The reciprocal is simply: 1 ∕ number
Example: Reciprocal of 8 is 1 ∕ 8
To get the reciprocal of a number, we divide 1 by the number.
Examples:
It is like turning the number upside down. We can think of a whole number as being “number ∕ 1”, so the reciprocal is just like “flipping it over”.
|
Number |
Reciprocal |
|
7 = 7 ∕ 1 |
1 ∕ 7 |
|
12 = 12 ∕ 1 |
1 ∕ 12 |
|
200 = 200 ∕ 1 |
1 ∕ 200 |
|
1500 = 1500 ∕ 1 |
1 ∕ 1500 |
Every number has a reciprocal except 0. This is because 1 ∕ 0 is undefined.
When we multiply a number by its reciprocal we get 1.
Examples:
2 × \(\frac{1}{2}\) = 1
5 × \(\frac{1}{5}\)= 1
Reciprocal of a fraction is found by flipping the whole fraction i.e. numerator goes down and the denominator comes up.
For example, the reciprocal of \(\frac{3}{5}\) is \(\frac{5}{3}\)
Multiplying a fraction by its reciprocal
When we multiply a fraction by its reciprocal we get 1:
For example:
\(\frac{5}{6}\) × \(\frac{6}{5}\) = 1
\(\frac{1}{3}\) × 3 = 1
To find the reciprocal of a mixed fraction, we must first convert it to an improper fraction, then turn it upside down.
For example: What is the reciprocal of \(2\frac{1}{3}\) (two and one-third)?
The reciprocal of a reciprocal takes us back to where we started:
For example, the reciprocal of 6 is \(\frac{1}{6}\) and the reciprocal of \(\frac{1}{6}\) is 6
The reciprocal can be shown with a little “-1” like this: x-1 = 1 ∕ x
For example: 4-1 = \(\frac{1}{4}\) = 0.25
The reciprocal is also called the Multiplicative Inverse.
