MAT 030/060 – Lesson 15
Integers (negative and positive whole numbers)
 Numbers greater than zero are called positive numbers.
 Numbers less than zero are called negative numbers.
 Zero is neither a negative nor a positive number.
To represent a negative number, you must write a negative sign in front of the
number: -12 -3 -217
If a number does not have a sign in front of it, it is assumed to be a positive
number.
 Two numbers that are the same distance from zero on the number line
but on opposite sides of zero are called opposites or additive inverses.
-4 and 4 are opposites
17 is the additive inverse of -17
 The absolute value of a number is the distance between zero and that
number on the number line; therefore, the absolute value of a number
is a positive number. The symbol for absolute value is | |
|5| = 5
|−18| = 18
|33| = 33
|−112| = 112
 If there is a negative sign before the absolute value sign, read “the
opposite of”
-|12| reads “the opposite of the absolute value of 12” which = -12
-|−27| reads “the opposite of the absolute value of -27 which = -27
Adding and subtracting integers
Rule for Adding Two Integers
 To add integers with the same sign, add the numbers and keep the
sign.
 To add integers with different signs, find the difference between the
numbers, and attach the sign of number with the larger absolute value.
Examples:
127 + 28 = 155
-6 + 13 = 7
-15 + (-67) = -82
The difference between 6 and 13 is 7
The larger absolute value of these two numbers is 13
Attach a positive sign to the answer (we don’t normally
write a positive sign)
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162 + (-247) = -85
The difference between 162 and 247 is 85
The larger absolute value of these two numbers is 247
Attach a negative sign to the answer
Practice:
-162 + 98 =
-2 + (-7) + 4 + (-6) =
-154 + (-37) =
-5 + (-2) + 9 + (-3) =
Rule for Subtracting Two Integers
 To subtract two integers, change the subtraction sign to addition,
Change the sign of the second number to its opposite and follow the
rules for addition of integers
Examples:
8 – 15
8 + (-15)
Change the subtraction sign to addition and change the sign of
the 15.
7
Follow rules for addition: the difference between 8 and 15
-7
The larger absolute value of the two numbers is 15, so attach
– sign.
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13 – (-24)
13 + 24
Change the subtraction sign to addition and change the sign
of the 24
37
Follow rules for addition
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(-15) – 75
(-15) + (-75)
Change the subtraction sign to addition and change the
sign of the 75
- 90
Follow rules for addition
Practice:
(-12) – 8 =
3 – (-15) =
-8 – 30 – (-12) -7 =
4 – (-3) – 12 – (-7) – 20 =
Rule for Multiplying and Dividing Two Integers
 To multiply and divide numbers with the same sign, the answer is
positive
 To multiply and divide numbers with different signs, the answer is
negative
Examples:
4 · 8 = 32
(-4)(-8) = 32
27 ÷ 9 = 3
-27 ÷ (-9) = 3
-4 · 8 = -32
(4)(-8) = -32
-27 ÷ 9 = -3
27 ÷ (-9) = -3
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Practice:
(-3)(-5) =
-42 · 62 =
-7(-8)(9)(-2) =
(-120) ÷ (-8) =
-81 ÷ 3 =
112 ÷ 2 =
-5(-4)(6)(-3) =
95 ÷ (-5) =