 Multiply integers

Lesson

Sign of the times

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 the product is the answer when two numbers are multiplied together.

Do you know what's really great? Your knowledge of times tables will really help you through this chapter.

You already know that the product of two positive integers is a positive integer Examples

$4\times5=20$4×5=20

$45\times100=4500$45×100=4500

So we only have a couple of extra rules to add to this existing knowledge:

The product of a positive integer and a negative integer is a negative integer. Examples

$\left(-4\right)\times5=-20$(4)×5=20

$16\times\left(-10\right)=-160$16×(10)=160

The product of two negative integers is a positive integer. Examples

$\left(-4\right)\times\left(-5\right)=20$(4)×(5)=20

$\left(-15\right)\times\left(-4\right)=60$(15)×(4)=60

$\left(-6\right)\times\left(-8\right)=48$(6)×(8)=48

Multiplying three integers

We can multiply three integers, two at a time, using the same rules.

The Associative Law of Multiplication states that This means that you can multiply these three integers in any order.

Examples

question 1

Evaluate: $-4\times5\times10$4×5×10

Think: Working from left to right, we first want to find the product of a negative number and a positive number, and then multiply the result by another positive number. We know that the product of a negative number and a positive number is a negative number, so our answer will be a negative number.

Do:

 $-4\times5\times10$−4×5×10 $=$= $-20\times10$−20×10 $=$= $-200$−200

Did you follow me? Here's another example to make sure.

question 2

Evaluate: $-3\times3\times\left(-8\right)$3×3×(8)

Word problems using multiplication

Some multiplication questions are written as word problems, which we can write as algebraic expressions.

question 3

Evaluate: A number $n$n is multiplied with $-7$7 to give $-56$56. What is the value of $n$n?

Think: That expression means $-7\times n=-56$7×n=56

Do$n=8$n=8

question 4

Evaluate: A number $n$n is multiplied with $-3$3 to give $21$21. What is the value of $n$n?

Explore

The following applet shows you the area that is formed when multiplying and the sign of the answer, depending on the signs of the numbers used.