Math Smart by Princeton Review

Author:Princeton Review
Language: eng
Format: epub
Publisher: Random House Children's Books
Published: 2018-01-16T05:00:00+00:00

CHAPTER 5

Algebra

Algebra: An Overview

Math is used to understand numbers and quantities and their relationships. So far in this book, you have been using math to figure out amounts. For instance, how many pears does John have, how many hats are in Emily’s closet, things like that.

There is another way to use math, for a slightly different purpose—to describe mathematical relationships in a more abstract way. It is called algebra. Algebra is math that uses letters to represent numbers.

These letters are referred to as variables. It makes sense, because it means that the value for a letter varies; it isn’t fixed. When variables are combined and set equal to other variables or numbers, it is called an equation.

A formula is a specific type of equation that is used to represent a particular relationship between things.

Say I wanted to tell you that for every gift you give me, I will thank you 3 times. Use g for gift, and t for thank you. We’ll call it the politeness formula. You can use algebra to write a formula that expresses this relationship in math form.

3g = t

This means 3 times the number of gifts equals the number of thank yous. The 3 goes with the gifts because this is set up as an equation, which means that both sides are equal. To make them equal in this case, since according to the formula there are more thank yous than gifts, we had to multiply the gifts by 3 to equal the thank yous. For instance, 1 gift means 3 thank yous. To set them equal to each other, we need to multiply the gift by 3.

And how does 3g indicate three times the number of gifts? Do you remember that numbers in parentheses next to each other means multiply? Like (3)(–4) = –12.

In algebra you can put the variables right next to each other, or numbers right next to a variable, like 3g, and it means multiply. And by the way, in algebra, whenever a number is being multiplied by a variable, that number is called the coefficient. In this case, g has a coefficient of 3. When a variable appears to stand alone, this means it has a coefficient of 1.

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