷ 63 = 10
✔ Final: 3/10

*(Or simplify earlier: 9/63 = 1/7, so 1/10 × 21/7 = 21/70 = 3/10 — same result)*

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Problem 4: 4/3 ÷ 20/27

Step 1: Flip second fraction → 27/20
Now: 4/3 × 27/20

Step 2: Multiply numerators → 4 × 27 = 108
Multiply denominators → 3 × 20 = 60
→ 108/60

Step 3: Simplify. Divide by 12:
108 ÷ 12 = 9
60 ÷ 12 = 5
✔ Final: 9/5 or 1 4/5

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Problem 5: 14/33 ÷ 56/99

Step 1: Flip second → 99/56
Now: 14/33 × 99/56

Step 2: Multiply numerators → 14 × 99 = 1386
Multiply denominators → 33 × 56 = 1848
→ 1386/1848

Step 3: Simplify. Let’s divide both by 462?
Wait — better to cancel before multiplying.

Notice:
14 and 56 → 14÷14=1, 56÷14=4
99 and 33 → 99÷33=3, 33÷33=1

So: (14/33) × (99/56) = (1/1) × (3/4) = 3/4

✔ Final: 3/4

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Problem 6: 8/3 × 14/64

Step 1: Multiply numerators → 8 × 14 = 112
Multiply denominators → 3 × 64 = 192
→ 112/192

Step 2: Simplify. Divide by 16:
112 ÷ 16 = 7
192 ÷ 16 = 12
✔ Final: 7/12

*(Or cancel first: 8/64 = 1/8, so 1/3 × 14/8 = 14/24 = 7/12 — same)*

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Problem 7: 20/3 × 11/9

Step 1: Multiply numerators → 20 × 11 = 220
Multiply denominators → 3 × 9 = 27
→ 220/27

This is already simplified. As mixed number: 27×8=216, remainder 4 → 8 4/27

But since question doesn’t specify, leave as improper fraction.

✔ Final: 220/27

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Problem 8: 3/9 × 7/14

Step 1: Simplify first fractions:
3/9 = 1/3
7/14 = 1/2

Now: 1/3 × 1/2 = 1/6

✔ Final: 1/6

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Problem 9: 5/3 ÷ 2/8

Step 1: Flip second → 8/2 = 4 (but let’s keep as fraction for now)
So: 5/3 × 8/2

Step 2: Multiply → 5×8 = 40, 3×2 = 6 → 40/6

Step 3: Simplify → divide by 2 → 20/3

✔ Final: 20/3 or 6 2/3

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Problem 10: 6/4 ÷ 9/15

Step 1: Flip second → 15/9
Now: 6/4 × 15/9

Step 2: Simplify first: 6/4 = 3/2
15/9 = 5/3

Now: 3/2 × 5/3 = (3×5)/(2×3) = 15/6

Step 3: Simplify → divide by 3 → 5/2

✔ Final: 5/2 or 2 1/2

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Problem 11: 17/12 ÷ 8/16

Step 1: Flip second → 16/8 = 2
So: 17/12 × 2/1 = 34/12

Step 2: Simplify → divide by 2 → 17/6

✔ Final: 17/6 or 2 5/6

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Problem 12: 5/6 × 21/5

Step 1: Notice 5 in numerator and denominator → cancel them
Left with: 1/6 × 21/1 = 21/6

Step 2: Simplify → divide by 3 → 7/2

✔ Final: 7/2 or 3 1/2

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Final Answers:

1. 5/13
2. 25/54
3. 3/10
4. 9/5
5. 3/4
6. 7/12
7. 220/27
8. 1/6
9. 20/3
10. 5/2
11. 17/6
12. 7/2

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Final Answer:
1. $\frac{5}{13}$
2. $\frac{25}{54}$
3. $\frac{3}{10}$
4. $\frac{9}{5}$
5. $\frac{3}{4}$
6. $\frac{7}{12}$
7. $\frac{220}{27}$
8. $\frac{1}{6}$
9. $\frac{20}{3}$
10. $\frac{5}{2}$
11. $\frac{17}{6}$
12. $\frac{7}{2}$