Homework help 4: multiplying and dividing fractions

If you can reduce fractions, and you can draw a straight line, you can multiply and divide fractions.

Honest.

Let’s look at

To multiply, extend the fraction bar across the middle, and multiply tops with tops and bottoms with bottoms. (There’s a little bum-shaking dance that goes “tops-tops / bottoms-bottoms / multiply across”, that I’ll let you picture for yourself.)

So: which cannot be reduced.

Simple!

If we have something like: 

We notice this can be reduced by dividing top and bottom by 21 to get

We could have reduced earlier in the problem.  Back when it said

Notice how the 7 and 14 have something in common (both divide by 7)? And the 6 and the 15 have something in common (both divide by 3)?

This is important – when multiplying fractions, ANY top can reduce with ANY bottom.  They don’t have to be in the same fraction.

SOOO – we could have done this problem by saying

Notice you get the same answer either way.  Reducing at the front or reducing at the end – as long as the arithmetic is correct, the answer is the same.  YAY MATH!

Now, division is just an extra step on the FRONT of a multiplication problem.  If you see a division symbol, first you flip the SECOND fraction, and then you turn it into a multiplication problem.

For example:

Notice that I DID NOT cancel the 3 and 30 in the first step, even though one was in the top, and one was in the bottom.  You can only cross-cancel (reduce in the front) in a MULTIPLICATION step.  Not a division step.  It’s bad form.

This makes a great place to point out that any number written over 1 is itself and vice versa.  (Huh?)  I like to say that you can put the “pants” on any number.  So if I’m trying to do fraction math and the number 4 pops up in a problem, I can “put his pants on” and re-write him as 4/1.  It’s the same thing, and much easier to keep the numerators and denominators straight.

Final example, putting it all together:

Great job!!  Next up – adding and subtracting fractions!

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5 Comments on “Homework help 4: multiplying and dividing fractions”

  1. I can’t stop doing the math bum-shaking dance! I can’t WAIT to embarrass my daughter by teaching her this.

  2. PragmaticMom says:

    Thanks! This is perfect for my 7th grade daughter who hates math!

  3. Ann says:

    More, more!!! Thanks for this refresher!!!


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