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Question

Verify commutativty of addition of rational numbers for each of the following pairs of rotional numbers:
(i) -115 and 47

(ii) 49 and 7-12

(iii) -35 and -2-15

(iv) 2-7 and 12-35

(v) 4 and -35

(vi) -4 and 4-7

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Solution

Commutativity of the addition of rational numbers means that if ab and cd are two rational numbers, then ab+cd=cd+ab.(i) We have -115 and 47. -115 + 47= -11×75×7+4×57×5=-7735+2035=-77+2035=-5735 47+-115=4×57×5+-11×75×7=2035+-7735=20-7735=-5735 -115 + 47=47+-115 Hence verified.(ii) We have 49 and 7-12. 49+-712= 4×49×4+-7×312×3=1636+-2136=16-2136=-536-712+49=-7×312×3+4×49×4=-2136+1636=-21+1636=-536 49+-712=-712+49 Hence verified.(iii) We have -35 and -2-15 or -35 and 215. -35+215=-915+215=-9+215=-715215+-35=215+-915=2-915=-715 -35+-2-15=-2-15+-35Hence verified.(iv) We have 2-7 and 12-35.-27+-1235=-2×57×5+-1235=-10-1235=-223512-35+2-7=-1235+-2×57×5=-12-1035=-2235 2-7+12-35=12-35+2-7Hence verified.(v) We have 4 and -35. 4+-35=4×51×5+-35=20-35=175 -35+4=-35+4×51×5=-3+205=175 4+-35=-35+4 Hence verified.(vi) We have -4 and 4-7. -41+-47=-4×71×7+-47=-28-47=-327 -47+-41=-47+-4×71×7=-4-287=-327-4+4-7=4-7-4 Hence verified.

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