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 represent each integer with counters
2 remove zero pairs
3 record value of remaining counters
Formulated Rules:
positive + positive = always positive 5 + 3 = 8
negative + negative = always negative -5 + -3 = -8
positive + negative = ?
If there are more positives, the answer will be positive. 5 + -3 = 2
If there are more negatives, the answer will be negative. -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 = ?
(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 = ____ 10 + -18 = -8
-7 – 2 = ____ -7 + -2 = -9
8 – (-7) = ____ 8 + (+7) = 15
-3 – (-11) = ____ -3 + (+11) = 8
Multiplying and Dividing Integers
Formulated Rules:
same signs (get along) different signs (do not get along)
positive ∙ positive = positive negative ∙ positive = negative
negative ∙ negative = positive positive ∙ negative = negative
12 ∙ 4 = 48 -5 ∙ 6 = -30
-9 ∙ -3 = 27 2 ∙ -11 = -22
* Use same rules for division
10 ÷ 7 = 70 -9 ÷ 5 = -45
-8 ÷ -6 = 48 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