Inverse numbers

Now we are going to learn about a very interesting topic in math. It is called "inverse numbers".

Definition. The inverse of a is a number which, when multiplied by a, yields one.

Let's substitute the number 5 in place of the variable a in this definition and try to read the definition:

The inverse of 5 is a number that, when multiplied by 5, gives one.

Is it possible to find a number that, when multiplied by 5, gives one? It is possible. Let's represent five as a fraction:

Then multiply this fraction by itself, but swap the numerator and denominator. In other words, multiply fraction by itself, only inverted:

What is the result of this? If we continue to solve this example, we will get one:

So the inverse of the number 5, is the number , because multiplying 5 by results in one.

The inverse can also be found for any other integer.

Examples:

• the inverse of number 2 is the fraction

• the inverse of number 2 is the fraction

• the inverse of number 2 is the fraction

It is also possible to find an inverse number for any other fraction. To do that, all you have to do is turn it over.

Examples:

• For fraction the inverse fraction is fraction
• For fraction the inverse fraction is fraction
• For fraction the inverse fraction is fraction

Video lesson

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