Chapter 2: Solving One-Step Equations and Inequalities

2.1

Properties of Numbers

Properties

• Commutative property of addition & multiplication:– Changing the order of the values you are adding or

multiplying does not change the sum or product

abba

6446

Properties

• Associative properties of addition & multiplication– Changing the grouping of the values you are adding

or multiplying does not change the sum or product

cbacba

372372

Example 1

• Carlos rented a set of golf clubs for $7 and a golf cart for $12. He paid a greens fee of $23. Find his total cost.

Properties

• Identity properties of addition & multiplication– The sum of any number and zero is the original

number– The product of any number and 1 is the original

number

Example 2• Name each property shown:

• 5 · 7 = 7 · 5

• c · 1 = c

• 7 + a = a + 7

• 5(xy) = (5x)y

Example 3

• Use mental math to simplify:

(81 + 6) + 9

Example 4

• Suppose you buy the school supplies, a highlighter for $.85, an eraser for $.35, and paper for $1.65. Use mental math to find the cost of the supplies.

Example 5

• Use mental math to simplify:

(4 · 9) · 5

Example 6

• Use mental math to simplify:

5 · 9 · 6 · (-2) · (-1)