Study Guide:
Variables and Expressions

 

Any letter used to represent an unspecified number is called a variable.

You can use variables to translate verbal expressions into algebraic expressions.

 

Words

Symbols
4 more than a number
a number decreased by 8
the product of 5 and a number
a number squared
x + 4
b - 8
5 c
h2

 

The algebraic expression xn represents a product in which each factor is the same. The small raised n is the exponent and it tells how many times the base, x, is used as a factor.

Example: Evaluate: 34

34 = 3 × 3 × 3 × 3

= 81

 

 

Write a verbal expression for each algebraic expression.

1. w - 1 2. ⅓ a3 3. 81 + 2x

Write an algebraic expression for each verbal expression.

4. a number decreased by 5 5. four times a number
6. 8 less than a number 7. a number divided by 6
8. a number multiplied by 37 9. the sum of a number and 9
10. 3 less than 5 times a number

11. twice the sum of 15 and a number
12. 7 more than the product of 6 and a number 13. 30 increased by 3 times the square of a number

Write each expression as an expression with exponents.

14. 7 × 7 × 7 15. 3 × p × p 16. 9(b)(b)(b)(b)(b)

Evaluate each expression

17. 2 3 18. 10 5 19. 4 4