Algebraic Expressions

SECTION 2.5. ALGEBRAIC EXPRESSIONS

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Here is an example using made-up money conversions:

Let's say 2 pounds = 1 dollar, and 1 pound = 150 yen, but you need to know how much 20 dollars is in yen.

You could blithely start out with this equation:

20 dollars * 1 dollar/2 pounds * 1 pound/150 yen = x

Is this the right equation?

Let's check the units...

dollars * dollars/pounds * pounds/yen = dollars²/yen

We get 'dollars squared over yen', not plain old yen. So, it can't be right. Let's try again using our cancellation method.

We want to go from dollars to yen via pounds. So, we start with dollars and convert to pounds.

dollars * pounds/dollars = pounds

Then we convert pounds to yen.

pounds * yen/pounds = yen

When we put this together, we get

dollars * pounds/dollars * yen/pounds = yen

This is what we want, so we just plug in the numbers and multiply it out.

20 dollars * 2 pounds/1 dollars * 150 yen/1 pound = 6000 yen/1 = 6000 yen

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