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Question

# source (i)89+−116(ii)3+5−7(iii)1−12 and 2−15(iv)−819+−457(v)79+3−4(vi)526+11−39(vii)−169+−512(viii)−138+536(ix)0+−35(x)1+−45(xi)−516+724

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Solution

## (i)89+−116LCM of 9,6=18∴89=8×29×2=1618and −116=−11×36×3=−3318Now 89+−116=1618+−3318=16−3318=−1718 (ii) 3+5−7=3+−57(5−7=5×(−1)−7×(−1)=−57)=31+−57=21−57=167 (iii) 1−12+2−15=−112+−215⎧⎪ ⎪⎨⎪ ⎪⎩∵1−12=1×(−1)−12×(−1)=−112and2−15=2×(−1)−15×(−1)=−215⎫⎪ ⎪⎬⎪ ⎪⎭LCM of 12,15=60∴−112=−1×512×5=−560and −215=−2×415×4=−860Now =−112+−215=−560+−860=−5−860=−1360 (iv) −819+−457LCM of 19,57=57∴−819=−8×319×3=−2457and −457=−4×157×1=−457Now −819+−457=−2457+−457=−24−457=−2857 (v) 79+3−479+3−4{∵3−4=3×(−1)−4×(−1)=−34}LCM of 9,4=36∴79=7×49×4=2836and −34=−3×94×9=−2736Now 79+−34=2836+−2736=28−2736=136 (vi) 526+11−39⇒526+−1139{∵1139=11×(−1)−39×(−1)−1139}LCM of 26,39=78∴526=5×326×3=1578and −1139=−11×239×2=−2278Now 526+−1139=1578+−2278=15−2278=−778 (vii) −169+−512LCM of 9,12=36∴−169=−16×49×4=−6436−512=−5×312×3=−1536Now −169+−512=−6436+−1536=−64−1536=−7936 (viii) −138+536LCM of 8,36=72∴−138=−13×98×9=−11772536=5×236×2=1072Now −138+536=−11772+1072=−117+1072=−10772 (ix) 0+−35=−35(Zeropropertyofaddition) (x) 1+−45=55+−45(11=1×51×5=55)=5−45=15 (xi) −516+724LCM of 16,24=48∴−516=−5×316×3=−1548and 724=7×224×2=1448Now −516+724=−1548+1448=−15+1448=−148

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