# Tell me the WHY behind cross-multiplying to add and subtract fractions

## Recommended Posts

Dd has been bumped up a grade in math! Yea!

They are reviewing some 5th grade concepts, and she had to do a worksheet with cross-multiplying to add and subtract fractions with unlike denominators.

Easy to show her the procedure, but I don't know how to explain why it works (I can explain the denominator, it's the cross-multiplying I need words for).

As an aside, her curriculum shows two ways to do it--one involves little stacked boxes--never saw that before! Kinda like lattice multiplication--nice, but time consuming...

Anyway, I looked at Khan Academy and didn't see an explanation--website would be helpful. I can look it up in Saxon, just don't really want to....:001_smile:

##### Share on other sites

Basically, you are finding a common denominator, just not necessarily the lowest common denominator, by cross multiplying.

##### Share on other sites

It might be helpful to work out

a/b + c/d

a/b * (bd/bd) + c/d * (bd/bd)

##### Share on other sites

Try purplemath.com, that is our go to resource for an alternate explanation to our math text.

##### Share on other sites

If you are adding 1/2 and 1/3 then you are adding one donkey and one horse. You cross them and get mules, which can then be added together.

Or: you need both fractions to have a common denominator, so that each numerator is describing the same kind of slice of the whole. The quickest way to do that is to cross-multiply.

Laura

##### Share on other sites

If you are adding 1/2 and 1/3 then you are adding one donkey and one horse. You cross them and get mules, which can then be added together.

I like that.:thumbup:

##### Share on other sites

If you are adding 1/2 and 1/3 then you are adding one donkey and one horse. You cross them and get mules, which can then be added together.

Cute, but inaccurate. When you cross multiply, you're not changing what the thing is. Cross multiplying is just a shortcut way of converting the fractions to have a common denominator. 3/12 is still 1/4, but a mule isn't a donkey.

If she really understand *why* 3/12 is still 1/4, then the next step should be easy.

http://www.youtube.com/watch?v=NF57T60CSPs&p=44BA501E7C4A9124&playnext=1&index=2 has a really good explanation of converting fractions if you need help with that.

##### Share on other sites

DD just watched the part of MUS Epsilon and they called it the "rule of four". It was a very good explanation!

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.