1.04 Multiply and divide integers
Introduction
We have looked at how to multiply whole numbers when they are positive. Now let's look at what happens when negative integers are included in questions. Remember that the product is the answer when two numbers are multiplied together.
Multiplication of integers
Exploration
The applet below allows us to select two integers to multiply by using the sliders to change the value and the check boxes to change the sign.
Blue tiles represent positive integers.
Orange tiles represent negative integers.
The product is shown as an array.
- What is the sign of the product of two positive integers?
- If you are looking at the product 3 \times \left(-4\right), how many tiles are in 3 groups of -4 tiles?
- What is the sign of the product of one positive and one negative integer?
- Is the product of 3 \times \left(-4\right) the same as -4 \times 3? Check this for other products.
- What is the sign of the product of two negative integers?
The product of two positive integers will result in a positive number, which is the same as that of two negative integers. In comparison, the product of one positive and one negative integer will result in a negative number.
Unlike adding and subtracting integers, where we can use the number line or counters, multiplication comes down to looking at the sign of factors.
If we are working with integers, we just need to determine what the sign will be, and then we can multiply the absolute values of the integers as we already know how to do.
Examples
Example 1
Find the value of: -4 \times 5
Example 2
Find the value of: -7 \times (-5)
If we are working with integers, we just need to determine what the sign will be, and then we can multiply the absolute values of the integers as we already know how to do.
Division of integers
The same principles that help us to multiply integers also apply to divide.
Exploration
Check that the rules for multiplication also work for division using the applet below.
The applet allows you to select two integers. The horizontal slider selects the divisor, the vertical slider selects the quotient, and the checkboxes change the sign of the integers.
- Blue tiles represent positive integers.
- Orange tiles represent negative integers.
- The dividend is shown as an array.
- What is the sign of the quotient of two positive integers?
- What is the sign of the quotient of two negative integers?
Same with multiplication, the quotient of two positive integers will result in a positive number, and it is also the same as the quotient of two negative integers. In comparison, the quotient of one positive and one negative integer will result in a negative number. The only difference between multiplication and division is that the division of two integers does not always results in another integer.
Examples
Example 3
Find the value of: 48 \div (-6)
Example 4
Evaluate: \dfrac{-60}{-10}