What are Integers??

Many situations cannot be represented by whole numbers. You may need negative

numbers to show a loss, a temperature below zero, or an opposite direction.

Definition

• Integers are the counting numbers, their opposites, and zero.

• The counting numbers are the positive integers.

• Their opposites are the negative integers.

• Zero is neither positive nor negative.

• Absolute value is the distance on a number line from an integer to zero. Absolute values are always positive or zero.

• Pairs of integers with the same absolute value are called opposites.

Example: the opposite of -10 is 10, the opposite of 3 is -3.

Work with a Partner

• Discuss how zero compares with any negative number.

• Compare these integers:

-15 __ -20 -32 __ 4

12 __ -12 -50__ -40

RULES:

• ADDING A POSITIVE AND NEGATIVE NUMBER WILL EQUAL THE SAME TYPE OF NUMBER AS THE LARGER NUMBER.

• ADDING TWO NEGATIVE NUMBERS WILL EQUAL A NEGATIVE NUMBER.

• TO SUBTRACT TWO NEGATIVE NUMBERS, CHANGE THE SIGN OF THE SECOND NUMBER AND THEN SOLVE AS ADDITION.

• TO SUBTRACT A POSITIVE AND NEGATIVE NUMBER, CHANGE THE SIGN OF THE SECOND NUMBER AND SOLVE AS AN ADDITION PROBLEM.

PRACTICE

Order the following integers

-23, 48, -50, 22, -12

-3, 8, -16, 25, -30

18, -18, 0, 36, -6

PRACTICE

-8 + 13 =

-19 + 12 =

20 – 27 =

-8 – (-13) =