• # question_answer 5) Fill in the following blanks. $\frac{15}{18}=\frac{}{6}=\frac{10}{}=\frac{}{30}$ [Are these equivalent ratios?] TIPS We can get equivalent ratios by multiplying or dividing the numerator and denominator by the same number,

In order to get the missing number, we consider the fact that $18=6\times 3$ i.e. when we divide 18 by 3, we get 6. So, to get the missing number of second ratio, 15 must also be divided by 3. Then, we have  $15\div 3=5$ Hence, the second ratio is $\frac{}{6}$ i.e. $\frac{15}{18}=\frac{}{6}$                  ?(i)                                                 Similarly, to get third ratio, we multiply both terms of second ratio by 2. $[\because 5\times 2=10]$ i.e.          $\frac{}{6}=\frac{5\times 2}{6\times 2}=\frac{10}{12}=10:12$ [multiplying numerator and denominator by 2] $\therefore$  $\frac{5}{6}=\frac{10}{12}$                                       ?(ii) Hence, the third ratio is 10/12. Now, to get the fourth ratio, we consider the fact that $30=6\times 5$ i.e. when we divide 30 by 6, we get 5. So, in second ratio we multiply by 5, i.e.                                 $\frac{5}{6}=\frac{5\times 5}{6\times 5}=\frac{25}{30}$ $\therefore$  $\frac{5}{6}=\frac{}{30}$                                            ?(iii) From Eqs. (i), (ii) and (iii), we have $\frac{15}{18}=\frac{}{6}=\frac{10}{}=\frac{}{30}$ Here, from above relation, we can say that all these are equivalent ratios.
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