Teaching Notes 1.17: Multiplying Two Integers
A common problem students have when multiplying integers is not recognizing that the product
of two negative numbers is a positive number.Students may then incorrectly write a negative
sign instead of the positive sign in the product.- Explain that the product of a positive integer and a negative integer is a negative integer.
To illustrate, offer the following pattern:- − 1 × 3 =− 3
- − 1 × 2 =− 2
- − 1 × 1 =− 1
- − 1 × 0 = 0
- − 1 ×(−1)= 1
- − 1 ×(−2)= 2
- − 1 ×(−3)= 3
Explain that as the multiplier is decreasing by 1, the product is increasing by 1. The pattern
continues and each answer is one more than the one before it. Emphasize that a negative
integer multiplied by a negative integer results in a positive product.
- Review the rules and examples for multiplying integers on the worksheet with your students.
If necessary, review absolute values with your students in 1.14: ‘‘Finding Absolute Values and
Opposites.’’
EXTRA HELP:
Multiplication is commutative; numbers can be multiplied in any order.ANSWER KEY:
(1) 32 (2)− 20 (3) 6 (4)− 18 (5) 63 (6)− 84 (7) 80 (8)− 56 (9)− 27 (10) 60 (11) 4 (12)− 48
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(Challenge)Disagree. Explanations may vary. The statement is true sometimes but not always.
For example, the statement is true if two integers with the same sign are multiplied or if three
positive integers are multiplied. But when three or any odd number of negative integers are
multiplied it is not true.
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