### Numbers: Fractions

### Reciprocal of a fraction

Reciprocal of a fraction

If we swap the numerator and the denominator in the fraction #\tfrac{2}{3}#, we get #\tfrac{3}{2}#. We now see that: \[\tfrac{2}{3} \times \tfrac{3}{2} =\tfrac{6}{6} = 1\]

In general it holds that:

*Two numbers are each other's reciprocal (also called inverse) if their product is #1#.*

**Examples**

\begin{array}{rcrcr}\tfrac{3}{5} &\times& \tfrac{5}{3} &=& 1\\\tfrac{1}{10} &\times& 10 &=& 1\\-\tfrac{4}{3} &\times& -\tfrac{3}{4} &=& 1\end{array}

#{{17}\over{7}}#

If we swap the numerator and the denominator of the fraction #{{7}\over{17}}#, we find #{{17}\over{7}}#. To double-check, we multiply the numbers and check if the product equals #1#.

\[{{7}\over{17}} \times {{17}\over{7}}=1\]

Therefore, the reciprocal of #{{7}\over{17}}# equals #{{17}\over{7}}#.

If we swap the numerator and the denominator of the fraction #{{7}\over{17}}#, we find #{{17}\over{7}}#. To double-check, we multiply the numbers and check if the product equals #1#.

\[{{7}\over{17}} \times {{17}\over{7}}=1\]

Therefore, the reciprocal of #{{7}\over{17}}# equals #{{17}\over{7}}#.

Unlock full access

Teacher access

Request a demo account. We will help you get started with our digital learning environment.

Student access

Is your university not a partner?
Get access to our courses via

Or visit omptest.org if jou are taking an OMPT exam.

**Pass Your Math**independent of your university. See pricing and more.Or visit omptest.org if jou are taking an OMPT exam.