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Integers and Absolute Value OBJECTIVE: 3-1 Integers and Absolute Value

VOCABULARY Integer: is any number from the set {…-3, -2, -1, 0, 1, 2, 3,…}where … means continues without end.

-4 -3 -2 -1 +1 +2 +3 +4 Zero is neither negative nor positive. Negative integers are integers less than zero. Positive integers are integers greater than zero. -4 -3 -2 -1 +1 +2 +3 +4

Integers that are greater than zero are called positive integers. VOCABULARY Integers that are greater than zero are called positive integers. Positive integers can be written with or without a + sign. +5 5 +10 10

Integers that are less than zero are called negative integers. VOCABULARY Integers that are less than zero are called negative integers. Negative integers are written with a - sign -5 -10 -100

VOCABULARY Opposite integers are the same distance from zero in opposite directions on the number line.

1. Graph -5 on the number line 2. Graph +2 on the number line EXAMPLE 1. Graph -5 on the number line 2. Graph +2 on the number line

1. Graph -3 on the number line 2. Graph +4 on the number line your turn 1. Graph -3 on the number line 2. Graph +4 on the number line

Write an integer to describe each situation: EXAMPLE Write an integer to describe each situation: The Dead Sea is 1,312 feet below sea level. Mt. Everest is 29,028 feet above sea level.

Write an integer to describe each situation: your turn Write an integer to describe each situation: The basketball player scored 18 points in the game. The scuba diver dove 400 feet below the surface of the water.

Write the opposite of each integer EXAMPLE Write the opposite of each integer 5. +4 6. 8 7. -3

Write the opposite of each integer your turn Write the opposite of each integer +6 12 -2

You can represent the integers from examples 1 and 2 on a number line. 4 units left 4 units right The numbers -4 and 4 are the same distance from 0, but on opposite sides of 0. So, -4 and 4 have the same absolute value.

The absolute value of an integer is the distance the number is from zero on a number line. │-4│ = 4

so Evaluate each expression. │-7│ = │5│ = 7 5 │- 5│ - │2│ = 5 – 2 = 3 │- 5│ - │2│ = 5 – 2 = 3 │- 9│ + │5│ = │26│ + │- 4│ = │- 10│ - 5 = 14 30 5

Carl is 14 (-14) feet below the surface. The surface is zero Carl is 14 (-14) feet below the surface. The surface is zero. Sawnose is 12 feet below Carl. Betty Crab is on the sea floor, 8 feet below Sawnose. Rockfish Larry is 7 feet above her. Jaws Daddy is 14 feet above Larry. Answer: 13 feet (-13)

Check for Understanding Study Guide 3-1

Homework Practice Sheet 3-1