# Evaluate each of the following:(i) $\frac{2}{3}-\frac{3}{5}$(ii) $\frac{-4}{7}-\frac{2}{-3}$(iii) $\frac{4}{7}-\frac{-5}{-7}$(iv) $-2-\frac{5}{9}$(v) $\frac{-3}{-8}-\frac{-2}{7}$(vi) $\frac{-4}{13}-\frac{-5}{26}$(vii) $\frac{-5}{14}-\frac{-2}{7}$.(viii) $\frac{13}{15}-\frac{12}{25}$(ix) $\frac{-6}{13}-\frac{-7}{13}$(x) $\frac{7}{24}-\frac{19}{36}$(xi) $\frac{5}{63}-\frac{-8}{21}$

To do:

We have to evaluate the given expressions.

Solution:

We know that,

$(-)\times(-)=(+)$

Therefore,

(i) $\frac{2}{3}-\frac{3}{5}=\frac{2\times5-3\times3}{15}$           (LCM of 3 and 5 is 15)

$=\frac{10-9}{15}$

$=\frac{1}{15}$

Therefore,

$\frac{2}{3}-\frac{3}{5}=\frac{1}{15}$ .

(ii) $\frac{-4}{7}-\frac{2}{-3}=\frac{-4}{7}+\frac{2}{3}$

$=\frac{-4\times3+7\times2}{21}$           (LCM of 7 and 3 is 21)

$=\frac{-12+14}{21}$

$=\frac{2}{21}$

Therefore,

$\frac{-4}{7}-\frac{2}{-3}=\frac{2}{21}$ .

(iii) $\frac{4}{7}-\frac{-5}{-7}=\frac{4}{7}-\frac{5}{7}$

$=\frac{4-5}{7}$

$=\frac{-1}{7}$

Therefore,

$\frac{4}{7}-\frac{-5}{-7}=\frac{-1}{7}$ .

(iv) $-2-\frac{5}{9}=\frac{-2}{1}-\frac{5}{9}$

$=\frac{-2\times9-5\times1}{9}$           (LCM of 1 and 9 is 9)

$=\frac{-18-5}{9}$

$=\frac{-23}{9}$

Therefore,

$-2-\frac{5}{9}=\frac{-23}{9}$ .

(v) $\frac{-3}{-8}-\frac{-2}{7}=\frac{3}{8}+\frac{2}{7}$

$=\frac{3\times7+8\times2}{56}$           (LCM of 8 and 7 is 56)

$=\frac{21+16}{56}$

$=\frac{37}{56}$

Therefore,

$\frac{-3}{-8}-\frac{-2}{7}=\frac{37}{56}$ .

(vi) $\frac{-4}{13}-\frac{-5}{26}=\frac{-4}{13}+\frac{5}{26}$

$=\frac{-4\times2+5\times1}{26}$           (LCM of 13 and 26 is 26)

$=\frac{-8+5}{26}$

$=\frac{-3}{26}$

Therefore,

$\frac{-4}{13}-\frac{-5}{26}=\frac{-3}{26}$ .

(vii) $\frac{-5}{14}-\frac{-2}{7}=\frac{-5}{14}+\frac{2}{7}$

$=\frac{-5\times1+2\times2}{14}$           (LCM of 14 and 7 is 14)

$=\frac{-5+4}{14}$

$=\frac{-1}{14}$

Therefore,

$\frac{-5}{14}-\frac{-2}{7}=\frac{-1}{14}$ .

(viii) $\frac{13}{15}-\frac{12}{25}=\frac{13\times5-12\times3}{75}$           (LCM of 15 and 25 is 75)

$=\frac{65-36}{75}$

$=\frac{29}{75}$

Therefore,

$\frac{13}{15}-\frac{12}{25}=\frac{29}{75}$ .

(ix) $\frac{-6}{13}-\frac{-7}{13}=\frac{-6+7}{13}$

$=\frac{1}{13}$

Therefore,

$\frac{-6}{13}-\frac{-7}{13}=\frac{1}{13}$ .

(x) $\frac{7}{24}-\frac{19}{36}=\frac{7\times3-19\times2}{72}$           (LCM of 24 and 36 is 72)

$=\frac{21-38}{72}$

$=\frac{-17}{72}$

Therefore,

$\frac{7}{24}-\frac{19}{36}=\frac{-17}{72}$ .

(xi) $\frac{5}{63}-\frac{-8}{21}=\frac{5}{63}+\frac{8}{21}$

$=\frac{5\times1+8\times3}{63}$           (LCM of 63 and 21 is 63)

$=\frac{5+24}{63}$

$=\frac{29}{63}$

Therefore,

$\frac{5}{63}-\frac{-8}{21}=\frac{29}{63}$ .

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Updated on: 10-Oct-2022

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