# Reciprocal

In mathematics, reciprocals are two numbers which multiply together to make 1. They are also called multiplicative inverses of each other. For example:

```* 3 and 1/3 are reciprocals because 3 × 1/3 = 1
* 10/12 and 1 1/5 are reciprocals because 10/12 × 1 1/5 = 1
* -0.2 and -5 are reciprocals because -0.2 × -5 = 1
* 1 and -1 are their own reciprocals because 1 × 1 = 1 and -1 × -1 = 1
* zero does not have a reciprocal because no number times 0 is 1
```

1 divided by a number gives the reciprocal of that number. For example,

```*the reciprocal of 8 is 1/8 (or 0.125) because 1 divided by 8 is 1/8.
*the reciprocal of 125 is 1/125 (or 0.008) because 1 divided by 125 is 1/125.
*the reciprocal of 2498 is 1/2498 because 1 divided by 2498 is 1/2498.
*the reciprocal of 98 is 1/98 because 1 divided by 98 is 1/98.
*the reciprocal of 77 is 1/77 because 1 divided by 77 is 1/77.
*the reciprocal of 345 is 1/345 because 1 divided by 345 is 1/345.
```

The reciprocals of fractions are other fractions where the numerator is on the bottom, and the denominator on top, e.g.:

```*the reciprocal of 4/2 is 2/4, because 4/2 times 2/4 equals 8/8, which also equals 1.
*the reciprocal of 1729/8128 is 8128/1729, because 1729/8128 times 8218/1729 equals 14053312/14053312, which equals 1.
```

This works because when you divide a number by itself, it will always equal 1.