# Multiplying top and bottom of a fraction [Solved!]

**Daniel** 10 Dec 2015, 09:37

### My question

In the example on the linked page you say: "We multiply top and bottom of each fraction with their denominators. This gives us a perfect square in the denominator in each case, and we can remove the radical"

My question is : in what situations am I allowed to use this particular method? Can it be applied to any equation involving fractions, or is it only possible when there are radicals?

### Relevant page

4. Addition and Subtraction of Radicals

### What I've done so far

Tried it with other examples, but couldn't draw a conclusion.

X

In the example on the linked page you say: "We multiply top and bottom of each fraction with their denominators. This gives us a perfect square in the denominator in each case, and we can remove the radical"
My question is : in what situations am I allowed to use this particular method? Can it be applied to any equation involving fractions, or is it only possible when there are radicals?

Relevant page
<a href="/exponents-radicals/4-addition-subtraction-radicals.php">4. Addition and Subtraction of Radicals</a>
What I've done so far
Tried it with other examples, but couldn't draw a conclusion.

## Re: Multiplying top and bottom of a fraction

**Newton** 11 Dec 2015, 08:14

Hi Daniel

This technique will only be worthwhile in a limited number of cases.

For an example where it wouldn't help at all, consider `1/2`.

If I multiply top and bottom by `2` (the denominator), I will get `2/4`. But so what? I just need to cancel and get back to `1/2`. I can do the multiplying, but it doesn't help me.

In the example that you are referring to, however, the 2 fractions become simpler since their denominators no longer have square roots.

Taking a simpler case:

`1/sqrt(3a)`

When I multiply top and bottom by `sqrt(3a)`, I get:

`1/sqrt(3a) xx sqrt(3a)/sqrt(3a) = sqrt(3a)/(3a)`

The process has "rationalized" the denominator.

Hope that makes sense.

Not sure if you made it to this page:

5. Multiplication and Division of Radicals (Rationalizing the Denominator)

About half way down, it has a heading "Rationalizing the Denominator". In the examples, you will see a method of multiplying top and bottom so we get rid of the square roots on the bottom. It was similar thinking (but actually simpler) that I was using in the example you are asking about.

Good luck with it.

X

Hi Daniel
This technique will only be worthwhile in a limited number of cases.
For an example where it wouldn't help at all, consider `1/2`.
If I multiply top and bottom by `2` (the denominator), I will get `2/4`. But so what? I just need to cancel and get back to `1/2`. I can do the multiplying, but it doesn't help me.
In the example that you are referring to, however, the 2 fractions become simpler since their denominators no longer have square roots.
Taking a simpler case:
`1/sqrt(3a)`
When I multiply top and bottom by `sqrt(3a)`, I get:
`1/sqrt(3a) xx sqrt(3a)/sqrt(3a) = sqrt(3a)/(3a)`
The process has "rationalized" the denominator.
Hope that makes sense.
Not sure if you made it to this page:
<a href="/exponents-radicals/5-multiplication-division-radicals.php">5. Multiplication and Division of Radicals (Rationalizing the Denominator)</a>
About half way down, it has a heading "Rationalizing the Denominator". In the examples, you will see a method of multiplying top and bottom so we get rid of the square roots on the bottom. It was similar thinking (but actually simpler) that I was using in the example you are asking about.
Good luck with it.

## Re: Multiplying top and bottom of a fraction

**Daniel** 12 Dec 2015, 03:17

Great, thanks

## Re: Multiplying top and bottom of a fraction

**Murray** 12 Dec 2015, 18:23

You're asking good questions, Daniel. All the best to you.

X

You're asking good questions, Daniel. All the best to you.

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