If each of the following pairs represents a pair of equivalent rational numbers- find the values of x-i- 23 -160-and -160-5x-ii- -37 -160-and -160-x4-iii- 35 -160-and -160-x-25-iv- 136 -160-and -160-65x

(i) 23=5x, #160;then #160;x=5 #215;32= #160;152(ii) 37=x4, #160;then #160;x= 37 #215;4= #160; 127(iii) 35=x 25, #160;then #160;x=35 #215; ...

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Standard VII

Mathematics

Definition of Sets

If each of th...

Question

If each of the following pairs represents a pair of equivalent rational numbers, find the values of x:
(i) $\frac{2}{3} and \frac{5}{x}$
(ii) $\frac{- 3}{7} and \frac{x}{4}$
(iii) $\frac{3}{5} and \frac{x}{- 25}$
(iv) $\frac{13}{6} and \frac{- 65}{x}$

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Solution

(i) $\frac{2}{3} = \frac{5}{x}, then x = 5 \times \frac{3}{2} = \frac{15}{2}$
(ii) $\frac{- 3}{7} = \frac{x}{4}, then x = \frac{- 3}{7} \times 4 = \frac{- 12}{7}$
(iii) $\frac{3}{5} = \frac{x}{- 25}, then x = \frac{3}{5} \times (- 25) = \frac{- 75}{5} = - 15$
(iv) $\frac{13}{6} = \frac{- 65}{x}, then x = \frac{6}{13} \times (- 65) = 6 \times (- 5) = - 30$

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Verify commutativity of addition of rational numbers for each of the following pairs of rational numbers: (i) $\frac{- 11}{5} a n d \frac{4}{7}$ (ii) $\frac{4}{9} a n d \frac{7}{- 12}$ (iii) $\frac{- 3}{5} a n d \frac{- 2}{- 15}$ (iv) $\frac{2}{- 7} a n d \frac{12}{- 35}$ (v) $4 a n d \frac{- 3}{5}$ (vi) $- 4 a n d \frac{4}{- 7}$