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# Variable Expressions

## Letters representing numbers in arithmetic expressions

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Variable Expressions

What if you were at the supermarket and saw the price of a loaf of bread, but you weren't sure how many loaves you wanted to buy? How could you represent the total amount of money spent on bread without knowing the amount of loaves?

### Converting Words to Math

When someone is having trouble with algebra, they may say, “I don’t speak math!” While this may seem weird to you, it is a true statement. Math, like English, French, Spanish, or Arabic, is a second language that you must learn in order to be successful. There are verbs and nouns in math, just like in any other language. In order to understand math, you must practice the language.

A verb is a “doing” word, such as running, jumping, or driving. In mathematics, verbs are also “doing” words. A math verb is called an operation. Operations can be something you have used before, such as addition, multiplication, subtraction, or division. They can also be much more complex like an exponent or square root

#### Example 2

What variable would you use to represent the length in yards of fabric?

We often use the first letter of the word that the variable represents. Since we want to represent length, we could use l\begin{align*}l\end{align*}. We could also use y\begin{align*}y\end{align*} for yards, to be more specific. Either choice would be good in this case.

#### Example 3

Suppose bananas cost 0.29 each. Write an expression for the cost of buying a certain quantity of bananas. First we must choose a variable for the quantity of bananas purchased. What variable would you choose? One good choice is b\begin{align*}b\end{align*}, for banana. Now, it costs0.29 for each banana, so we multiply that by the number of bananas purchased:

0.29(b)\begin{align*}\0.29(b)\end{align*} #### Example 4 Suppose your bank account charges you a9 fee every month plus $2 for every time you use an ATM of another bank. Write an expression for the charges every month. The bank charges$2 for every ATM withdrawal from another bank. That means 2 times the number of times you use the ATM of another bank is the amount of money charged. What variable should you use to represent the number of ATM withdrawals from another bank? One good choice would be A\begin{align*}A\end{align*}, for ATM. So the charges for the ATM are represented as follows: 2(A)\begin{align*}2(A)\end{align*} But the bank also charges us a fixed9 every month, so we have to add that to the expression:

2(A)+9\begin{align*}2(A)+9\end{align*}

### Review

In 1–5, choose an appropriate variable to describe each situation.

1. The number of hours you work in a week
2. The distance you travel
3. The height of an object over time
4. The area of a square
5. The number of steps you take in a minute

In 6–10, write an expression to describe each situation.

1. You have a job earning $2000 a month 2. Avocados are sold for$1.50 each
3. A car travels 50 miles per hour for a certain number of hours
4. Your vacation costs you $500 for the airplane ticket plus$100 per day
5. Your cell phone costs $50 a month plus$0.25 for each text message

In 11–15, underline the math verb(s) in the sentence.

1. Six times v\begin{align*}v\end{align*}
2. Four plus y\begin{align*}y\end{align*} minus six
3. Sixteen squared
4. U\begin{align*}U\end{align*} divided by three minus eight
5. 225 raised to the 12\begin{align*}\frac{1}{2}\end{align*} power

To see the Review answers, open this PDF file and look for section 1.1.

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Color Highlighted Text Notes

### Vocabulary Language: English Spanish

operation

Operations are actions performed on variables, constants, or expressions. Common operations are addition, subtraction, multiplication, and division.

Variable

A variable is a symbol used to represent an unknown or changing quantity. The most common variables are a, b, x, y, m, and n.

Exponent

Exponents are used to describe the number of times that a term is multiplied by itself.

Operations

Operations are actions performed on variables, constants, or expressions. Common operations are addition, subtraction, multiplication, and division.

Square Root

The square root of a term is a value that must be multiplied by itself to equal the specified term. The square root of 9 is 3, since 3 * 3 = 9.