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## Algebra Worksheets

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What is algebra?

Algebra is a method for finding answers to questions about how much, how often or how many.

It does this in two steps. The first step is changing a problem described in words into the same problem described by numbers and symbols. A kind of short-hand recipe that keeps the important information. The second step is using the rules of algebra to change the symbols and numbers around. Done correctly, this shuffling makes the problem easier to understand and answers the original question.

One of the key ideas is to use letters in place of numbers that aren't yet known. By using X or Y to stand in the place of something unknown (or something that can change) the algebraic expression can show us how things are related - even when we don't know exactly how many of those things we have.

Suppose you are interested in how many feet are on six dogs. (Maybe you want to buy them shoes?) You count the feet on one dog (4) and multiply by the number of dogs you have (6). The recipe looks like this: 4 x 6 = 24. Twenty-four feet total.

Algebra introduces the idea of variables. So that this one recipe (for six dogs) could be made into a more general recipe, or formula, for any number of dogs.

Put D for the number of dogs and F for the total number of feet. Then, you get the algebraic formula: 4 x D = F. This works for 6 dogs, or 20 dogs, or any number of dogs at all. It even works for zero dogs. But there is more. The rules of algebra allow us to shuffle the formula around. So, we could rearrange it to show how many dogs we would need to get a certain number of feet. F 4 = D.

How is algebra used in the real world?

Algebra is used to answer all sorts of questions.

• If gas costs X dollars a gallon, and I get Y miles per gallon, how much will it cost me to go a hundred miles?
• How long will it take to do my math homework if I can do X problems in an hour?
• If I can print Y pages a minute on my printer, how many pages can I print in a half-hour?
• If electricity costs X cents, and my computer uses Y amount of electricity, how much does it cost to leave my computer on all day?

A basic problem in algebra.

A common calculation people do is figuring out their mileage. They want to know how many miles per gallon their car is getting. If you asked, they probably wouldn't think of it as algebra, but it is.

In words, the problem is this: I used 15 gallons of gas to go 330 miles, how many miles am I getting per gallon?

Putting this into an algebraic formula (using M to stand for miles and G to stand for gallons) would look like this: M G = miles per gallon.

Using the actual numbers where the letters are gives the answer: 330 15 = 22. The neat thing is that no matter how many miles you drive or how many gallons of gas you use, the formula will still work.

Who invented algebra?

The roots of algebra go back more than a thousand years. Many of the ideas were around even longer, but in 800 AD, a Persian mathematician, Al-Khwarizmi, wrote a book which explained the methods clearly. He described the use of symbols and how to manipulate them in a regular fashion. So, although no one really invented algebra - it grew up over many centuries of problem solving - Al-Khwarizmi is considered one of the 'fathers of algebra'.