# Three Digit Addition with Regrouping - Expanded Form

Content Three Digit Addition with Regrouping - Expanded Form
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## Addition with Regrouping Hundreds

What is addition with expanded form with regrouping? This text teaches you how to use expanded form when solving three-digit addition problems (regrouping).

Expanded form is an addition strategy we can use to help solve equations. Expanded form is a way of writing numbers to emphasise the value each digit has. For example, three hundred and forty-five can be rewritten in expanded form as three hundred plus forty plus five. We can use this format to help when adding with regrouping.

## Three-Digit Addition with Regrouping using Expanded Form

Let’s use the example three hundred and eighty one plus ninety-nine.

First, rewrite the equation in expanded form, one on top of the other.

Then, start adding the ones column. Here the sum is ten. Since ten has zero ones and one ten, we write zero in the ones place. Then, we regroup, or move, the ten to the top of the tens place.

Next, add the tens column. Here the sum is one hundred and eighty. One hundred and eighty has one hundred and eight tens, so we write eighty in the tens place. Then, we regroup one hundred to the top of the hundreds place.

Now, add up the hundreds column and write the sum, four hundred, below.

Finally, take the answer out of expanded form by adding it together.

## Three Digit Addition using Expanded Form – Summary of Steps

These are the necessary steps for addition with regrouping using the expanded form.

Step # What to do
1 Rewrite the equation in expanded form, one on top of the other.
2 Add the ones column. If the sum has a ten, regroup and
write it above the tens place.
Then, write the ones value in the ones place.
3 Add the tens column. If the sum has a hundred,
write that above the hundreds place.
Then, write the value of the ten in the tens place.
4 Add up the hundreds column and
write the sum below in the hundreds place.
5 Take the answer out of expanded form by adding it together.

Have you practised yet? On this website, you can also find three-digit expanded form addition worksheets and three digit addition with regrouping word problems.

### TranscriptThree Digit Addition with Regrouping - Expanded Form

Mr. Squeaks is learning how to ski this weekend! At the end of the day, he would love to know how well he did. Except, he can't quite work out how to add the three digit numbers. Let's help Mr. Squeaks by showing him "Three Digit Addition with Regrouping - Expanded Form" Remember, expanded form is a way of writing numbers to emphasise the VALUE each digit has. For example, three hundred and forty-five can be rewritten in expanded form as three hundred plus forty plus five. We can use this format to help us add with regrouping. On Saturday, Mr. Squeaks skied three hundred and eighty one metres on Bunny Run and ninety-nine metres on Star Pass. What distance did he cover altogether? "Let's rewrite it in expanded form, one on top of the other." Start with adding the ones column. The sum is ten. Ten has ZERO ones and ONE ten, so we write zero in the ones place, and we REGROUP, or move, the ten to the top of the TENS place. Next, add the tens column. The sum is one hundred and eighty. One hundred and eighty has ONE hundred and EIGHT tens, so we write EIGHTY in the tens place, and we REGROUP one hundred to the top of the HUNDREDS place. Add up the hundreds column and write the sum below. Finally, take the answer out of expanded form by adding it together. Mr. Squeaks skied four hundred and eighty metres on his first day! Let's help Mr. Squeaks calculate his total on Sunday. He skied six hundred and thirty metres on Snow Powder Pass and two hundred and seventy eight metres on Double Trouble Trail. How far did he ski altogether? "Remember, first rewrite the equation in expanded form, one on top of the other." Begin by adding the ones column. What is the sum? The sum is eight ones so we write eight HERE in the ones place. Where do we add next? Next, we add the tens column. The sum is one hundred. One hundred has ONE hundred and ZERO tens. Where should we write our sum? We write a zero in the tens place and we REGROUP one hundred to the top of the HUNDREDS place. What is the sum of the hundreds column? The sum is nine hundred which we write HERE. What is the final step? Take the answer out of expanded form by adding it together. Mr. Squeaks skied nine hundred and eight metres on his second day! But where has Imani been? As Mr. Squeaks searches, let's remember! First, rewrite the equation in expanded form, one on top of the other. Add the ones column. If the sum has a ten, regroup and write it above the TENS place. Write the ones value in the ones place. Next, add the tens column. If the sum has a hundred, write that above the HUNDREDS place. Write the value of the ten in the tens place. Add up the hundreds column and write the sum below. Finally, take the answer out of expanded form by adding it together. "WOAH, LOOK OUT!" "Is that where you've been this whole time?" "Totally tubular, Squeaks!" "Wanna join me?!"

"WOAH, LOOK OUT!"

## Three Digit Addition with Regrouping - Expanded Form 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 with Regrouping - Expanded Form.
• ### Use place value to find the value of the 5.

Hints

What place is the 5 in?

Remember to think about the expanded form place value: Hundreds, Tens and Ones. These place value blocks represent 257.

Solution

The value of the 5 is 50, since it is in the tens place. When we expand this number, we get 200 + 50 + 7.

• ### What's the correct equation in expanded form?

Hints

Remember, expanded form is showing the numbers in hundreds, tens and ones. Line up both numbers based on place value.

Here's an example of 430 in expanded form.

We need to add the length of the two paths that Imani sleighed along.

Solution

134 + 78 are added like this in expanded form. The hundreds, tens and ones place line up.

134 is partitioned into: 100 + 30 + 4

78 is partitioned into: 70 + 8 (there are 0 hundreds)

• ### Help solve this problem in expanded form.

Hints

Remember, create the expanded form first, then add starting at the ones column. Regroup as needed.

Look at this example to remember how to regroup based on place value.

Partition 423 on the top row and partition 248 on the second row.

Solution

To add 423 + 248

• First, put the numbers in expanded form.
• Then, starting at the ones place, add 3 + 8 to get 11. Since 11 cannot be in the ones column, regroup the 10 into the tens column, and keep the one 1.
• Next, you add the tens column, 10 + 20 + 40 to get 70. No regrouping needs to happen in this step.
• Then, you add the hundreds column, 400 + 200 to get 600.
• Lastly, you add up 600 + 70 + 1 to get 671.

• ### Solve using expanded form.

Hints

We need to add together the two distances that Imani and Mr Squeaks each sleighed.

Remember, write out the equation in expanded form.

Then, starting from the ones place, add them together. Regroup as needed.

Solution

Together, Imani and Mr. Squeaks sleighed for 603 feet!

To add 430 + 173:

• First, put the numbers in expanded form.
• Then, starting at the ones place, add 0 + 3 to get 3. No regrouping needs to happen.
• Next, you add the tens column, 30 + 70 to get 100. Since 100 cannot be in the tens column, regroup the 100 into the hundreds column, with 0 tens left.
• Then, you add the hundreds column, 100 + 400 + 100 to get 600.
• Lastly, you add up 600 + 00 + 3 to get 603.

• ### What's the expanded form?

Hints

Remember, expanded form shows hundreds + tens + ones.

Here's an example of 435 in expanded form.

Solution

123 in expanded form is: 100 + 20 + 3.

• ### Find the equation solved correctly in expanded form.

Hints

Remember, add the numbers together using expanded form. Start at the ones place, and regroup as needed.

Check your regrouping in the tens and hundreds columns.

Solution

To add 345 + 278:

• First, put the numbers in expanded form.
• Then, starting at the ones place, add 5 + 8 to get 13. Since 13 cannot be in the ones column, regroup the 10 into the tens column, and keep the 3 ones.
• Next, you add the tens column, 10 + 40 + 70 to get 120. Since 120 cannot be in the tens column, regroup the 100 into the hundreds column, and keep the 20.
• Then, you add the hundreds column, 100 + 300 + 200 to get 600.
• Lastly, you add up 600 + 20 + 3 to get 623.
Mr. Squeaks and Imani will have to drive 623 miles altogether to get home. What a long day!