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Mathematics

Evaluate:

(5×215)(6×29)\Big(-5 \times \dfrac{2}{15}\Big) - \Big(-6 \times \dfrac{2}{9}\Big)

Rational Numbers

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Answer

(5×21×15)(6×21×9)=(1015)(129)=(23)(43)=(2(4)3)=(2+43)=(23)\Big(\dfrac{-5 \times 2}{1 \times 15}\Big) - \Big(\dfrac{-6 \times 2}{1 \times 9}\Big)\\[1em] =\Big(\dfrac{-10}{15}\Big) - \Big(\dfrac{-12}{9}\Big)\\[1em] =\Big(\dfrac{-2}{3}\Big) - \Big(\dfrac{-4}{3}\Big)\\[1em] =\Big(\dfrac{-2 - (-4)}{3}\Big)\\[1em] =\Big(\dfrac{-2 + 4}{3})\\[1em] =\Big(\dfrac{2}{3}\Big)

Hence, (5×512)(6×29)=(23)\Big(-5 \times \dfrac{5}{12}\Big) - \Big(-6 \times \dfrac{2}{9}\Big) = \Big(\dfrac{2}{3}\Big)

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