How do you determine whether the ratios are equivalent: 12/5 and 36/15?

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How do you determine whether the ratios are equivalent: 12/5 and 36/15?

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Answer 1 · 2016-12-29T14:10:37

$ratios are equivalent$ $"ratios are equivalent"$

Explanation:

$The ratio \frac{12}{5}$ $"The ratio " 12/5$ is in $simplest form .$ $color(blue)"simplest form".$ That is no other factor except 1 will divide into them.

$If we now simplify the ratio \frac{36}{15}$ $"If we now simplify the ratio " 36/15$

36 and 15 both have a $common factor$ $color(blue)"common factor"$ of 3 which we can divide them by.

$\Rightarrow \frac{36}{15} = \frac{36 \div 3}{15 \div 3} = \frac{12}{5}$ $rArr36/15=(36÷3)/(15÷3)=12/5$

Usually written using $cancelling$ $color(blue)"cancelling"$ as follows.

$36/15=cancel(36)^(12)/cancel(15)^5=12/5$

$"Since " 36/15" reduces to the same value " 12/5" then the ratios are equivalent"$

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How do you determine whether the ratios are equivalent: 12/5 and 36/15?

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