Name __________________________________ Date __________________ Hour ________ Honors Alg. 1

1-1 Variables and Expressions

A ____________________________ consists of sums and/or products of numbers and variables. In the algebraic

expression 0.10𝑑, the letter 𝑑 is called a variable. In algebra, ___________________ are symbols used to represent

unspecified numbers or values. Any letter may be used as a variable.

0.10𝑑 2𝑥 + 4 3 +𝑧

6 𝑝 ∙ 𝑞 4𝑐𝑑 ÷ 3𝑚𝑛

A _________ of an expression may be a number, a variable, or a product or quotient of numbers and variables. There

are two separate sub-sets of terms, depending on what they contain:

2𝑥 + 4

In a multiplication expression, the quantities being multiplied are ______________ and the result is the _____________.

A raised dot or set of parentheses is often used to indicate a product. Many products do not contain any notation that

they are in fact a product.

𝑥𝑦 𝑥 ∙ 𝑦 𝑥(𝑦) (𝑥)𝑦 (𝑥)(𝑦)

An expression like 𝑥𝑛 is called a _____________. The word power can also refer to the exponent. The _______________

indicated the number of times the base is used as a factor. In an expression of the firm 𝑥𝑛, the ______ is 𝑥. The

expression 𝑥𝑛 is read “𝑥 to the 𝑛th power.” When no exponent is shown, it is implied to be _____.

Let’s begin by translating algebraic expressions to English descriptions.

Examples 1. 3𝑥4 2. 5𝑧4 + 16 “three times 𝑥 to the fourth power”

3. 16𝑢2 − 3 4. 1

2𝑎 +

6𝑏

7

Goal 1: Write Verbal Expressions

You also need to know some key English words which represent specific Algebraic operations. You are given the

following bank of English phrases. Match each of them to an Algebraic operation and fill them in to the corresponding

row.

Bank: more than of product of quotient of sum plus difference minus divided by times increased by less than subtracted from added to decreased by multiplied by divided by”

Operation English phrase

Addition

Subtraction

Multiplication

Division

Let’s finish by putting it all together: write an algebraic expression for each verbal (English) expression.

Examples 5. a number 𝑡 more than 6 6. 10 less than the product of 7 and 𝑓 6 + 𝑡 or 𝑡 + 6 7. two thirds of the volume 𝑣 8. Mr. Martinez orders 250 key chains printed with his athletic team’s logo and 500 pencils with its web address. Write an algebraic expression that represents the cost of the order. Let 𝑘 be the cost of one key chain, and 𝑝 be the cost of one pencil.

Goal 2: Write Algebraic Expressions