ShmoopTube

Where Monty Python meets your 10th grade teacher.

Search Thousands of Shmoop Videos

Multiplying Rational Expressions 2529 Views


Share It!


Description:

Multiplying rational expressions is as easy as adding the exponents and simplifying. Ta da!

Language:
English Language

Transcript

00:04

Multiplying Rational Expressions, a la Shmoop.

00:08

In the distant future, arguments between friends and roommates will be solved with math.

00:13

Today, we'll see how it might be used to solve a problem between two roommates on a space

00:17

station orbiting Jupiter.

00:19

Meet Xavier and Yumi.

00:27

Their dilemma is represented by the following...

00:30

4 x over 5 y squared times 20 x-squared y over y to the fourth.

00:36

Now let's talk about what they have in common.

00:39

Remember, usually when we multiply fractions, we multiply across top and bottom.

00:44

But when we see a chance, we can simplify first by canceling any duplicate factors.

00:49

Looking at our problem, we can see that the 20 in the top of the second fraction

00:53

and the 5 in the bottom of the first fraction are both factors of 5.

00:58

We can simplify by dividing 20 by 5 to get 4,

01:02

and divide the 5 on the bottom by 5 to get 1.

01:06

Looking at the second fraction, we can cancel the top y with the y to the fourth on the bottom...

01:13

leaving y to the power of three.

01:15

Now we can just multiply across the top of the two fractions...

01:18

4 x times 4 x-squared equals 16 x-cubed.

01:24

And multiply across the bottom... y-squared times y-cubed...

01:28

...remember that we multiply two terms with the same base, and we can add the two exponents...

01:34

in this case, the 2 and 3, to get y to the fifth.

01:38

So the answer is 16 x cubed over y to the power of 5.

01:42

And on the space station orbiting Jupiter, this result means that it's Xavier's turn

01:46

to take out the plutonium.

01:49

Don't forget to shut the airlock.

Up Next

Tangent Half-Angle Formula
1362 Views

Mosquitos need their caffeine, just like the rest of us. Wouldn't think zipping around and stinging people all day long sap your energy?

Related Videos

Simplifying Rational Expressions
1396 Views

Rational expressions are too complex... it's about time someone simplified them.

Operations with Rational Expressions
8687 Views

It's impressive that these expressions are able to stay so rational even when they're having operations performed on them.

SAT Math 4.5 Numbers and Operations
203 Views

SAT Math 4.5 Numbers and Operations