Reciprocal of a Number

Reciprocal of a Number

The reciprocal of a nonzero number is the value that multiplies with it to give 1. In fraction form, you find it by swapping the numerator and denominator. For whole numbers, first write the number as a fraction, for example (5 = \frac{5}{1}), then flip it to get (\frac{1}{5}).

How to find it

1. Check that the number is not 0. Zero has no reciprocal.
2. Rewrite the number as a fraction if needed.
   • Example: (3 = \frac{3}{1})
3. Invert the fraction.
   • (\frac{3}{1} \to \frac{1}{3})
4. Simplify the answer if possible.
   • Example: (\frac{6}{8}) becomes reciprocal (\frac{8}{6} = \frac{4}{3}).

Useful checks

Multiply your answer by the original number. If the product is 1, your reciprocal is correct.

• Example: (4 \times \frac{1}{4} = 1)
• Example: (\frac{2}{3} \times \frac{3}{2} = 1)

Reminder

• The reciprocal of a fraction is found by flipping it.
• The reciprocal of a whole number is usually a unit fraction.
• Always simplify exact answers when possible.