ShmoopTube

00:03

Gettin' shmoopy with it...shmoopy with it... Woo-hoo woo-hoo.

00:08

Sorry. We try to be way too cool.

00:10

Simplify: 4 minus 2/3 all over 3/4 plus 5/8.

00:15

And here are the potential answers...

00:21

Whoa. We've got fractions on fractions on fractions.

00:26

No need to feel overwhelmed though. We just have to pick this one apart piece by piece.

00:30

The big skill set being tested here is all about common denominators.

00:34

So for starters we just add 3/4 and 5/8. The common denominator here should be clear...

00:40

all we have to do is turn that 4 into an 8 and we're all good.

00:44

We make 3/4 into 6/8... and 6/8 plus 5/8 is 11/8.

00:49

Now to the numerator, where we have 4 minus 2/3.

00:52

4 is the same as 4 over 1... so we can multiply top and bottom by 3 to get a common denominator...

00:59

...and we have 12 over 3 minus 2 over 3 to get 10 over 3 in the numerator.

01:07

So the simplified problem thus far looks like this:

01:10

Now remember that dividing by a fraction is the same as multiplying by its inverse.

01:15

So we multiply 10 over 3 by 8 over 11 to get 80 over 33.

01:22

Oh joy -- we have a 33 in the denominator in the answer set.

01:26

To get our mixed number, we reduce... 33 goes into 80 twice 14 leftover... that is, it reduces

01:37

to 2 and 14/33.

01:42

The answer is B.

01:44

As in "Bling."

Full Transcript