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Question

Express $\frac{3}{4}$ as a rational number with denominator: (i) 20 (ii) 36 (iii) 44 (iv) −80

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Solution

3/4 as rational number with denominator: (i) $20\mathrm{is}:\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\frac{3×5}{4×5}=\frac{15}{20}\left(\mathrm{multiplying}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\text{by}5\right)$ (ii) $36\mathrm{is}:\phantom{\rule{0ex}{0ex}}\frac{3×9}{4×9}=\frac{27}{36}\left(\mathrm{multiplying}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\text{by}9\right)$ (iii) $44\mathrm{is}:\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\frac{3×11}{4×11}=\frac{33}{44}\left(\mathrm{multiplying}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\text{by}11\right)$ (iv) $-80\mathrm{is}:\phantom{\rule{0ex}{0ex}}\frac{3×-20}{4×-20}=\frac{-60}{-80}\left(\mathrm{multiplying}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\text{by}-20\right)$

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