A 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.
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?