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Adding and Subtracting Integers Study Guide
Integers: are all whole numbers on the number line, including 0 and
negative numbers.
Positive Numbers: are all numbers that are greater than zero (+)
Negative Numbers: are all numbers that are less than zero (-)
Below is a number line.
Negative Numbers (-)
Positive Numbers (+)
________________________________________________________________________
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Integer: a counting number, zero, or the opposite of a counting number […2, -1, 0, 1, 2…]
NOT a fraction, decimal, or percent -2.5, ¾ , 35%
Integers are used to represent everyday situations in word problems.
positive situations
negative situations
above
below
deposit
withdraw
rise
fall
gain
loss
after
before
increase
decrease
Absolute Value
-The distance a number is from zero on the number line.
An absolute value is never negative.
Examples: l -5 l = 5 and l 5 l = 5
Adding Integers
Same signs – you add and keep the sign
Different signs – you subtract and take the sign of the larger number
NO OTHER CHANGES ARE MADE! DO NOT CHANGE ADDITION TO SUBTRACTION!
Examples:
-8 + (-2) = -10 same signs so you add and keep the negative sign
6 + (-3) = 3
different signs so you subtract and take positive sign since 6 is larger #
-7 + 5 = -2
different signs so you subtract and take negative sign since 7 is larger #
Subtracting Integers
You change subtraction to addition. Then follow the adding integers rules.
To change subtraction to addition: Use KCO – keep, change, opposite
1. Keep the first number the same. It does not change!
2. Change subtraction to addition.
3. Take the opposite of the next number.
Examples:
9 – 13 = 9 + (-13) = -4
17 – 7 = 17 + (-7) = 10
-2 – (-5) = -2 + 5 = 3
-10 – 2 = -10 + (-2) = -12
4 – (-11) = 4 + 11 = 15
change to
change to
change to
change to
change to
addition:
addition:
addition:
addition:
addition:
9 + (-13); different signs so subtract
17 + (-7); different signs so subtract
-2 + 5; different signs so subtract
-10 + (-2); same signs so add
4 + 11 = 15; same signs so add
Zero Pair: the pairing of a positive with a negative; has a value of zero
1
represent each integer with counters
2
3
remove zero pairs
record value of remaining counters
Example:
-2 + 6 +2 =
6