RD Sharma solution class 7 chapter 9 Ratio and Proportion Exercise 9.2

Exercise 9.2

Page-9.10

Question 1:

Which ratio is larger in the following pairs?
(i) 3 : 4 or 9 : 16
(ii) 15 : 16 or 24 : 25
(iii) 4 : 7 or 5 : 8
(iv) 9 : 20 or 8 : 13
(v) 1 : 2 or 13 : 27

Answer 1:

(i) Writing the ratios as fractions, we have
        3 : 4 = $\frac{3}{4}$ and 9 : 16 = $\frac{9}{16}$
     Now, LCM of 4 and 16 = 16.
     Making the denominator of each fraction = 16, we have
         $\frac{3}{4}$ = $\frac{3 \times 4}{4 \times 4}$ = $\frac{12}{16}$ and the other fraction = $\frac{9}{16}$
         Of $\frac{12}{16}$ and $\frac{9}{16}$,  clearly $\frac{12}{16}$>$\frac{9}{16}$.
          Therefore, $\frac{3}{4}$>$\frac{9}{16}$.
(ii) Writing the ratios as fractions, we have
        15 : 16 = $\frac{15}{16}$ and 24 : 25 = $\frac{24}{25}$
     Now, LCM of 16 and 25 = 400.
     Making the denominator of each fraction = 400, we have
         $\frac{15}{16}$ =  $\frac{15 \times 25}{16 \times 25}=$$\frac{375}{400}$ and the other fraction = $\frac{24 \times 16}{25 \times 16}=$$\frac{384}{400}$
        Clearly, 384 > 375. So, $\frac{384}{400}$ > $\frac{375}{400}$.
          Therefore, $\frac{24}{25}$>$\frac{15}{16}$.
(iii) Writing the ratios as fractions, we have
        4 : 7 = $\frac{4}{7}$ and 5 : 8 = $\frac{5}{8}$
     Now, LCM of 7 and 8 = 56.
     Making the denominator of each fraction = 56, we have
            $\frac{4\times 8}{7 \times 8}=$$\frac{32}{56}$ and the other fraction = $\frac{5 \times 7}{8 \times 7}=$$\frac{35}{56}$
        Clearly, 36 > 32. So, $\frac{35}{56}$ > $\frac{32}{56}$.
          Therefore, $\frac{5}{8}$>$\frac{4}{7}$.
(iv) Writing the ratios as fractions, we have
       9 : 20 = $\frac{9}{20}$ and 8 : 13 = $\frac{8}{13}$
     Now, LCM of 20 and 13 = 260.
     Making the denominator of each fraction = 260, we have
          $\frac{9\times 13}{20 \times 13}=$$\frac{117}{260}$ and the other fraction = $\frac{8 \times 20}{13 \times 20}=$$\frac{160}{260}$
        Clearly, 160 > 117. So, $\frac{160}{260}$ > $\frac{117}{260}$.
          Therefore, $\frac{8}{13}$>$\frac{9}{20}$.
(v) Writing the ratios as fractions, we have
       1 : 2 = $\frac{1}{2}$ and 13 : 27 = $\frac{13}{27}$
     Now, LCM of 2 and 27 = 54.
     Making the denominator of each fraction = 54, we have
          $\frac{1\times 27}{2 \times 27}=$$\frac{27}{54}$ and the other fraction = $\frac{13 \times 2}{27 \times 2}=$$\frac{26}{54}$
        Clearly, 27 > 26. So, $\frac{27}{54}$ > $\frac{26}{54}$.
          Therefore, $\frac{1}{2}$>$\frac{13}{27}$.

Question 2:

Give two equivalent ratios of 6 : 8.

Answer 2:

We have
              $\frac{6}{8} = \frac{6÷2}{8÷2} = \frac{3}{4}$
     Therefore, 3 : 4 is an equivalent ratio of 6 : 8.
               $\frac{6}{8} = \frac{6\times 2}{8\times 2} = \frac{12}{16}$
 Hence, 3 : 4 and 12 : 16 are equivalent ratios of 6 : 8.

Question 3:

Fill in the following blanks: $\frac{12}{20}=\frac{\boxed{ }}{5}=\frac{9}{\boxed{ }}$

Answer 3:

$\frac{12}{20}= \frac{\left(\right) }{5}= \frac{9}{\left(\right)}$
 Let $\frac{12}{20}= \frac{\left(x\right) }{5}= \frac{9}{\left(y\right)}$.
Then, $\frac{12}{20}= \frac{\left(x\right) }{5}$ ⇒ 12 $\times$ 5 = 20x  ⇒ x = $\frac{12 \times 5}{20}$ = 3.
Also, $\frac{12}{20}= \frac{9 }{\left(y\right)}$ ⇒ 12y = 20 $\times$ 9 ⇒ y = $\frac{20 \times 9}{12}$ = 15.
Therefore, $\frac{12}{20}= \frac{\left(3\right) }{5}= \frac{9}{\left(15\right)}$.