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Three Digit Addition with Regrouping - Expanded Form

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Three Digit Addition with Regrouping - Expanded Form
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Basics on the topic Three Digit Addition with Regrouping - Expanded Form

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In This Addition with Expanded Form with Regrouping Video...

Mr. Squeaks is going to ski school over the weekend! He is curious to know how far he skied on the slopes each day. We teach Mr. Squeaks how to use expanded form when solving three-digit addition problems (regrouping) to determine the distance he skied.

What is addition with expanded form with regrouping?

Expanded Form is an addition strategy we can use to help solve equations. Expanded form is a way of writing numbers to emphasize the value each digit has. For example, three hundred 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.

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How to do Three-Digit Addition with Regrouping using Expanded Form

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

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

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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.

25015_17_add_ones_column.svg

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

25015_21_add_tens_column.svg

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

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

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Summary of Steps: Addition with Regrouping Using Expanded Form

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

  • Next, 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.

  • Next, 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.

  • Afterwards, add up the hundreds column and write the sum below in the hundreds place.

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

Have you practiced yet? On this website, you can also find three-digit expanded form addition with regrouping examples on worksheets and exercises.

Transcript Three Digit Addition with Regrouping - Expanded Form

Mr. Squeaks is learning how to ski this weekend! At the end of the day, he is curious to know how well he did. Except, he can't quite figure out how to add to 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 emphasize the value each digit has. For example, three hundred 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 eighty one feet on Bunny Run and ninety-nine feet on Star Pass. What distance did he cover in all? 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 eighty. One hundred eighty has one hundred and eight tens, so we write eight 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 feet his first day! Let's help Mr. Squeaks calculate his total on Sunday. He skied six hundred thirty feet on Snow Powder Pass and two hundred seventy eight feet on Double Trouble Trail. How far did he ski in all? 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 a hundred. A 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 eighty feet 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 learned? 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.

    Solution

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

  • 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.

    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

    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 tubed 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 to get home. What a long day!