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Finding the Reciprocal


The reciprocal of an integer is that number divided by 1. So, the reciprocal of 3 is 13 rac{1}{3}. Fractions also have reciprocals, which just involves swapping the numerator and the denominator. So, the reciprocal of 34 rac{3}{4} is 43 rac{4}{3}, or 1 13 rac{1}{3}.


Reciprocal - A number's reciprocal is 1 divided by that number.
Denominator - The bottom number of a fraction, it tells you how many parts of a whole a fraction is made up of (e.g. $$ rac{1}{3}$$ has a denominator of 3, meaning you split a whole up into three parts.)
Numerator - The top number of a fraction, it tells you how many of the denominator segments you have. (e.g. $$ rac{2}{3}$$ has a numerator of 2 and a denominator of 3, meaning you split a whole up into three parts, and then keep two of those parts.)
Mixed Fraction - A fraction with a whole number and a fraction (e.g. 6 $$ rac{1}{3}$$ )
Improper Fraction - A top-heavy fraction, where the numerator is bigger than the denominator (e.g. $$ rac{19}{3}$$)


To find the reciprocal of an integer, just divide 1 by that number.

The reciprocal of 5 is 15 rac{1}{5}

The reciprocal of 7 is 17 rac{1}{7}

The reciprocal of 86932 is 186932 rac{1}{86932}


The reciprocal of a fraction is the fraction flipped upside down. Just swap the denominator and the numerator.

The reciprocal of 27 rac{2}{7} is 72 rac{7}{2}

The reciprocal of 619 rac{6}{19} is 196 rac{19}{6}

The reciprocal of 4876198 rac{487}{6198} is 6198487 rac{6198}{487}

If the numerator is 1, then the reciprocal will be a whole number:

The reciprocal of 17 rac{1}{7} is 71 rac{7}{1}, or 7.

Mixed Fractions

To find the reciprocal of a mixed fraction, you need to turn it into an improper (or top-heavy) fraction.

So, to find the reciprocal of 6 13 rac{1}{3}, we create the improper fraction 193 rac{19}{3}. The reciprocal is then the numerator and denominator switched: 319 rac{3}{19}

Multiplying together two reciprocals will give the answer 1:

23 rac{2}{3} x 32 rac{3}{2} = 66 rac{6}{6} = 1


Finding the Reciprocal (Example #1)

2332=1\dfrac{2}{3} * \dfrac{3}{2} = 1
Therefore the reciprocal (multiplicative inverse) of 23\dfrac{2}{3} is 32\dfrac{3}{2}

Finding the Reciprocal (Example #2)

3443=1-\dfrac{3}{4} * -\dfrac{4}{3} = 1
Therefore the reciprocal (multiplicative inverse) of 34-\dfrac{3}{4} is 43-\dfrac{4}{3}

Finding the Reciprocal (Example #3)

7557=1\dfrac{7}{5} * \dfrac{5}{7} = 1
Therefore the reciprocal (multiplicative inverse) of 75\dfrac{7}{5} is 57\dfrac{5}{7}

Finding the Reciprocal (Example #4)

111111=1\dfrac{1}{11} * \dfrac{11}{1} = 1
Therefore the reciprocal (multiplicative inverse) of 111\dfrac{1}{11} is 111\dfrac{11}{1}

Finding the Reciprocal Worksheets (PDF)

Finding the Reciprocal Worksheet 1

Finding the Reciprocal Worksheet 2

Finding the Reciprocal Worksheet 3