 maths > fractions

Reciprocal of a fraction

what you'll learn...

overview

"Reciprocal" or "multiplicative inverse" of a fraction is another fraction that results in $1$$1$ when the two fractions are multiplied.

invert to reverse

The word "reciprocal" means: backwards; in reverse.

Consider the multiplication $4×3$$4 \times 3$

•  $4$$4$ is the multiplicand

•  $3$$3$ is the multiplier

•  $12$$12$ is the product

The multiplier has modified the multiplicand.
How to reverse or take backward the multiplication?
The reverse of the multiplier $3$$3$ is the reciprocal $\frac{1}{3}$$\frac{1}{3}$
Because the product $12$$12$, when multiplied by the reciprocal $\frac{1}{3}$$\frac{1}{3}$ gives the multiplicand $4$$4$.

Reciprocal is also called the multiplicative inverse.

Consider the multiplication $\frac{2}{3}×\frac{5}{8}=\frac{5}{12}$$\frac{2}{3} \times \frac{5}{8} = \frac{5}{12}$

•  $\frac{2}{3}$$\frac{2}{3}$ is the multiplicand

•  $\frac{5}{8}$$\frac{5}{8}$ is the multiplier

•  $\frac{5}{12}$$\frac{5}{12}$ is the product

The reverse of the multiplier $\frac{5}{8}$$\frac{5}{8}$ is the reciprocal $\frac{8}{5}$$\frac{8}{5}$
The product $\frac{5}{12}$$\frac{5}{12}$, when multiplied by the reciprocal $\frac{8}{5}$$\frac{8}{5}$ gives the multiplicand $\frac{2}{3}$$\frac{2}{3}$.

Reciprocal is also called the multiplicative inverse.

"Reciprocal" or "multiplicative inverse" of a fraction is the fraction that inverses the number to a product result $1$$1$.

Reciprocal of a Fraction: For a fraction $\frac{p}{q}$$\frac{p}{q}$, the "Reciprocal" or "multiplicative inverse" is $\frac{q}{p}$$\frac{q}{p}$ as $\frac{p}{q}×\frac{q}{p}=1$$\frac{p}{q} \times \frac{q}{p} = 1$.

examples

What is the reciprocal of $\frac{14}{18}$$\frac{14}{18}$?
The answer is '$\frac{18}{14}$$\frac{18}{14}$'

What is the reciprocal of $1\frac{3}{4}$$1 \frac{3}{4}$
The answer is '$\frac{4}{7}$$\frac{4}{7}$'. The mixed fraction $1\frac{3}{4}$$1 \frac{3}{4}$has to be converted to equivalent improper fraction $\frac{7}{4}$$\frac{7}{4}$ before finding the reciprocal $\frac{4}{7}$$\frac{4}{7}$

summary

»  Multiplicative inverse
reciprocal means "backwards; in reverse"
→  reciprocal of $\frac{a}{b}$$\frac{a}{b}$ is $\frac{b}{a}$$\frac{b}{a}$

Outline