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Mathematics

Verify whether the given statement is true or false:

−724÷3−16=3−16÷−724\dfrac{-7}{24} \div \dfrac{3}{-16} = \dfrac{3}{-16} \div \dfrac{-7}{24}

Rational Numbers

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Answer

Solve the L.H.S. and the R.H.S. separately by multiplying the dividend with the reciprocal of the divisor, and then compare them.

Solving L.H.S.,

⇒−724÷3−16⇒−724×−163⇒(−7)×(−16)24×3=11272=149\Rightarrow \dfrac{-7}{24} \div \dfrac{3}{-16} \\[1em] \Rightarrow \dfrac{-7}{24} \times \dfrac{-16}{3} \\[1em] \Rightarrow \dfrac{(-7) \times (-16)}{24 \times 3} = \dfrac{112}{72} = \dfrac{14}{9}

Solving R.H.S.,

⇒3−16÷−724⇒3−16×24−7⇒3×24(−16)×(−7)=72112=914\Rightarrow \dfrac{3}{-16} \div \dfrac{-7}{24} \\[1em] \Rightarrow \dfrac{3}{-16} \times \dfrac{24}{-7} \\[1em] \Rightarrow \dfrac{3 \times 24}{(-16) \times (-7)} = \dfrac{72}{112} = \dfrac{9}{14}

As L.H.S. ≠≠ R.H.S., division of rational numbers is not commutative.

Hence, the given statement is false.

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