question_answer 1)

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,                        

Answer:

                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.