Fractions : Reciprocal of a fraction

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 $4 \times 3$ $4 xx 3$

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

Reciprocal is also called the multiplicative inverse.

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

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

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

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

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

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 $\frac{p}{q}$ $p/q$ , the "Reciprocal" or "multiplicative inverse" is $\frac{q}{p}$ $q/p$ as $\frac{p}{q} \times \frac{q}{p} = 1$ $p/q xx q/p = 1$ .

examples

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

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

summary

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

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