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Multiplying top and bottom of a fraction [Solved!]

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

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

Great, thanks

X

Great, thanks

Re: Multiplying top and bottom of a fraction

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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