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) =
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