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.


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.


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!


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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