Question

How do you find the value of \[\dfrac{1}{2} \div \dfrac{3}{2}\] ?

Answer 1

Hint: This problem is simple to solve. The approach we will use is that we will change the sign of division to multiplication and then we will take the next ratio in its reciprocal form. Such that instead of division the problem will change into multiplication directly but the answer will be the correct. This is nothing but
\[\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b} \times \dfrac{d}{c}\]

Complete step-by-step answer:
Given that \[\dfrac{1}{2} \div \dfrac{3}{2}\]
Now we will use the method mentioned above
\[\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b} \times \dfrac{d}{c}\]
\[\dfrac{1}{2} \div \dfrac{3}{2} = \dfrac{1}{2} \times \dfrac{2}{3}\]
Now just cancel 2 from the above terms
\[\dfrac{1}{2} \div \dfrac{3}{2} = \dfrac{1}{3}\]
This is the correct answer.
So, the correct answer is “$\dfrac{1}{3}$”.

Note: Note that the denominator of both the ratios is same then we can cancel them directly as
\[\dfrac{a}{b} \div \dfrac{c}{b} = \dfrac{a}{b} \times \dfrac{b}{c} = \dfrac{a}{c}\]
But the formula mentioned above in the main solution is for general ratios in division. We know that if the ratios in division can be expressed as
\[\dfrac{a}{b} \div \dfrac{c}{b} = \dfrac{{\dfrac{a}{b}}}{{\dfrac{c}{b}}} = \dfrac{a}{b} \times \dfrac{b}{c} = \dfrac{a}{c}\]
This approach also can be used. Here the denominators are the same and only that makes the problem easy but if all the four numbers are different then we can use the general formula.
\[\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b} \times \dfrac{d}{c}\]