# Negative indices and reciprocals

**Negative indices**

Negative indices follow the following law as per the examples below:

The second index law is as follows,

3² ÷ 3⁴ = 3(²¯⁴) = 3¯²

When combining both laws, the following is deduced,

**Reciprocals**

A reciprocal of a number is when it is raised to the power of –1.

The reciprocal of a number is what we multiply the number by to get 1.

A calculator can be used to find reciprocals by using the following key:

Points to note:

- When a number is written as a fraction, the reciprocal can be found by swapping the numerator and the denominator
*a*/*b*×*b*/*a*will always equal 1.

**Finding the reciprocals**

Points to note:

- When finding the reciprocal of a decimal, write it first and then invert it
- Improper fractions can be written as mixed numbers if needed
- If a number is provided as a decimal, then its reciprocal is also given as a decimal.