Grade 4 Maths Resources (2.6.2 Multiplying Improper Fractions ... - Free Printable

Let's solve each problem on the worksheet step by step. We are multiplying improper fractions and simplifying where possible.

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1. $ \frac{4}{3} \times \frac{15}{7} $

Multiply numerators: $ 4 \times 15 = 60 $
Multiply denominators: $ 3 \times 7 = 21 $
So, $ \frac{60}{21} $

Now simplify:
Both divisible by 3 → $ \frac{60 \div 3}{21 \div 3} = \frac{20}{7} $

✔ Answer: $ \frac{20}{7} $ (or $ 2\frac{6}{7} $)

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2. $ \frac{4}{5} \times \frac{12}{8} $

First, simplify $ \frac{12}{8} = \frac{3}{2} $

Now: $ \frac{4}{5} \times \frac{3}{2} $

Numerator: $ 4 \times 3 = 12 $
Denominator: $ 5 \times 2 = 10 $ → $ \frac{12}{10} $

Simplify: divide numerator and denominator by 2 → $ \frac{6}{5} $

✔ Answer: $ \frac{6}{5} $ (or $ 1\frac{1}{5} $)

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3. $ \frac{7}{5} \times \frac{30}{21} $

Simplify $ \frac{30}{21} = \frac{10}{7} $ (divide numerator and denominator by 3)

Now: $ \frac{7}{5} \times \frac{10}{7} $

Cancel common factors:
- 7 in numerator and denominator → cancel
- 10 and 5 → 10 ÷ 5 = 2

So: $ \frac{1}{5} \times \frac{10}{1} = \frac{10}{5} = 2 $

✔ Answer: $ 2 $

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4. $ \frac{24}{13} \times \frac{9}{8} $

Multiply: $ \frac{24 \times 9}{13 \times 8} = \frac{216}{104} $

Simplify:
- Divide numerator and denominator by 8:
$ 216 \div 8 = 27 $, $ 104 \div 8 = 13 $ → $ \frac{27}{13} $

✔ Answer: $ \frac{27}{13} $ (or $ 2\frac{1}{13} $)

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5. $ \frac{9}{8} \times \frac{28}{7} $

Simplify $ \frac{28}{7} = 4 $

Now: $ \frac{9}{8} \times 4 = \frac{9 \times 4}{8} = \frac{36}{8} $

Simplify: divide by 4 → $ \frac{9}{2} $

✔ Answer: $ \frac{9}{2} $ (or $ 4\frac{1}{2} $)

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6. $ \frac{17}{6} \times \frac{30}{12} $

Simplify $ \frac{30}{12} = \frac{5}{2} $

Now: $ \frac{17}{6} \times \frac{5}{2} = \frac{85}{12} $

This is already simplified.

✔ Answer: $ \frac{85}{12} $ (or $ 7\frac{1}{12} $)

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7. $ \frac{11}{9} \times \frac{50}{33} $

Look for common factors:
- 11 and 33 → 33 ÷ 11 = 3 → cancel 11 with 33 → becomes 1 and 3
- 9 and 50 → no common factor
- 50 and 9 → no

So: $ \frac{11}{9} \times \frac{50}{33} = \frac{1}{9} \times \frac{50}{3} = \frac{50}{27} $

✔ Answer: $ \frac{50}{27} $ (or $ 1\frac{23}{27} $)

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8. $ \frac{7}{6} \times \frac{18}{5} $

Look for simplifications:
- 7 and 5 → no
- 6 and 18 → 18 ÷ 6 = 3 → so 6 cancels with 18 → 1 and 3

So: $ \frac{7}{1} \times \frac{3}{5} = \frac{21}{5} $

✔ Answer: $ \frac{21}{5} $ (or $ 4\frac{1}{5} $)

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9. $ \frac{16}{7} \times \frac{25}{32} $

Look for simplifications:
- 16 and 32 → 32 ÷ 16 = 2 → so 16/32 = 1/2

So: $ \frac{1}{7} \times \frac{25}{2} = \frac{25}{14} $

✔ Answer: $ \frac{25}{14} $ (or $ 1\frac{11}{14} $)

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10. $ \frac{9}{4} \times \frac{8}{3} $

Simplify:
- 9 and 3 → 9 ÷ 3 = 3
- 8 and 4 → 8 ÷ 4 = 2

So: $ \frac{3}{1} \times \frac{2}{1} = 6 $

✔ Answer: $ 6 $

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✔ Final Answers:

1. $ \frac{20}{7} $
2. $ \frac{6}{5} $
3. $ 2 $
4. $ \frac{27}{13} $
5. $ \frac{9}{2} $
6. $ \frac{85}{12} $
7. $ \frac{50}{27} $
8. $ \frac{21}{5} $
9. $ \frac{25}{14} $
10. $ 6 $

Let me know if you'd like these as mixed numbers or want a printable version!