# Three digit Subtraction with Regrouping

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## Subtraction with Regrouping Hundreds

There are lots of different methods to solve subtractions when working with 3 digit numbers. This video shows how to solve subtraction with 3 digit numbers on a number line.

## Subtraction with Regrouping Hundreds – Number Lines

To help solve a 3 digit subtraction with regrouping, we can model with a number line. Open number lines are helpful because they allow us to see the movement while taking away an amount during subtraction.

These are the steps you need to keep in mind when subtracting from 3 digit numbers using number lines:

Step # What to do
1 Draw the number line and plot the larger number
in the equation on the right side.
2 Write the second number in the equation, or
the amount taken away, in expanded form.
3 Skip count back by the hundreds, tens,
then ones of the second number,
plotting the answers as you go.
4 The final number you land on is the solution.

## Subtraction with Regrouping Hundreds – Example

Let’s look into how to subtract 3 digit numbers. We use the example of four hundred and thirty two minus one hundred and fifty six to illustrate how to use open number line subtraction with 3 digits. First, draw a line and plot the larger number in the equation on the right side.

Then, write the second numbers in the equation, or amount we are taking away, in expanded form. One hundred and fifty-six becomes one hundred plus fifty plus six.

Beginning with the hundreds, count back each hundred and plot the answer, three hundred and thirty two.

Then, move to the tens and count back for each ten. Plot the answer, two hundred and eighty two.

Finally, move to the ones and count back for each of the ones. Two hundred and seventy-six is the number we end up on, so this is our solution!

## Subtraction with Regrouping Hundreds – Summary of Steps

These are the steps you need to keep in mind when subtracting from 3 digit numbers using number lines:

• First, draw the number line and plot the larger number in the equation on the right side.

• Next, write the second number in the equation, or the amount taken away, in expanded form.

• Next, count back in the hundreds, tens, then ones of the second number, plotting the answers as you go.

• The final number you land on is the solution.

## Subtraction with Regrouping Hundreds – Worksheets

Have you practised 3 digit subtraction on number line worksheets yet? On this website, you can find worksheets and interactive exercises where you can become even more confident in 3 digit subtraction with regrouping.

### TranscriptThree digit Subtraction with Regrouping

Sir Squeaks and Imani have travelled back in time to the Middle Ages where they meet King Theodore. He is extremely upset because someone has stolen from his vault! Many jewels and coins are missing. He doesn’t know how many were taken, so Sir Squeaks and Imani will help him using three-digit subtraction on a number line. Remember, number lines are useful tools that help us model equations. We can use an open number line to see the movement whilst taking away an amount during subtraction. Let's use four hundred and thirty-two minus one hundred and fifty-six as an example. First, draw a line and plot the larger number on the right-hand side. Then, write the amount we are taking away in expanded form. One hundred and fifty-six becomes one hundred plus fifty plus six. Beginning with the hundreds, count back each hundred and plot the answer, this gets us to three hundred and thirty-two. Then, move on to the tens, skip count back for each ten and plot the answer, two hundred and eighty-two. Finally, move on to the ones and count back for each of the ones. Two hundred and seventy-six is the number we end up on so this is our solution! King Theodore knows that he had two hundred and fifteen jewels, now two hundred and six are left. Let's use a number line to help calculate how many were taken. Let's begin by drawing our number line and plotting two hundred and fifteen on the right-hand side. Next, we write two hundred and six in expanded form, two hundred plus zero plus six. Beginning with the hundreds, count back one hundred, then two hundred and plot the answer, fifteen. Next, move to the tens. Since there are no tens we have nothing to count so we move on to the ones and count back one, two, three, four, five, six! Plot nine since we finished there. Nine is our solution. Sir Squeaks reports that nine jewels were stolen from the vault. King Theodore also had five hundred and twenty-five coins and now four hundred and eighty-five are left. What are our steps? First, draw the number line and plot five hundred and twenty-five on the right-hand side. Secondly, write four hundred and eighty-five in expanded form- four hundred plus eighty plus five. Now begin to count back for each hundred: one hundred, two hundred, three hundred, four hundred and write the answer, one hundred and twenty-five. Where do we count next? We count the tens and count back eight tens until we reach and plot forty-five! What happens next? We count back the ones: one, two, three, four, five! We finished on forty so write it here. Forty is our solution. So, Imani reports that forty coins were taken from the vault! Wait, who is this? Before we find out, let's summarise! Remember, to help solve subtractions, we can use an open number line. First, draw the number line and plot the larger number on the right-hand side. Secondly, write the amount to be taken away in expanded form. Thirdly, skip count back, first by the hundreds, then the tens, then the ones, plotting the answers as you go. The final number plotted is the solution. "I'm so glad you're back! There has been a theft!" "About that...you see, I was trying out a new invisibility spell this morning when I was called away for an emergency. But I'm back now and it's as simple as..."

## Three digit Subtraction with Regrouping 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 Subtraction with Regrouping.
• ### Missing golden coins.

Hints

How do we partition 137 into hundreds, tens and ones?

Look at how the number to subtract has been partitioned and written in expanded form.

Which number line counts back in hundreds, then tens, then ones?

Solution

This is the correct solution, as the number 137 has been correctly partitioned and written in its expanded form of 100 + 30 + 7.

• ### Help Imani and Mr. Squeaks.

Hints

This image shows the first and second steps to be taken when solving a subtraction using a number line.

What happens after the smaller number has been written in expanded form?

Solution

The correct order of the steps to solve a subtraction on a number line is:

• First, draw the number line and plot the larger number on the right side.
• Write the amount to be taken away in expanded form.
• Count back along the number line in hundreds, then tens, then ones, plotting the answers as you go.
• Look at the final number you plot, this is the solution.

• ### How many gems were taken?

Hints

Once you have put the larger number on the right side, partition the smaller number into the expanded form and count back.

What will 123 be when written in expanded form?

Count back in the hundreds first, then the tens, then the ones, plotting your answers along the way.

Solution

The steps to solve this are:

• First write the larger number, 235, on the right side.
• Next partition the smaller number, 123, and write in expanded form as 100 + 20 + 3.
• Count back first the hundreds and plot the answer, which is 135.
• Count back the tens and plot the answers, first 125 then 115.
• Count back the ones - there are 3 - so plot the answer of 112.
• 112 is the final number plotted so this is the answer.
• ### Help Mr. Squeaks and Imani.

Hints

Try drawing your own number line, putting the larger number on the right, writing the smaller number in expanded form, and then subtracting.

First subtract by counting back in hundreds, then tens, then ones.

Solution
• 432 - 156 = 276
Start at 432, count back one hundred to reach 332, count back five tens to reach 282, and finally, count back six ones to reach 276.
• 354 - 131 = 223
Start at 354, count back one hundred to reach 254, count back three tens to reach 224, and finally, count back one to reach 223.
• 642 - 371 = 271
Start at 642, count back three hundreds to reach 342, count back seven tens to reach 272, and finally, count back one to reach 271.
• ### Stolen crystals.

Hints

Look at how the number has been written in expanded form; first, the hundreds have been subtracted. What is 350 - 100?

From 250 another 100 is subtracted. What is 250 - 100?

Count back in steps of ten from 250.

Make sure to count back in ones for the last part of the subtraction problem.

Solution
• 350 - 225 = 125.
• 350 is the larger number and so is written on the right side of the number line.
• 225 is the smaller number and has been re-written in expanded form as 200 + 20 + 5.
• Count back 100 to reach 250.
• Count back another 100 to reach 150.
• Count back 10 to reach 140.
• Count back another 10 to reach 130.
• Count back 5 ones to reach 125.
• 125 is the final number plotted so this is the answer.
• ### Solve the subtractions.

Hints

Make sure to partition the smaller number into hundreds, tens and ones, and write in expanded form before counting back.

Remember to plot the answers along the number line as you go.

Solution

437 - 129 = 308

464 - 283 = 181

532- 308 = 224

538 - 341 = 197