Evaluate:
38+−512+37+312+−58+−27\dfrac{3}{8} + \dfrac{-5}{12} + \dfrac{3}{7} + \dfrac{3}{12} + \dfrac{-5}{8} + \dfrac{-2}{7}83+12−5+73+123+8−5+7−2
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(38+−58)+(−512+312)+(37+−27)=−28+−212+17=−14+−16+17\Big(\dfrac{3}{8} + \dfrac{-5}{8}\Big) + \Big(\dfrac{-5}{12} + \dfrac{3}{12}\Big) + \Big(\dfrac{3}{7} + \dfrac{-2}{7}\Big) \\[1em] = \dfrac{-2}{8} + \dfrac{-2}{12} + \dfrac{1}{7} \\[1em] = \dfrac{-1}{4} + \dfrac{-1}{6} + \dfrac{1}{7} \\[1em](83+8−5)+(12−5+123)+(73+7−2)=8−2+12−2+71=4−1+6−1+71
LCM of 4 ,6 and 7 is 2 x 2 x 3 x 7 = 84
−1×214×21+−1×146×14+1×127×12=−2184+−1484+1284=(−21)+(−14)+1284=−2384\dfrac{-1 \times 21}{4 \times 21} + \dfrac{-1 \times 14}{6 \times 14} + \dfrac{1 \times 12}{7 \times 12} \\[1em] = \dfrac{-21}{84} + \dfrac{-14}{84} + \dfrac{12}{84} \\[1em] = \dfrac{(-21) + (-14) + 12}{84} \\[1em] = \dfrac{-23}{84} \\[1em]4×21−1×21+6×14−1×14+7×121×12=84−21+84−14+8412=84(−21)+(−14)+12=84−23
∴ 38+−512+37+312+−58+−27=−2384\dfrac{3}{8} + \dfrac{-5}{12} + \dfrac{3}{7} + \dfrac{3}{12} + \dfrac{-5}{8} + \dfrac{-2}{7} = \dfrac{-23}{84}83+12−5+73+123+8−5+7−2=84−23
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23+−45+13+25\dfrac{2}{3} + \dfrac{-4}{5} + \dfrac{1}{3} + \dfrac{2}{5}32+5−4+31+52
47+0+−89+−137+179\dfrac{4}{7} + 0 + \dfrac{-8}{9} + \dfrac{-13}{7} + \dfrac{17}{9}74+0+9−8+7−13+917
For each pair of rational number, verify commutative property of addition of rational numbers.
−87\dfrac{-8}{7}7−8 and 514\dfrac{5}{14}145
59\dfrac{5}{9}95 and 5−12\dfrac{5}{-12}−125
