Year 6 Maths Worksheets - ThriveTutors | Online Tutoring Platform - Free Printable

Absolutely! Let’s solve all the multiplication and division problems step by step. We’ll convert mixed numbers to improper fractions, multiply or divide as needed, simplify, and convert back to mixed numbers if required.

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## ✔ Multiplication Problems

1. $6 \frac{8}{9} \times 12 \frac{1}{2}$

Convert to improper fractions:
- $6 \frac{8}{9} = \frac{62}{9}$
- $12 \frac{1}{2} = \frac{25}{2}$

Multiply:
$$
\frac{62}{9} \times \frac{25}{2} = \frac{62 \times 25}{9 \times 2} = \frac{1550}{18}
$$

Simplify:
Divide numerator and denominator by 2: $\frac{775}{9}$

Convert to mixed number:
$775 ÷ 9 = 86$ remainder 1 → $\boxed{86 \frac{1}{9}}$

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2. $4 \frac{3}{6} \times 11 \frac{7}{12}$

First, simplify $4 \frac{3}{6} = 4 \frac{1}{2} = \frac{9}{2}$

$11 \frac{7}{12} = \frac{139}{12}$

Multiply:
$$
\frac{9}{2} \times \frac{139}{12} = \frac{1251}{24}
$$

Simplify:
Divide numerator and denominator by 3: $\frac{417}{8}$

Convert to mixed number:
$417 ÷ 8 = 52$ remainder 1 → $\boxed{52 \frac{1}{8}}$

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3. $3 \frac{3}{6} \times 1 \frac{1}{3}$

Simplify: $3 \frac{3}{6} = 3 \frac{1}{2} = \frac{7}{2}$

$1 \frac{1}{3} = \frac{4}{3}$

Multiply:
$$
\frac{7}{2} \times \frac{4}{3} = \frac{28}{6} = \frac{14}{3}
$$

Convert to mixed number: $4 \frac{2}{3}$ → $\boxed{4 \frac{2}{3}}$

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4. $\frac{7}{9} \times 6 \frac{2}{5}$

Convert: $6 \frac{2}{5} = \frac{32}{5}$

Multiply:
$$
\frac{7}{9} \times \frac{32}{5} = \frac{224}{45}
$$

Convert to mixed number: $224 ÷ 45 = 4$ remainder 44 → $\boxed{4 \frac{44}{45}}$

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5. $\frac{4}{5} \times 6 \frac{3}{4}$

Convert: $6 \frac{3}{4} = \frac{27}{4}$

Multiply:
$$
\frac{4}{5} \times \frac{27}{4} = \frac{108}{20} = \frac{27}{5}
$$

Convert to mixed number: $5 \frac{2}{5}$ → $\boxed{5 \frac{2}{5}}$

*(Note: The 4s cancel out: $\frac{\cancel{4}}{5} \times \frac{27}{\cancel{4}} = \frac{27}{5}$)*

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6. $\frac{4}{10} \times 4 \frac{1}{3}$

Simplify $\frac{4}{10} = \frac{2}{5}$

Convert: $4 \frac{1}{3} = \frac{13}{3}$

Multiply:
$$
\frac{2}{5} \times \frac{13}{3} = \frac{26}{15}
$$

Convert to mixed number: $1 \frac{11}{15}$ → $\boxed{1 \frac{11}{15}}$

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7. $\frac{4}{8} \times \frac{43}{7}$

Simplify $\frac{4}{8} = \frac{1}{2}$

Multiply:
$$
\frac{1}{2} \times \frac{43}{7} = \frac{43}{14}
$$

Convert to mixed number: $3 \frac{1}{14}$ → $\boxed{3 \frac{1}{14}}$

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8. $\frac{4}{12} \times \frac{19}{3}$

Simplify $\frac{4}{12} = \frac{1}{3}$

Multiply:
$$
\frac{1}{3} \times \frac{19}{3} = \frac{19}{9}
$$

Convert to mixed number: $2 \frac{1}{9}$ → $\boxed{2 \frac{1}{9}}$

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9. $\frac{2}{5} \times \frac{19}{4}$

Multiply:
$$
\frac{2 \times 19}{5 \times 4} = \frac{38}{20} = \frac{19}{10}
$$

Convert to mixed number: $1 \frac{9}{10}$ → $\boxed{1 \frac{9}{10}}$

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## ✔ Division Problems

Remember: To divide fractions, multiply by the reciprocal.

1. $1 \frac{2}{3} \div 5$

Convert: $1 \frac{2}{3} = \frac{5}{3}$

Divide by 5 = multiply by $\frac{1}{5}$:

$$
\frac{5}{3} \times \frac{1}{5} = \frac{5}{15} = \frac{1}{3}
$$

→ $\boxed{\frac{1}{3}}$

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2. $13 \frac{5}{9} \div 5$

Convert: $13 \frac{5}{9} = \frac{122}{9}$

Divide by 5 = multiply by $\frac{1}{5}$:

$$
\frac{122}{9} \times \frac{1}{5} = \frac{122}{45}
$$

Convert to mixed number: $2 \frac{32}{45}$ → $\boxed{2 \frac{32}{45}}$

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3. $\frac{100}{7} \div 4 \frac{1}{3}$

Convert: $4 \frac{1}{3} = \frac{13}{3}$

Reciprocal is $\frac{3}{13}$

Multiply:
$$
\frac{100}{7} \times \frac{3}{13} = \frac{300}{91}
$$

Convert to mixed number: $3 \frac{27}{91}$ → $\boxed{3 \frac{27}{91}}$

*(Check: 91 × 3 = 273; 300 - 273 = 27)*

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4. $\frac{7}{2} \div 5 \frac{6}{8}$

Simplify $5 \frac{6}{8} = 5 \frac{3}{4} = \frac{23}{4}$

Reciprocal: $\frac{4}{23}$

Multiply:
$$
\frac{7}{2} \times \frac{4}{23} = \frac{28}{46} = \frac{14}{23}
$$

→ $\boxed{\frac{14}{23}}$

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5. $17 \div \frac{9}{5}$

Divide by fraction = multiply by reciprocal: $17 \times \frac{5}{9} = \frac{85}{9}$

Convert to mixed number: $9 \frac{4}{9}$ → $\boxed{9 \frac{4}{9}}$

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6. $13 \div \frac{59}{12}$

Multiply by reciprocal: $13 \times \frac{12}{59} = \frac{156}{59}$

Convert to mixed number: $2 \frac{38}{59}$ → $\boxed{2 \frac{38}{59}}$

*(Check: 59 × 2 = 118; 156 - 118 = 38)*

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## 🎯 Final Answers:

Multiplication:

1. $ \boxed{86 \frac{1}{9}} $
2. $ \boxed{52 \frac{1}{8}} $
3. $ \boxed{4 \frac{2}{3}} $
4. $ \boxed{4 \frac{44}{45}} $
5. $ \boxed{5 \frac{2}{5}} $
6. $ \boxed{1 \frac{11}{15}} $
7. $ \boxed{3 \frac{1}{14}} $
8. $ \boxed{2 \frac{1}{9}} $
9. $ \boxed{1 \frac{9}{10}} $

Division:

1. $ \boxed{\frac{1}{3}} $
2. $ \boxed{2 \frac{32}{45}} $
3. $ \boxed{3 \frac{27}{91}} $
4. $ \boxed{\frac{14}{23}} $
5. $ \boxed{9 \frac{4}{9}} $
6. $ \boxed{2 \frac{38}{59}} $

Let me know if you’d like a printable version or step-by-step video explanations! 😊