Download Math 6 Multiply and Divide Integers

Multiplying & Dividing Integers
Multiplying AND Dividing Integers follow the same rules:
If the SIGNS are the SAME, the product or quotient is always POSITIVE.
(4)(8) = 32
− 5 ∙ −8 = 40
−81
28 ÷ 4 = 7
−9
=9
If the SIGNS are DIFFERENT, the product or quotient is always NEGATIVE.
−5(9) = −45
(3)(−4) = −12
27 ÷ −3 = −9
−60
12
= −5
If you are asked to perform repeated multiplication or division with integers, you must follow the order of
operations and work from the LEFT to the RIGHT.
−8 ∙ (−3) ∙ (−2)
(3)(4)(−1)(−5)
100 ÷ (−2) ÷ 5
24 ∙ (−2)
12(−1)(−5)
−50 ÷ 5
−48
−12(−5)
−10
60
YOU TRY IT: Find each product or quotient.
7(−5)
(−8)(−1)
45
−64
−9
−8
−8(−1)(−4)
−81 ÷ 3 ÷ 3
− 11 ∙ 12
−5 ∙ 3 ∙ −2
−5(−8)
−10
Multiplying & Dividing INTEGERS on Number Lines
Name: _________________________
Any time you see repeated arrows along a number line, you are looking at a multiplication or a division model.
It all depends on how you interpret the model verbally. See examples:
−6 ÷ 3 = −2
6 ÷3=2
Negative 6 divided into 3 groups
Each group has a value of -2
6 divided into 3 groups
Each group has a value of 2
_____________________________________________________________________
Negative 15 divided into 5 groups
−15 ÷ 5 = −3
Each group has a value of -3
_____________________________________________________________________
4 ∙ 6 = 24
OR
24 ÷ 4 = 6
(divide into 4 groups or 6 each)
6 ∙ 4 = 24
OR
24 ÷ 6 = 4
(divide into 6 groups of 4 each)
Modeling Integer Multiplication and Division
Directions: Draw a model for each problem on the number lines provided. Write the answer to each problem
on the blank space.
1)
−5 ∙ 4 = ________
2)
−15 ÷ −3 = _______
3)
3 ∙ 4 = ________
4)
−12 ÷ 4 = ________
Directions: Write a multiplication problem AND a division problem for each model given.
Number Line Model
Multiplication
Division
Multiplying & Dividing INTEGERS with Chip Models
Name: __________________________
*Just like number line models, integer chip models for multiplication and division are very similar.
See examples below:
−10 ÷ −5 = 2
Negative 10 divided into 5 negative chips each,
gives you 2 groups.
−10 ÷ 2 = −5
Negative 10 divided into 2 groups, where each
group has 5 negative chips.
______________________________________________________________________
-
−8 ÷ 4 = −2
Negative 8 divided into 4 groups, where each
group has 2 negative chips.
−8 ÷ −2 = 4
Negative 8 divided into -2 chips each, gives you
4 groups.
______________________________________________________________________
3(−2) = −6
3 groups of 2 negatives
−6 ÷ 3 = −2
6 negatives divided into 3 groups of -2 each
______________________________________________________________________
YOU TRY IT: Write a multiplication problem AND a division problem represented by the model below:
Multiplication: ____________________
Division: ____________________