Multiplying and Dividing Integers

Grade 7: The Learning Equation Math

12.06 Multiplying and Dividing Integers

Refresher pp 34-5

The student will:

multiply integers concretely, pictorially, and symbolically.

Multiply the following numbers and remember the rules for multiplying integers. factor x factor = product
Question	Work	Sign	Answer
4 x 3 =	4 groups of is	Positive	4 x 3 = 12 The product of two positive factors is positive.
5 x -6 =	5 groups of is	Negative	5 x -6 = -30 The product of a negative and positive factor is negative.
-3 x 2 =	-3 groups of is the negative of which is	Negative	-3 x 2 = -6 The product of a negative and positive factor is negative.
-2 x -5 =	-2 groups of is the negative of which is	Positive	-2 x -5 = 10 The product of two negative factors is positive.
Note: Same signs the answer is positive. Different signs the answer is negative.

Lesson on Multiplication of Integers

Mulitplying Integers	Range
	-10 to 10
	-100 to 100
Hold down Shift and click the Reload button on your browser to try again. source: Subtraction 2

divide integers concretely, pictorially, and symbolically.

Divide the following numbers and remember the rules for dividing integers. Quotient � divisor = dividend
Question	Work	Sign	Answer
12 � 3 =	shared into 3 groups has 4 in each group.	Positive	12 � 3 = 4 The quotient of two negative numbers factors is positive.
30 � -6 =	30 � 6 is the opposite of 30 � (-6). Since 30 � 6 has 5 in each group, 30 � (-6) must have -5 in each group	Negative	30 � -6 = -5 The quotient of a positive and negative number is negative.
-15 � 5 =	divided into 5 groups has -3 in each group.	Negative	-15 � 5 = -3 The quotient of a positive and negative number is negative.
-10 � -2 =	divided into groups of -2 is is 5 groups of -2.	Positive	-10 � -2 = 5 The quotient of two negative numbers factors is positive. Note: I changed the method somewhat for this example. If I followed the previous examples we would need to work with negative groups: -2 groups x ____ in each group = -10 I switched to the following for this example because order of multiplication does not matter: -2 in each group x ____ groups = -10 Therefore -10/-2 in each group = 5 groups
Notice: Same signs the answer is positive. Different signs the answer is negative.

Lesson on Division of Integers

Dividing Integers	Range
	-10 to 10
	-100 to 100
Hold down Shift and click the Reload button on your browser to try again. source: Subtraction 2

multiply and divide integers with a scientific calulator.

Multiplying and Dividing Integer Calculations

You can calculate integer products and quotients on a scientific calculator. Use this calculator to check the learn the procedure, then make up your own examples.

Press Reload/Refresh if the calculator does not show properly.

Product/ Quotient	Calculator Input	Standard Name
8 x 4	8 4	32
-8 x 4	8 4	-32
8 x -4	8 4	-32
-8 x -4	8 4	32
8 � 4	8 4	2
-8 � 4	8 4	-2
8 � -4	8 4	-2
-8 � -4	8 4	2