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If your starting number is a fraction, what do you need to do when trying to find the reciprocal of a number?

By David Moody on the 11th of June, 2012

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    All you need to do is flip the fraction.  The goal is that the original number and the reciprocal will equal 1 when multiplied together.  For example, 3/5 and 5/3 are reciprocals of each other because (3/5)*(5/3)=15/15=1.

    Refine By Alex on the 17th of January, 2013

Suggested reading…

Find the reciprocal of a number

Numbers

The reciprocal of a number is simply the number that you must multiply the number by to have the product of 1. Simply put the reciprocal of a number is just ‘1 over the number’.

For Example:

The reciprocal of 5 is 1/5 because 5 x 1/5 = 1

The reciprocal of 18 is 1/18 because 18 x 1/18 = 1

So you can see that to find the reciprocal of any number you can just follow this formula:

x * 1/x = 1

 

Fractions

If you are trying to find the reciprocal of a fraction, it is still very simple to do. You just have to remember to find the fraction that you must multiply the original fraction by to have the product of 1.  Simply put just turn the fraction upside down.

For Example:

The reciprocal of 3/5 is 5/3= 15/15 = 1/1

The reciprocal of 4/9 is 9/4= 36/36 = 1/1

The reciprocal of 8/3 is 3/8 = 24/24= 1/1

Note if you start with a fraction that is ‘1 over something’, then you’ll end up with a whole number, since anything divided by 1 is just itself.

For example:

The reciprocal of 1/5 is 5/1 = 1

The reciprocal of 1/18 is 18/1 = 1

The reciprocal of 1/20 is 20

The reciprocal of 1/x is x

The reciprocal of 1/3x is 3x

 

Zero

The last thing to note is that zero has no reciprocal because you can't divide anything by zero.

Decimals

e.g. 0.125 as a reciprocal

 

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