Study Guide: Integers and Integer Operations
Name:
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
Adding Integers
Model the addition of integers using zero pairs.
Zero Pair: the pairing of a positive with a negative; has a value of zero
1
2
3
represent each integer with counters
remove zero pairs
record value of remaining counters
Formulated Rules:
positive + positive = always positive
negative + negative = always negative
5+3=8
-5 + -3 = -8
positive + negative = ?
If there are more positives, the answer will be positive.
If there are more negatives, the answer will be negative.
5 + -3 = 2
-5 + 3 = -2
In other words…
1 identify the larger number
2 the sign (positive or negative) of the larger number will be the sign of the answer
3 subtract the numbers
Example:
12 + -15 = ?
Subtract
15 – 12 = 3
so the answer is -3.
Practice:
8 + -5 = ?
The larger numbers is 15,
which is negative… therefore,
the answer will be negative.
(Are there more positives or negatives?)
(How many more?)
Answer: ____
Subtracting Integers
Use the KISS method to turn the subtraction problem into an addition problem.
Then, add the numbers accordingly.
KISS = Keep It, Switch, Switch (add the opposite)
Examples:
10 – 18 = ____
-7 – 2 = ____
8 – (-7) = ____
-3 – (-11) = ____
10 + -18 = -8
-7 + -2 = -9
8 + (+7) = 15
-3 + (+11) = 8
Multiplying and Dividing Integers
Formulated Rules:
same signs (get along)
positive ∙ positive = positive
negative ∙ negative = positive
12 ∙ 4 = 48
-9 ∙ -3 = 27
different signs (do not get along)
negative ∙ positive = negative
positive ∙ negative = negative
-5 ∙ 6 = -30
2 ∙ -11 = -22
* Use same rules for division
10 ÷ 7 = 70
-8 ÷ -6 = 48
-9 ÷ 5 = -45
3 ÷ -6 = -18
Practice
Complete the following equations. Draw a picture to model some of your work!
1.
-3 + -10 = _____
2.
4 + -12 = _____
3.
-5 + -5 = _____
4.
2 – 8 = _____
5.
5 – (-4) = _____
6.
-13 – 3= _____
7.
3 ● (-5) = _____
8.
-2(-12) = _____
9.
-4 ● 8 = _____
10.
-72 ÷ 9 = _____
11.
55 ÷ (-5) = _____
12.
-24 = _____
-2