Multiplicative Inverse / Reciprocal

Multiplicative Inverse / Reciprocal of Fractions Video

Multiplicative Inverse / Reciprocal of Fractions

The Multiplicative Inverse, or Reciprocal, is one of a pair of numbers that, when multiplied together, equal 1.

$n * \frac{1}{n} = 1$

Let’s look at several examples to better understand what this means:

ex.1 How to find the reciprocal of a simple fraction.

To find the reciprocal of $\tfrac{5}{7}$ you can just “flip it over”

Therefore, the reciprocal of $\tfrac{5}{7}$ is $\tfrac{7}{5}$

Because $\tfrac{5}{7} * \tfrac{7}{5}$ = 1

So, $\tfrac{5}{7}$ and $\tfrac{7}{5}$ are reciprocal of each other.

ex.2 How to find the reciprocal of a whole number.

To find the reciprocal of $25$, you must first turn $25$ into a fraction.

$25 = \tfrac{25}{1}$

Therefore, the reciprocal of $25 is $\tfrac{1}{25}$

Because $25 * \tfrac{1}{25}$ = 1

So, $25$ and $\tfrac{1}{25}$ are reciprocal of each other.

ex.3 How to find the reciprocal of a mixed number.

To find the reciprocal of 4$\tfrac{2}{3}$ you must first turn 4$\tfrac{2}{3}$ into a fraction.

4$\tfrac{2}{3} = \tfrac{14}{3}$

Therefore the reciprocal of 4$\tfrac{2}{3}$ is $\tfrac{3}{14}$

Because $\tfrac{14}{3} * \tfrac{3}{14}$ = 1

So, 4$\tfrac{2}{3}$ and $\tfrac{3}{14}$ are reciprocal of each other.

ex.4 How to find the reciprocal of a negative fraction.

To find the reciprocal of $-\tfrac{6}{11}$ you can just “flip it over” and keep the sign

Therefore, the reciprocal of $-\tfrac{6}{11}$ is $-\tfrac{11}{6}$

Because $-\tfrac{6}{11} * -\tfrac{11}{6}$ = 1

So, $-\tfrac{6}{11}$ and $-\tfrac{11}{6}$ are reciprocal of each other.

So, to find the reciprocal of a number.

You first turn the number into a fraction, $\color{blue}{n = \tfrac{n}{1}}$

Then “flip it over,” $\color{blue}{\tfrac{1}{n}}$

These pair of numbers, $\color{blue}{n}$ and $\color{blue}{\tfrac{1}{n}}$, are reciprocals of each other