Math Week 10

Topics

1. Multiplying Fractions
2. Dividing Fractions
3. Dividing Mixed Numbers

Multiplying Fractions

In my opinion, multiplying is the easiest operation to handle with fractions.  There’s 3 simple steps:

1. Multiply the Numerators
2. Multiply the Denominators
3. Simplifiy

Here’s an example:

Another way to think about multiplying by a fraction, is to think about dividing by it’s reciprocal.  A reciprocal is just the inverse of a fraction, so with the one-half above, it’s reciprocal would be  2 so

Here’s a visual representation what this would look like.

The more complex the fractions, the harder it is to visualize, but the concept is the same.  Multiply the top, multiply the bottom, simplify.

Now it is possible to simplify before multiplying, which to some is easier than simplifying after.    You look at the numbers that are diagonal  from each other, so in this case, the 6 and the 12, and the 10 and the 5.  If there is a common factor, you can divide them down before multiplying to simplify the multiplication as well.

Notice, that even though we simplified before, our results were same as when we simplified after.

The only other thing we now throw into the mix, is mixed numbers.  Remember these are when we have a whole number and a fraction.  You have to convert the mixed number into its fraction form, and then, the math is the same.

Dividing Fractions/Mixed Numbers

The students will be spending a couple of days learning the concept of dividing with just fractions before we throw in the mixed numbers, but the idea is  the same, so to save some time, I’m combining them into one lesson here.  There will be three days this week, making sure they completely understand it as this is the one new operation with fractions in the sixth grade core.

To put it into sixth grade terms, dividing fractions is gross, so we don’t do it.  Rather, than dividing by a fraction, we multiply by its reciprocal.  I began discussing this at the start of the multiplying sections, so I’ll just quickly review.   Remember, a reciprocal is just the inverse of the fraction.  Some kids like to say re”flip”rocal because to find the reciprocal, you just flip the fraction.

Once you understand the reciprocal, division is the exact same as multiplying.