Integer Arithmetic Review Sheet & Helpful Reminders
(How to Solve Problems with Signed Numbers)
Reminder: absolute value is defined as “the distance a number
is from zero”.
Just remember that distance can never be negative, so
absolute value means to use that number in its positive form.
Addition Rules:
1. Pos. + Pos. = Pos. (add & keep the same sign):
2. Neg. + Neg. = Neg. (add & keep the
same sign):
3. Pos. + Neg. = Answer takes the sign of
the larger #, Subtract the numbers
Examples:
2 + 8 = 10
-3 + -7 = -10
3 + -8 = -5
4. Neg. + Pos. = Answer takes the sign of
the larger #, Subtract the numbers
-3 + 8 = 5
Multiplication Rules:
1. Pos. x Pos. = Pos. (same signs =
pos. answer)
2. Neg. x Neg. = Pos. (same signs =
pos. answer)
3. Pos. x Neg. = Neg. (different signs =
neg. answer)
4. Neg. x Pos. = Neg. (different signs =
neg. answer)
Division Rules (same as Multiplication Rules):
1. Pos.  Pos. = Pos. (same signs =
pos. answer)
2. Neg.  Neg. = Pos. (same signs =
pos. answer)
3 x 8 = 24
-3 x-8 = 24
3 x -8 = -24
-3 x 8 = -24
24  8 = 3
-24  –8 = 3
3. Pos.  Neg. = Neg. (different signs =
neg. answer)
24 -8 = -3
4. Neg.  Pos. = Neg. (different signs =
neg. answer)
-24 8 = -3
Definition of Subtraction: Subtraction is defined as adding the
opposite.
(Reminder: opposites are numbers with opposite signs – they have the
same absolute value, they are just in different directions away from zero.)
Subtraction Rules:
1. 3 – 8 is the same as 3 + -8
2. –3 – 8 is the same as –3 + -8
3. 3 - -8 is the same as 3 + 8
4. –3 - -8 is the same as –3 + 8
(follow addition rule #3)
(follow addition rule #2)
(follow addition rule #1)
(follow addition rule #4)
SUMMARY:
1. Multiplication and division rules are the same: When
multiplying or dividing two numbers with the same signs, the
solution is positive; however, when multiplying or dividing two
numbers with different signs the solution is negative.
2. For addition and subtraction, all you have to learn is how to
change subtraction to addition properly. Then, follow the
addition rules. Same signs means add and keep that sign, but
different signs mean to subtract and keep the “sign of the larger
absolute value number”.
3. Shortcut Reminders:
 When you multiply or divide an even number of
negatives, the result is positive since all negatives
pair up with another one.
o Example: -2 x -2 x -2 x -2 = 16
o Example: -30 ÷ -3 ÷ -5 ÷ -1 = 2
o Example: -50 ÷ 5 x -2 ÷ 4 x 8 = 40
 When you multiply or divide an odd number of
negatives, the result is negative since there is one
negative left over after all others pair up and
become positive. The one left over changes the
whole result back to negative.
o Example: -2 x -2 x -2 = -8
o Example: -30 ÷ 3 ÷ -5 ÷ -1 = -2
Example: 8 x -3 ÷ 12 x -8 ÷ -4 = -4