Question

exercise 1.4
divide the following and simplify if possible. show improper fractions as fractions.

1. \\(\frac{1}{2} \div \frac{2}{4}\\)
2. \\(\frac{5}{22} \div 7\frac{2}{4}\\)
3. \\(\frac{6}{8} \div \frac{9}{12}\\)
4. \\(3\frac{1}{3} \div 10\\)

Explanation:

Step1: Flip divisor, multiply

$\frac{1}{2} \div \frac{2}{4} = \frac{1}{2} \times \frac{4}{2}$

Step2: Multiply numerators/denominators

$\frac{1 \times 4}{2 \times 2} = \frac{4}{4}$

Step3: Simplify the fraction

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

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Step1: Convert mixed number to improper fraction

$7\frac{2}{4} = \frac{7 \times 4 + 2}{4} = \frac{30}{4}$

Step2: Flip divisor, multiply

$\frac{5}{22} \div \frac{30}{4} = \frac{5}{22} \times \frac{4}{30}$

Step3: Cancel common factors, multiply

$\frac{5 \times 4}{22 \times 30} = \frac{1 \times 2}{11 \times 15} = \frac{2}{165}$

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Step1: Flip divisor, multiply

$\frac{6}{8} \div \frac{9}{12} = \frac{6}{8} \times \frac{12}{9}$

Step2: Cancel common factors, multiply

$\frac{6 \times 12}{8 \times 9} = \frac{1 \times 3}{2 \times 1} = \frac{3}{2}$

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Step1: Convert mixed number to improper fraction

$3\frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3}$

Step2: Rewrite 10 as fraction, flip

$10 = \frac{10}{1}$, so $\frac{10}{3} \div \frac{10}{1} = \frac{10}{3} \times \frac{1}{10}$

Step3: Cancel common factors, multiply

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

Answer:

1. $1$
2. $\frac{2}{165}$
3. $\frac{3}{2}$
4. $\frac{1}{3}$