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3.17 Multiples

Lesson

Are you ready?

Remember how we found that multiplication is the same as  repeated addition? 

Examples

Example 1

Write this addition as a multiplication: 3+3+3+3+3+3

Worked Solution
Create a strategy

We can rewrite this as a multiplication in the form: \text{Number of groups}\times\text{amount in each group}

Apply the idea

We have 6 groups of 3 so we can rewrite this as:3+3+3+3+3+3=6\times 3

Idea summary

We can rewrite repeated addition as a multiplication in the form: \text{Number of groups}\times\text{amount in each group}

Multiples

We're going to think about the relationship between repeated addition and the times tables, using a number line to help us understand multiples.

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Exploration

Drag the sliders to find the first 12 multiples of any numbers between 1 and 12.

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We can use our times tables to find multiples of a number. For example, the 6th multiple of 5 is 6\times 5=30.

Examples

Example 2

Write down the 7th multiple of 3.

Worked Solution
Create a strategy

Multiply the numbers together.

Apply the idea

The 7th multiple of 3 can be written as:

\displaystyle 7\times 3\displaystyle =\displaystyle 21Multiply 7 by 3
Idea summary
  • A multiple is the result of a number being multiplied by an integer.

  • A common multiple is a multiple of more than one number.

  • The lowest common multiple is the first multiple that is common to two numbers.

Outcomes

MA3-4NA

orders, reads and represents integers of any size and describes properties of whole numbers

MA3-6NA

selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation

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