overview

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

invert to reverse

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

Consider the multiplication $4\times 3$

• $4$ is the multiplicand

• $3$ is the multiplier

• $12$ is the product

The multiplier has modified the multiplicand.

How to reverse or take backward the multiplication?

The reverse of the multiplier $3$ is the reciprocal $\frac{1}{3}$

Because the product $12$, when multiplied by the reciprocal $\frac{1}{3}$ gives the multiplicand $4$.

Reciprocal is also called the multiplicative inverse.

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

• $\frac{2}{3}$ is the multiplicand

• $\frac{5}{8}$ is the multiplier

• $\frac{5}{12}$ is the product

The reverse of the multiplier $\frac{5}{8}$ is the reciprocal $\frac{8}{5}$

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

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 $1$.

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

examples

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

The answer is '$\frac{18}{14}$'

What is the reciprocal of $1\frac{3}{4}$

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

summary

» Multiplicative inverse

*reciprocal means "backwards; in reverse"*

→ reciprocal of $\frac{a}{b}$ is $\frac{b}{a}$

Outline

The outline of material to learn "fractions" is as follows.

• * click here for detailed outline of Fractions *

→ __Part of whole__

→ __Dividing a group__

→ __Fractions as Directed numbers__

→ __Like and Unlike Fractions__

→ __Proper and Improper Fractions__

→ __Equivalent & Simplest form__

→ __Converting unlike and like Fractions__

→ __Simplest form of a Fraction__

→ __Comparing Fractions__

→ __Addition & Subtraction__

→ __Multiplication__

→ __Reciprocal__

→ __Division__

→ __Numerical Expressions with Fractions__

→ __PEMA / BOMA__