3. Multiplication and division

Lesson

We can rewrite repeated addition as multiplication. Let's try this problem to practice.

Answer the following:

a

Write this addition as a multiplication: 12+12+12+12+12+12+12+12

Worked Solution

b

Find the value of 8 \times 12.

Worked Solution

Idea summary

If we add something over and over, it's like having many groups of that number. When we have groups of something, we call that multiplication, and we use \times for multiplication.

6+6+6+6+6 is the same as 5 groups of 6, or 5 \times 6.

In this video we see how rows and columns (called an array), can be used to solve multiplication.

Which of these number sentences describe the array?

There may be more than one correct answer.

A

16 \times 8 =2

B

8 \times 2 = 16

C

16 \times 2 =8

D

2 \times 8 =16

Worked Solution

Idea summary

We get the same answer whichever way we look at our array.

We can also see how arrays can be used to solve division.

We can divide 84 by 6 by drawing 84 dots in 6 rows.

a

To work this out we can count groups of 6 until we reach 84.

But that could take a long time if we go 1 group of 6 at a time, so let's count up in larger groups.

If we first count 10 groups of 6, how many dots will we have used?

Worked Solution

b

How many dots are remaining when we take away the first 60?

Worked Solution

c

How many columns of 6 dots will we have in the group of 24?

Worked Solution

d

Here is the complete array.

Using this, what is 84 \div 6?

Worked Solution

Idea summary

We can use an array to show multiplication (groups of) and division (sharing into groups of), which helps us to write out the numerical problems.