Drill #2 The sum of 18, negative 8, and 5.5. The quotient of 82 and -4. The square of the product of 2 squared and 3. The difference of negative 16 and negative 5.

1-1 Variables and Expressions Objective: To translate verbal expressions into mathematical expressions and vice versa.

Variables** Definition: Symbols that are used to represent unspecified numbers. Any letter may be used to represent a variable. Examples: d r x t y a b c

Distance = rate * time If d = r * t complete the following table: d r ? 3 2 6 10

Algebraic Expression** An expression that contains at least one variable. Examples:

Factors and product** Factors: Quantities being multiplied. Product: The result of multiplication

Verbal Expression** An expression in English that represents an algebraic expression. Examples: Eight less than a twice a number. Twice a number decreased by eight. The difference of twice a number and eight.

Words for Addition Words for Subtraction More than Increased by The sum of Is added to Words for Subtraction Less than Decreased by The difference of Is subtracted from

Words for Multiplication The product of Twice (thrice) a number Is multiplied by Words for Division The quotient of Is divided by Fractions (e.g. one third = divided by 3)

Power, base, and exponent**

Representations of powers Symbols Verbal Expression Meaning 5 to the first power 5 5 to the second power or 5 squared 5 * 5 5 to the third power or 5 cubed 5 * 5 * 5 5 to the fourth power 5 * 5 * 5 * 5 3 times a to the fifth power 3 * a * a * a * a * a x to the nth power x * x * x … * x n times

What happens when we multiply powers? Why? When we take a power to a power?

Writing verbal expressions 5 + 10 = 15 (6 + 5) 7 2x + 7

Writing algebraic expressions Three times number a the third power A number t decreased by 6 Two more than twice a number x The quotient of r and s