Question

While dividing a fraction by another fraction, we ______________ the first fraction by the ________________ of the other fraction.

Answer 1

Hint: The question requires the knowledge of a fraction division. The question asks us how to divide a given fraction with another fraction.

Complete step-by-step answer:
A fraction represents a part of a whole or, more generally, any number of equal parts. When we speak in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.
Let a fraction \[\dfrac{x}{y}\]be divided by another fraction\[\dfrac{a}{b}\].
Now let us see how it works:
\[
\Rightarrow \dfrac{x}{y}\div \dfrac{a}{b}=\dfrac{\dfrac{x}{y}}{\dfrac{a}{b}} \\
\Rightarrow \dfrac{x}{y}\div \dfrac{a}{b}=\dfrac{x\times b}{y\times a} \\
\Rightarrow \dfrac{x}{y}\div \dfrac{a}{b}=\dfrac{x}{y}\times \dfrac{b}{a} \\
\]
Hence we see that \[\dfrac{b}{a}\]is the reciprocal fraction of \[\dfrac{a}{b}\] and it is multiplied to the fraction\[\dfrac{x}{y}\].
Hence the complete sentence is;
While dividing a fraction by another fraction, we multiply the first fraction by the reciprocal of the other fraction.

Note: Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next we multiply the two numerators. Then we multiply the two denominators. Finally we simplify the fractions if needed. If a mixed fraction is given we have to turn the mixed fraction into improper fraction. Then divide with the other fraction. If both dividend fraction and divisor fraction is mixed fraction then we need to convert both in improper fraction. It is recommended to simplify both the fractions before performing the division operation.