Question

How do you divide $\dfrac{1}{{16}} \div \dfrac{3}{4}$?

Answer 1

Hint: In this question we have to divide the fractions, first reciprocate the second fraction in the question, i.e.,$\dfrac{3}{4}$ by interchanging its numerator with the denominator, then multiplying the reciprocal of the second fraction with the first fraction, and then further simplifying the fraction we will get the required answer.

Complete step-by-step solution:
Given expression is $\dfrac{1}{{16}} \div \dfrac{3}{4}$,
When the division symbol is given with fractions, we always reciprocal one of the fractions. i.e., either the first fraction or the second. Reciprocal means inverting the fraction; writing the numerator as the denominator and the denominator as the numerator. Also note that when we reciprocal fractions the division symbol is converted to the multiplication symbol.
Here we will reciprocal the second fraction, i.e.,$\dfrac{3}{4}$,
Reciprocal of $\dfrac{3}{4}$will be $\dfrac{4}{3}$ ,
Now multiplying the reciprocal of the second fraction with the first fraction then the expression can be rearranged as,
$ \Rightarrow \dfrac{1}{{16}} \div \dfrac{3}{4} = \dfrac{1}{{16}} \times \dfrac{4}{3}$,
Now simplifying we get,
$ \Rightarrow \dfrac{1}{{16}} \div \dfrac{3}{4} = \dfrac{1}{3} \times \dfrac{1}{4}$,
Now multiplying the two denominators we get,
$ \Rightarrow \dfrac{1}{{16}} \div \dfrac{3}{4} = \dfrac{1}{{12}}$.
So, the required answer is $\dfrac{1}{{12}}$.
$\therefore $ When we divide $\dfrac{1}{{16}}$ with $\dfrac{3}{4}$ then the required answer is $\dfrac{1}{{12}}$.

Note: We can reciprocate a fraction by simply switching the denominator with the numerator. Reciprocating the fraction changes the sign because the inverse of multiplication is division. Dividing the fractions is division of fraction or as same as multiplying the fraction by the reciprocal which is inverse of the other fraction. We can get the reciprocal of a fraction by interchanging its numerator with its denominator. This method of dividing the fraction by multiplying with the reciprocal. The reciprocal of multiplication is division. Multiplication is inverse of division.