Multiplying Reciprocals

You know that a reciprocal is a fraction whose numerator and denominator have been reversed. For example:

What is the reciprocal of the fraction $\frac{18}{11}$ ?

Reciprocals have a special relationship when they are multiplied together. If you multiply a fraction by its reciprocal, the product will always be the number 1. For example:

Show that the fractions $\frac{7}{5}$ and $\frac{5}{7}$ are reciprocals.

How well do you understand the concept of a reciprocal fraction? Use the activity below to find out.

$\frac{1}{2}$
0
1

The product of a fraction and its reciprocal will always be the number 1.

No, because the product of $\frac{9}{4}$ and $\frac{4}{7}$ is not 0.
No, because the product of $\frac{9}{4}$ and $\frac{4}{7}$ is not 1.
No, because the product of $\frac{9}{4}$ and $\frac{4}{7}$ is not $\frac{1}{2}$ .

The product of a fraction and its reciprocal will always be the number 1.

$\frac{5}{3} + \frac{3}{5} = 1$
$\frac{5}{3} \cdot \frac{3}{5} = 1$
$\frac{5}{3} \ \div\ \frac{3}{5} = 1$

The product of a fraction and its reciprocal will always be the number 1.

Questions answered correctly:

Questions answered incorrectly:

Question

Does the number 0 have a reciprocal? Why or why not?

Set up the multiplication problem.	$\frac{7}{5} \cdot \frac{5}{7}$
Use cross-cancelation to reduce the fractions before multiplying.	$\frac{\overset{1}{\cancel{7}}}{\underset{1}{\cancel{5}}} \cdot \frac{\overset{1}{\cancel{5}}}{\underset{1}{\cancel{7}}}$
Multiply the numerators and then multiply the denominators.	$\frac{1}{1} \cdot \frac{1}{1} = \frac{1}{1}$
Make sure that your answer is in simplest form.	$\frac{1}{1} = 1 \ \div\ 1 = 1$

What happens when you multiply reciprocal fractions?

Let's have a look...

Let's Practice

1. If two fractions are each other's reciprocal, what is their product?

2. Is the fraction $\frac{9}{4}$ the reciprocal of the fraction $\frac{4}{7}$ ?

3. Which shows that the fractions $\frac{5}{3}$ and $\frac{3}{5}$ are reciprocals?

Summary

Question

What happens when you multiply reciprocal fractions?

Let's have a look...

Let's Practice

1. If two fractions are each other's reciprocal, what is their product?

2. Is the fraction 94 \frac{9}{4} the reciprocal of the fraction 47 \frac{4}{7} ?

3. Which shows that the fractions 53 \frac{5}{3} and 35 \frac{3}{5} are reciprocals?

Summary

Question

2. Is the fraction $\frac{9}{4}$ the reciprocal of the fraction $\frac{4}{7}$ ?

3. Which shows that the fractions $\frac{5}{3}$ and $\frac{3}{5}$ are reciprocals?