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Mathematics

For each pair of rational numbers, given below, verify that the multiplication is commutative:

3 and −89\dfrac{-8}{9}

Rational Numbers

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Answer

To prove:

3×−89=−89×33 \times \dfrac{-8}{9} = \dfrac{-8}{9} \times 3

Taking LHS:

3×−89=3×−81×9=−249=−833 \times \dfrac{-8}{9}\\[1em] =\dfrac{3 \times -8}{1 \times 9}\\[1em] =\dfrac{-24}{9}\\[1em] =\dfrac{-8}{3}

Taking RHS:

−89×3=−8×39×1=−249=−83\dfrac{-8}{9} \times 3\\[1em] =\dfrac{-8 \times 3}{9 \times 1}\\[1em] =\dfrac{-24}{9}\\[1em] =\dfrac{-8}{3}

∴ LHS = RHS

3×−89=−89×33 \times \dfrac{-8}{9} = \dfrac{-8}{9} \times 3

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