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Algebraic Expressions

Algebraic Expressions

At a Glance - How to Solve a Math Problem

We've been doing this solving thing all along; this part is a little refresher. If you've been performing different steps or doing them in a backwards order...oopsies.

There are only three steps to solving a math problem.

1. Figure out what the problem is asking.
2. Solve the problem.
3. Check the answer.

Finito. That's it.

Sample Problem

If M denotes miles and K denotes kilometers, here are the conversion rates between M and K:

K = 1.609M
M = 0.6214K

The distance from Jenny's house to her parents' house is 500 miles. In fact, that was the most attractive selling point. How many kilometers is this?

Let's work through the steps.

1. Figure out what the problem is asking.

We want to find a number in kilometers that represents the same distance as 500 miles.

2. Solve the problem.

We need to use one of the two given formulas, and we need to be careful to use the right one. Since the problem gave a number of miles and we want a number of kilometers, we need to use the formula K = 1.609M.

We substitute 500 for M, and evaluate to get K = 1.609(500) = 804.5 kilometers.

For Jenny, that sounds even better than 500 miles. She'll need to remember to mention this 804.5 kilometers thing to her mother the next time she explains why she can't make it for Thanksgiving.

3. Check the answer.

First of all, is the answer reasonable? We didn't get a ridiculous number of kilometers or get an answer in furlongs, did we?

We want a distance, so we know the answer had better not be negative. Yep, 804.5 isn't negative, which is reassuring. The number of kilometers it takes to travel a certain distance is bigger than the number of miles it takes to travel that distance—this is something you eventually get a feel for if you pay enough attention to maps—so the answer should be bigger than 500. Yep again, 804.5 is bigger than 500, which is also reassuring. Doesn't it feel good to be this reassured?

Is the answer right?

If it's right, then when we substitute 804.5 for kilometers in the second formula, we should calculate 500 miles.

0.6214(804.5) = 499.9163

That's about 500. Since most of these conversion formulas aren't exact, we can be fairly confident that we have the right answer. Jenny had better not let her mom see that 499.9163 number, though. Talk about giving her unnecessary ammunition.

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