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Mathematics

Find the reciprocal of each of the following fractions:

(i) 913\dfrac{9}{13}

(ii) 2382\dfrac{3}{8}

Fractions

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Answer

(i) 913\dfrac{9}{13}

The reciprocal of a fraction ab\dfrac{a}{b} is ba\dfrac{b}{a}.

So, the reciprocal of 913\dfrac{9}{13} is 139\dfrac{13}{9}.

Hence, the reciprocal of 913\dfrac{9}{13} is 139\dfrac{13}{9}.

(ii) 2382\dfrac{3}{8}

First, convert the mixed fraction into improper fraction.

238=2×8+38=198\Rightarrow 2\dfrac{3}{8} = \dfrac{2 \times 8 + 3}{8} = \dfrac{19}{8}

The reciprocal of 198\dfrac{19}{8} is 819\dfrac{8}{19}.

Hence, the reciprocal of 2382\dfrac{3}{8} is 819\dfrac{8}{19}.

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