Select the ratio that is equivalent to $12 : 14$

6 : 2

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6 : 7

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3 : 8

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5 : 7

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Solution

The correct option is B $6 : 7$
Given ratio is $12 : 14$
It can be rewritten as $\frac{12}{14} = \frac{6 \times 2}{7 \times 2}$
Cancelling $2$ from numerator and denominator, we get
$\frac{12}{14} = \frac{6}{7}$ i.e $6 : 7$
Hence, the answer is $6 : 7$ .

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Verify the following :

(i) $\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})$
(ii) $\frac{- 15}{4} \times (\frac{3}{7} + \frac{- 12}{5}) = (\frac{- 15}{4} \times \frac{3}{7}) + (\frac{- 15}{4} \times \frac{- 12}{5})$
(iii) $(\frac{- 8}{3} + \frac{- 13}{12}) \times \frac{5}{6} = (\frac{- 8}{3} \times \frac{5}{6}) + (\frac{- 13}{12} \times \frac{5}{6})$
(iv) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$