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Question

Verify commutativity of addition of rational numbers for each of the following pairs of rational numbers: (i) 115 and 47 (ii)49 and 712 (iii) 35 and 215 (iv) 27 and 1235 (v) 4 and 35 (vi) 4 and 47

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Solution

(i) 115 and 47115+47115=11×75×7=7735and 47=4×57×5=2035115+47=7735+2035=77+2035=5735and47+115=20357735=207735=5735115+47=47+115

(ii) 49 and 7127×(1)12×(1)=712Now 49+712LCM of 9,12=3649=4×49×4=1636712=7×312×3=213649+712+49

(iii) 35 and 215215=2×(1)15×(1)=215LCM of 5 and 15=1535=3×35×3=915Now 35+215=915+2159+215=715and 215+35=215+915=2915=71535+215=215+35

(iv) 27 and 1235LCM of 7,35=3527=2×(5)7×(5)=10351235=12×(1)35×(1)=1235Now 27+1235=1035+1235=101235=2235and 1235+27=1235+1035=121035=223527+1235=1235+27

(v) 4 and 35LCM of 1,5=541=4×51×5=205Now 41+35=205+35=2035=175and 35+41=35+205=3+205=1754+35=35+4

(vi) 4 and 4741 and 47(47=4×(1)7×(1)=47)41=4×71×7=287and47=2847=327and 47+(4)=47+287=4287=3274+47=47+(4)


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