# Three digit Addition on a Number Line - Number Line

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## 3 Digit Addition with Regrouping on Number Lines

Addition and subtraction are taught in maths in the early stages. We are familiar with the addition or subtraction process from real life examples. Also, we do some mathematical operations like addition or subtraction at least a couple of times a day. In this learning text, we will show addition using the number line to add 3-digit numbers. This text will explain how number lines can visualise three-digit addition with regrouping. You can refresh your memory on how to create number lines for additions.

## Three Digit Addition with Regrouping on a Number Line – Explanation

The number line can help us to model an equation. In our examples, we use an open number line to show the movement while adding different amounts.

We are going to add two numbers: 306 and 262.

• Firstly, draw a number line and plot the larger number on the left-hand side of the drawn number line.
• Secondly, write the amount you are adding in expanded form.

Then, start adding starting with hundreds, jump by hundreds twice and plot the answer.

Now move to the tens and start jumping by tens six times and write the answer.

Finally, move to the ones and skip forwards twice and put the final answer.

Our solution from the addition of adding 306 to 262 is 568.

## Three Digit Addition with Regrouping on a Number Line – Practice Example

We are going to show another example of 3-digit addition with a regrouping of the open number line. This time we are going to add 568 and 143. We are going to follow the same steps:

• Firstly, draw a number line and plot the larger number on the left-hand side of the drawn number line.
• Secondly, write the amount you are adding in expanded form

• Then, start adding beginning with hundreds and jump by hundreds once and plot the answer.
• Then, move to the tens and start jumping by tens four times and write the answer.
• Finally, move to the ones and jump forward three times and put the final answer.

Our solution from the addition of 568 and 143 is 711.

## Three Digit Addition with Regrouping on Number Lines – Summary

To solve addition equations with regrouping we can model with an open number line and follow the steps:

Step # What to Do
1 Draw a number line and plot the larger lumber on the left-hand side.
2 Write the amount you are adding in expanded form.
3 Count forwards by the hundreds, tens and ones, plotting the number as you go.
4 The final number is the solution.

Now you should be able to show addition using the number line to add 3-digit numbers. Feel free to watch the video explaining the addition using an open number line to add 3-digit numbers, or complete the worksheet.

How do you add 3-digit numbers on a number line?
How do you add 4-digit numbers on a number line?

## Three digit Addition on a Number Line - Number Line exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Three digit Addition on a Number Line - Number Line.
• ### What is the expanded form of the number 555?

Hints

Look at the number 555.

• How many hundreds are in this number?
• How many tens are in this number?
• How many ones are in this number?

There are 5 hundreds in 555, which is 500.

As an example, 262 in expanded form is 200 + 60 + 2.

Solution

The expanded form of 555 is: 500 + 50 + 5.

There are:

• 5 hundreds or 500
• 5 tens or 50
• 5 ones or 5
• 500 + 50 + 5 = 555

• ### How do you use a number line for three digit addition with regrouping?

Hints

200 + 30 + 2 is the expanded form of 232.

• How many hundreds are in 232?
• Count forwards by two hundreds. One hundred has already been done for you.

200 + 30 + 2 is the expanded form of 232.

• How many tens are in 232?
• Count forwards by three tens.

200 + 30 + 2 is the expanded form of 232.

• How many ones are in 232?
• Count forwards by two ones.

In each box you should fill in either 100, 10 or 1.

Solution

First, write the number you are adding in expanded form. Then, count forwards on the number line in intervals.

Here we can see that 232 = 200 + 30 + 2.

• There are 2 hundreds so we count forwards by 100 twice.
• There are 3 tens so we count forwards by 10 three times.
• There are 2 ones so we count forwards by 1 twice.

347 + 232 = 579

• ### What is 443 + 321?

Hints
• First, write the number you are adding in expanded form.
• 341 in expanded form is 300 + 40 + 1.

Then, count forwards in steps of 100, 10 and 1.

Solution

443 + 321 = 764

321 = 300 + 20 + 1

• 443 + 300 = 743
• 743 + 20 = 763
• 763 + 1 = 764
Therefore 443 + 321 = 764.

• ### Solve 643 + 143.

Hints
• First, write the number you are adding in expanded form.
• How many tens do you need to add?

How many ones in 143?

Then, count forwards in steps of 100, 10 and 1.

Solution

643 + 143 = 786

143 = 100 + 40 + 3

• 643 + 100 = 743
• 743 + 40 = 783
• 783 + 3 = 786

Therefore 643 + 143 = 786.

• ### Which number line shows 333 + 222?

Hints

How many hundreds are in this number? There are two hundreds, so this choice is incorrect.

How many tens are in this number? There are two tens, so this choice is incorrect.

Solution

This number line shows 333 + 222.

• ### Find the solution for each addition problem.

Hints
• First, write the number you are adding in expanded form.
• The expanded form of 120 is: 100 + 20 + 0.
• Then, count forwards in steps on the number line.
• First, write the number you are adding in expanded form.
• The expanded form of 154 is: 100 + 50 + 4.
• Then, count forwards in steps on the number line.
Solution
• 242 + 120 = 362
• 172 + 154 = 326