When we solve addition and subtraction problems, estimating our answer gives us an idea of what to expect. In this video, we see how we can estimate the answer to addition or subtraction problems, using a number line to help us.

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Examples

Example 2

We want to estimate the answer to 258-26.

Round each of the two numbers to the nearest and then subtract them.

Worked Solution

Create a strategy

Use a number line to round each number to the nearest ten.

Apply the idea

Looking at the number line below, 258 is closer to 260 than to 250.

So 258 rounded to the nearest ten is 260.

Looking at the number line below, 26 is closer to 30 than to 20.

So 26 rounded to the nearest ten is 30.

To find 260-30 we can plot 260 on a number line and jump back by 30:

260 - 30 = 230

Find the value of 258-26.

Worked Solution

Create a strategy

Use a number line to subtract.

Apply the idea

Start at 258 and jump back 26 units.

258-26=232

Reflect and check

We can see that the answers are very similar, so the estimation of 230 was a good approximation for the actual answer of 232.

Idea summary

If we don't need an exact answer to a problem, we can use estimating to find out a close-enough answer. We can also use estimating to check our answers, so it is a great skill to learn.

Add and subtract three numbers

How can we solve a problem with more than one part? Have a look at this video to see some different ways to do this.

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Examples

Example 3

Find the value of 570+25+4.

Worked Solution

Create a strategy

Use a place value table to add the numbers.

Apply the idea

Write the digits in the place value table.

	Hundreds	Tens	Units
	5	7	0
		2	5
+			4
=

Add the digits in each place value column.

	Hundreds	Tens	Units
	5	7	0
		2	5
+			4
=	5	9	9

570 + 25 + 4 = 599

Idea summary

By adding in a different order, we may be able to use strategies such as Bridge to 10, to help us solve a problem. The number lines below show how we can solve 7 + 5 + 3 by changing the order, and still arrive at the same answer of 15.

Number lines showing addition of 7, 5, and 3 in two different orders. Ask your teacher for more information.

Outcomes

ACMNA073

Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems

ACMNA076

Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder

ACMNA083

Find unknown quantities in number sentences involving addition and subtraction and identify equivalent number sentences involving addition and subtraction

2.07 Estimation and multistep questions

Ideas

Are you ready?

Examples

Example 1

Add and subtract by estimating first

Examples

Example 2

Add and subtract three numbers

Examples

Example 3

Outcomes

ACMNA073

ACMNA076

ACMNA083

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