Fractions: Multiplying by more interesting fractions – and then DIVIDING by them. (Part Two)

To find 1/8 of something, we divide that thing by 8. What if we wanted to know what 3/8 of something was?

You’d be doing the same thing 3 times, so you would multiply by 3.

(72 is a whole number – so it’s all in one group. 72 ÷1 is… 72.) “John has saved 5/6 of the 72 dollars he needs. How much has he saved? How much does he still need to save?” … Of means multiply, so this problem will look like this:

Divide 72 by 6… then multiply by 5. 60

What would that *look* like?

If I divide that 72 dollars into 6 groups (as the denominator tells me to do), then each “1/6” will have 12 dollars. 6/6 of 72 will be 6 out of six… the whole thing. 6/6 is 1… 1 x 72 is 72.

5/6 is going to be most of the money… 5 x 12 or 60 dollars. 5/6 is going to be most of the money… 5 x 12 or 60 dollars.

Of means multiply… BUT if you multiply by a fraction that’s smaller than one, you don’t have your “whole thing” – so your answer will be smaller. So… 5/6 of 72 is the same as 1/6 of 72…which is 12… times 5, which is 60.

It would be the same as ½. How much would 3/6 of 72 be?

We could draw every fraction to check that out… or we could practice division… but if the numerator is half of the denominator, then the fraction is equivalent to ½.

Which of these fractions are the same as a half?

How could you tell which ones were *more* than a half?

Dividing by fractions But enough with the multiplying, already… time to cover a division problem that is much easier to understand when you can see it.

WATCH YOUR LANGUAGE!!!!!!! Divided by doesn’t mean divided into… doesn’t me a fraction of. If I say 6 ÷ 6, my answer will be the number of times I can get six away from six, which is ONE WHOLE TIME. As a fraction, that would look like this:

6 ÷ 2 is 3 6 ÷ 3 = 2

6 / 6 is ONE.

What happens if I divide 6 by ½ ?

How many *halves* can I get out of six whole oranges? After all, I’m just not that hungry…

No matter how I slice ‘em (as long as they’re in half), I’ll get 12.

In math, this looks like In math, this looks like

And the way to get this without drawing everything is:

“Copy, Change, Flip” is the recipe…

The concept is that if I divide by a big ol’ whole number, I get smaller… but if I divide by a little piece, I can spread things out further so I get bigger.

You try drawing 5 ÷ 1/3

Now to mix ‘em up… watch that language ½ of 50 ___ 50 ÷ ½ = ___ 1/3 of 18 = ____ 18 ÷ 1/3 = ____

Next stop… adding fractions… but don’t forget – OF means MULTIPLY