Multiplying Integers Using Integer Chips
Concept
An integer is defined as a number that can be written without a fractional component. For example, 11, 8, 0, and −1,908 are integers whereas √5, Π are not integers. The set of integers consists of zero, the positive natural numbers, and their additive inverses.
The multiplication of integers is one of the basic operations performed on integers. Multiplication of integers is the same as the repetitive addition which means adding an integer a specific number of times.
When modeling integers, we can use colored chips to represent these integers. One color can represent a positive number and another color can represent a negative number. Here, a yellow chip will represent a positive integer and a red chip will represent a negative integer.
Rules
Case 1: Multiplying two positive integers
Create as many groups of the second number using yellow chips as indicated by the first number.
Case 2: Multiplying two negative integers
Create as many groups of the second number using red chips as indicated by the first number. Inverse the final answer as negative groups are the opposite of positive groups.
Case 3: Multiplying one positive and one negative integer.
i. If the first number is positive and second is negative, create as many groups of the second number using red chips as indicated by the first number.
ii. If the first number is negative and second is positive, create as many groups of the second number using yellow chips as indicated by the first number. Inverse the final answer as negative groups are the opposite of positive groups.
Example
Multiply.
-2 x -3
Solution
Case 2: Multiplying two negative integers
Create as many groups of the second number using red chips as indicated by the first number. Here we need to create -2 groups of -3. As we cannot create negative groups, we will create 2 groups of -3.
Inverse the final answer as negative groups are the opposite of positive groups.
-2 x -3 = 6 .
Practice Multiplying Integers Using Integer Chips
Practice Problem 1
Select the multiplication problem that is modeled below.
Create 5 sets of 3 positives
Practice Problem 2
Select the multiplication problem that is modeled below.
Create 2 sets of 3 negatives
Practice Problem 3
Select the multiplication problem that is modeled below.
Create 5 sets of 5 negatives
An integer is a number with no decimal or fractional part, from the set of negative and positive numbers, including zero.
Positive Integers: An integer is positive if it is greater than zero. Example: 1, 2, 3 . . .
Negative Integers: An integer is negative if it is less than zero. Example: -1, -2, -3 . . .
Integer chips – Are colored chips with signs. One color represents a positive number and another color represents a negative number.
Absolute value – the positive distance that a number is from 0 on a number line.
Additive inverses – two integers that are opposites.
Opposites – two integers that are the same distance from 0 on a number line but in opposite directions, like -5 and 5.
Pre-requisite Skills
Integers and Absolute Value
Order of Operations
Adding Integers
Subtracting Integers