Grade 6 Equivalent Fractions Worksheets | Math Worksheets - Free Printable

To solve the problems involving dividing fractions, we use the rule:

$$
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}
$$

This means we multiply the first fraction by the reciprocal of the second fraction. Let's solve each problem step by step.

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Problem 1: $\frac{1}{4} \div \frac{3}{4}$

$$
\frac{1}{4} \div \frac{3}{4} = \frac{1}{4} \times \frac{4}{3} = \frac{1 \cdot 4}{4 \cdot 3} = \frac{4}{12} = \frac{1}{3}
$$
Answer: $\boxed{\frac{1}{3}}$

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Problem 2: $\frac{3}{10} \div \frac{6}{11}$

$$
\frac{3}{10} \div \frac{6}{11} = \frac{3}{10} \times \frac{11}{6} = \frac{3 \cdot 11}{10 \cdot 6} = \frac{33}{60} = \frac{11}{20}
$$
Answer: $\boxed{\frac{11}{20}}$

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Problem 3: $\frac{6}{8} \div \frac{6}{7}$

$$
\frac{6}{8} \div \frac{6}{7} = \frac{6}{8} \times \frac{7}{6} = \frac{6 \cdot 7}{8 \cdot 6} = \frac{42}{48} = \frac{7}{8}
$$
Answer: $\boxed{\frac{7}{8}}$

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Problem 4: $\frac{2}{15} \div \frac{4}{7}$

$$
\frac{2}{15} \div \frac{4}{7} = \frac{2}{15} \times \frac{7}{4} = \frac{2 \cdot 7}{15 \cdot 4} = \frac{14}{60} = \frac{7}{30}
$$
Answer: $\boxed{\frac{7}{30}}$

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Problem 5: $\frac{3}{5} \div \frac{12}{9}$

$$
\frac{3}{5} \div \frac{12}{9} = \frac{3}{5} \times \frac{9}{12} = \frac{3 \cdot 9}{5 \cdot 12} = \frac{27}{60} = \frac{9}{20}
$$
Answer: $\boxed{\frac{9}{20}}$

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Problem 6: $\frac{10}{11} \div \frac{5}{8}$

$$
\frac{10}{11} \div \frac{5}{8} = \frac{10}{11} \times \frac{8}{5} = \frac{10 \cdot 8}{11 \cdot 5} = \frac{80}{55} = \frac{16}{11}
$$
Answer: $\boxed{\frac{16}{11}}$

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Problem 7: $\frac{3}{8} \div \frac{2}{7}$

$$
\frac{3}{8} \div \frac{2}{7} = \frac{3}{8} \times \frac{7}{2} = \frac{3 \cdot 7}{8 \cdot 2} = \frac{21}{16}
$$
Answer: $\boxed{\frac{21}{16}}$

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Problem 8: $\frac{5}{7} \div \frac{8}{3}$

$$
\frac{5}{7} \div \frac{8}{3} = \frac{5}{7} \times \frac{3}{8} = \frac{5 \cdot 3}{7 \cdot 8} = \frac{15}{56}
$$
Answer: $\boxed{\frac{15}{56}}$

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Problem 9: $\frac{5}{12} \div \frac{2}{10}$

$$
\frac{5}{12} \div \frac{2}{10} = \frac{5}{12} \times \frac{10}{2} = \frac{5 \cdot 10}{12 \cdot 2} = \frac{50}{24} = \frac{25}{12}
$$
Answer: $\boxed{\frac{25}{12}}$

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Problem 10: $\frac{2}{3} \div \frac{8}{15}$

$$
\frac{2}{3} \div \frac{8}{15} = \frac{2}{3} \times \frac{15}{8} = \frac{2 \cdot 15}{3 \cdot 8} = \frac{30}{24} = \frac{5}{4}
$$
Answer: $\boxed{\frac{5}{4}}$

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Problem 11: $\frac{7}{8} \div \frac{14}{35}$

$$
\frac{7}{8} \div \frac{14}{35} = \frac{7}{8} \times \frac{35}{14} = \frac{7 \cdot 35}{8 \cdot 14} = \frac{245}{112} = \frac{35}{16}
$$
Answer: $\boxed{\frac{35}{16}}$

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Problem 12: $\frac{5}{21} \div \frac{8}{21}$

$$
\frac{5}{21} \div \frac{8}{21} = \frac{5}{21} \times \frac{21}{8} = \frac{5 \cdot 21}{21 \cdot 8} = \frac{105}{168} = \frac{5}{8}
$$
Answer: $\boxed{\frac{5}{8}}$

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Final Answers:

1. $\boxed{\frac{1}{3}}$
2. $\boxed{\frac{11}{20}}$
3. $\boxed{\frac{7}{8}}$
4. $\boxed{\frac{7}{30}}$
5. $\boxed{\frac{9}{20}}$
6. $\boxed{\frac{16}{11}}$
7. $\boxed{\frac{21}{16}}$
8. $\boxed{\frac{15}{56}}$
9. $\boxed{\frac{25}{12}}$
10. $\boxed{\frac{5}{4}}$
11. $\boxed{\frac{35}{16}}$
12. $\boxed{\frac{5}{8}}$