Question

1. \\(\frac{9}{13} \div 9\\)\
2. \\(\frac{11}{22} \div \frac{1}{2}\\)\
3. \\(2\frac{9}{20} \div 5\frac{2}{5}\\)\
4. \\(3\frac{1}{2} \div 9\frac{1}{2}\\)\
5. \\(5 \div 25\\)\
6. \\(\frac{10}{3} \div \frac{1}{6}\\)

Explanation:

Step1: Rewrite division as multiplication

$\frac{9}{13} \div 9 = \frac{9}{13} \times \frac{1}{9}$

Step2: Simplify and multiply

$\frac{9}{13} \times \frac{1}{9} = \frac{1}{13}$

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Step1: Rewrite division as multiplication

$\frac{11}{22} \div \frac{1}{2} = \frac{11}{22} \times \frac{2}{1}$

Step2: Simplify and multiply

$\frac{11}{22} \times \frac{2}{1} = \frac{22}{22} = 1$

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Step1: Convert mixed numbers to improper fractions

$2\frac{9}{20} = \frac{49}{20}, \quad 5\frac{2}{5} = \frac{27}{5}$

Step2: Rewrite division as multiplication

$\frac{49}{20} \div \frac{27}{5} = \frac{49}{20} \times \frac{5}{27}$

Step3: Simplify and multiply

$\frac{49}{20} \times \frac{5}{27} = \frac{49}{4} \times \frac{1}{27} = \frac{49}{108}$

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Step1: Convert mixed numbers to improper fractions

$3\frac{1}{2} = \frac{7}{2}, \quad 9\frac{1}{2} = \frac{19}{2}$

Step2: Rewrite division as multiplication

$\frac{7}{2} \div \frac{19}{2} = \frac{7}{2} \times \frac{2}{19}$

Step3: Simplify and multiply

$\frac{7}{2} \times \frac{2}{19} = \frac{7}{19}$

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Step1: Rewrite division as fraction

$5 \div 25 = \frac{5}{25}$

Step2: Simplify the fraction

$\frac{5}{25} = \frac{1}{5}$

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Step1: Rewrite division as multiplication

$\frac{10}{3} \div \frac{1}{6} = \frac{10}{3} \times \frac{6}{1}$

Step2: Simplify and multiply

$\frac{10}{3} \times \frac{6}{1} = 10 \times 2 = 20$

Answer:

1. $\frac{1}{13}$
2. $1$
3. $\frac{49}{108}$
4. $\frac{7}{19}$
5. $\frac{1}{5}$
6. $20$