Question

1. \\(\frac{21}{5} \div \frac{28}{15} =\\) 9. \\(\frac{6}{7} \div \frac{3}{14} =\\) 5. \\(4 \div 24 =\\) 10. \\(2\frac{1}{2} \div 3\frac{3}{4} =\\)

Explanation:

Step1: Rewrite division as multiplication

$\frac{21}{5} \div \frac{28}{15} = \frac{21}{5} \times \frac{15}{28}$

Step2: Simplify and multiply

$\frac{21 \times 15}{5 \times 28} = \frac{21 \times 3}{28} = \frac{63}{28} = \frac{9}{4}$

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Step1: Simplify the division

$4 \div 24 = \frac{4}{24}$

Step2: Reduce the fraction

$\frac{4}{24} = \frac{1}{6}$

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Step1: Rewrite division as multiplication

$\frac{6}{7} \div \frac{3}{14} = \frac{6}{7} \times \frac{14}{3}$

Step2: Simplify and multiply

$\frac{6 \times 14}{7 \times 3} = \frac{6 \times 2}{3} = \frac{12}{3} = 2$

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Step1: Convert mixed numbers to improper fractions

$2\frac{1}{2} = \frac{5}{2}$, $3\frac{3}{4} = \frac{15}{4}$

Step2: Rewrite division as multiplication

$\frac{5}{2} \div \frac{15}{4} = \frac{5}{2} \times \frac{4}{15}$

Step3: Simplify and multiply

$\frac{5 \times 4}{2 \times 15} = \frac{5 \times 2}{15} = \frac{10}{15} = \frac{2}{3}$

Answer:

1. $\frac{9}{4}$
2. $\frac{1}{6}$
3. $2$
4. $\frac{2}{3}$