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Multiplication of Fractions

Simplify : 3/...

Question

Simplify $:$ $\frac{3}{4}$ $\div$ $($ $\frac{1}{6}$ $\div$ $\frac{1}{2}$ $)$

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Solution

Step 1 : Simplifying the first bracket
$\frac{1}{6}$ $\div$ $\frac{1}{2}$
Step 2: Write the reciprocal of the second fraction ( that one you want to divide by ) with the sign of multiplication (×) and do multiplication
$\frac{1}{6}$ $\times$ $\frac{2}{1}$ $=$ $\frac{1 \times 2}{6 \times 1}$ $=$ $\frac{2}{6}$
$\frac{3}{4}$ $\div$ $($ $\frac{1}{6}$ $\div$ $\frac{1}{2}$ $)$ $=$ $\frac{3}{4}$ $\div$ $\frac{2}{6}$
Step 3: Write the reciprocal of the second fraction ( that one you want to divide by ) with the sign of multiplication (×) and do multiplication
$\frac{3}{4}$ $\times$ $\frac{6}{2}$ $=$ $\frac{3 \times 6}{4 \times 2}$ $=$ $\frac{18}{8}$
Step 4: Simplify the fraction
$\frac{18}{8}$ $=$ $\frac{18 \div 2}{8 \div 2}$ $=$ $\frac{9}{4}$
Divide numerator $9$ by the denominator $4$
Hence $,$ $\frac{3}{4}$ $\div$ $($ $\frac{1}{6}$ $\div$ $\frac{1}{2}$ $)$ $=$ $2 \frac{1}{4}$

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