# Writing and Evaluating Expressions

variable is a letter or symbol that represents a quantity that can change.   The most common variables are x, y, and z.

A constant is a quantity that doesn’t change.

An algebraic expression is a variable or combination of variables, constants, numbers, and operations.

Examples:

Consider the expression: x2 + 5y + 3x + 6

• The variables are x and y
• There are 4 terms: x2, 5y, 3x, and 6
• The terms that involve a variable are variable terms and 6 is a constant
• The numbers in front of the variables are called coefficients.   The coefficient of x2 is 1.   The coefficient of 5y is 5.   The coefficient of 3x is 3.
• The expression is the sum of all 4 terms

When you write an expression, you are writing them how you would write regular numbers in a word problem. Here are examples.

• “the sum of 8 and y” translates to “8 + y”
• “4 less than x” translates to “x – 4”
• “x multiplied by 13″ translates to “13x”
• “the difference of 5 and y” translates to “5 – y”
• “the quotient of 9 more than x and x” translates to “(x + 9)/x”

Practice writing expressions.

1) The rental fee for a bike is \$10 plus \$3 for each hour the bike is used. How much will it cost if you rent the bike for a certain number of hours? Write the expression that would give you the cost.

You are going to pay \$10 plus \$3 per hour.
\$10 + \$3h

To evaluate an expression, we substitute a value in for the variable.
How much would it cost to rent the bike for one hour or for five hours?

\$10 + \$3h
Put 1 in for h.
10 + (3 × 1) = 10 + 3 = \$13

\$10 + \$3h
Put 5 in for h.
10 + (3 × 5) = 10 + 15 = \$25

## Evaluate these Expressions

1) 4b + 12 for b = 9  That’s four times b plus twelve.

2)  2x² + 5x – 6 when x = 3

3)  s² – 15 for s = 5

4)  a/7 for a = 56

5)  3h + 2 for h = 10

6)  The formula for finding the Volume of a rectangular prism can be stated as V = lwh,

where l = length of the prism, w = width of the prism, and h = height of the prism.

What is the Volume of a prism with l = 33, w = 47, and h = 15?

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