Fractions Multiplying by more interesting fractions and then

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

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

�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.

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

“John has saved 5/6 of the 72 dollars he needs. How much has he

“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: (72 is a whole number – so it’s all in one group. 72 ÷ 1 is… 72. )

60 Divide 72 by 6… then multiply by 5.

60 Divide 72 by 6… then multiply by 5.

�What would that *look* like?

�What would that *look* like?

If I divide that 72 dollars into 6 groups (as the denominator tells me

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

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

�So… 5/6 of 72 is the same as 1/6 of 72…which is 12… times

�So… 5/6 of 72 is the same as 1/6 of 72…which is 12… times 5, which is 60. 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.

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

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

�We could draw every fraction to check that out… or we could practice division…

�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?

Which of these fractions are the same as a half?

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

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

�But enough with the multiplying, already… time to cover a division problem that is

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

�Divided by doesn’t mean divided into… doesn’t me a fraction of. �If I say

�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: WATCH YOUR LANGUAGE!!!!!!!

6 ÷ 2 is 3 6÷ 3=2

6 ÷ 2 is 3 6÷ 3=2

6 / 6 is ONE.

6 / 6 is ONE.

What happens if I divide 6 by ½ ?

What happens if I divide 6 by ½ ?

How many *halves* can I get out of six whole oranges? After all, I’m

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

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:

And the way to get this without drawing everything is:

“Copy, Change, Flip” is the recipe…

“Copy, Change, Flip” is the recipe…

The concept is that if I divide by a big ol’ whole number, I

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

�You try drawing 5 ÷ 1/3

�Now to mix ‘em up… watch that language �½ of 50 ___ � 50

�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

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