Topics
3. Integers
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Stage 3

3.03 Compare integers

Lesson
Practice
Lesson

Are you ready?

As we are about to compare positive and negative numbers, make sure you can first  order and compare positive  numbers. Try this question first.

Examples

Example 1

We want to work out which of 2 numbers is the biggest.

a

Plot 29 and 23 on the number line below:

202530
Worked Solution
Create a strategy

Work out how many units 1 space represents.

Apply the idea
202530

Since there are 5 spaces between 20 and 25, on the number line, each space represents 1 unit.

To plot 29, start at 25 and jump 4 spaces to the right.

To plot 23, we can start at 20 and jump 3 spaces to the right.

b

Write the two numbers from smallest to biggest.

Worked Solution
Create a strategy

The smaller a number is, the further to the left on a number line it is.

Apply the idea

We can see on the number line from part (a) that 23 is further to the left which means it is smaller than 29. So the numbers in order are:23,\, 29

Idea summary

When we compare two integers on a number line, the integer further to the right is always greater.

Compare integers

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Examples

Example 2

Neil enters an elevator at the 6th floor above ground (the ground floor being zero). The elevator goes down 3 floors, then up 8 floors and finally it goes down 4 floors.

a

Does Neil end up above or below the ground floor?

Worked Solution
Create a strategy

Use a number line to show the movement.

Apply the idea

This number line shows the upward direction of the elevator as going right (positive) and downward direction as going left (negative).

-5051015

Starting from 6, count 3 floors down (left).

-5051015

Move up (right) 8 floors.

-5051015

Jump back 4 floors down (left).

The point ended to the right side of the 0, which means the elevator is above the ground floor.

b

On which floor does he end up?

Worked Solution
Create a strategy

Use the final number line from part (a).

Apply the idea

In part (a) the last point was on 7 to the right of 0:

-5051015

So Neil ended up on the 7th floor above ground level.

Idea summary

As numbers decrease, they move to the left. You can use this to help you compare integers. Integers that are more to the left are less than numbers that more to the right on a number line.

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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