Three digit Subtraction with Regrouping - Expanded Form
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Basics on the topic Three digit Subtraction with Regrouping - Expanded Form
Subtraction with Regrouping – Expanded Form
What is the expanded form in subtraction? Expanded form is a way to write a number that emphasises the value each digit holds. In a subtraction equation, we can write each number in expanded form to make regrouping easier. Look at the number 678 in expanded form in the illustration below.
Subtraction with Regrouping and Expanded Form – Example
Let’s use this example to try expanded form subtraction with regrouping. Let’s subtract eight hundred and fifty minus ninety-nine to model our steps. First, write eight hundred and fifty and ninety-nine in expanded form with the larger number on top. We'll put separation lines in place of the addition signs, so we don't confuse ourselves as we subtract.
Then, we subtract the ones column: zero minus nine. Since we cannot subtract from zero, we will regroup a ten from the tens place. Now, we subtract ten minus nine. Write the difference, one, below.
Then, we subtract the tens column, forty minus ninety. Since there is not enough to subtract from, we regroup one hundred from the hundreds place. We can now subtract: one hundred and forty minus ninety. Write the difference, fifty, below.
Next, we subtract the hundreds column: seven hundred minus zero. We write the difference, seven hundred, below. Finally, put the answer back in standard form by adding it together. Seven hundred plus fifty plus one becomes seven hundred and fifty-one.
Subtraction with Regrouping and Expanded Form – Summary
Remember, we can write each number in a subtraction equation using expanded form to make regrouping easier.
| Step # | What to do |
|---|---|
| 1 | Subtract the ones column. If there is not enough to subtract from, regroup a ten from the tens place and subtract. |
| 2 | Move to the tens and the hundreds place repeating this process as necessary. |
| 3 | Put the answer back in standard form by adding it together. |
- First, subtract the ones column. If there is not enough to subtract from, regroup a ten from the tens place and subtract.
- Then, move to the tens and the hundreds place repeating this process as necessary.
- Finally, put the answer back in standard form by adding it together.
Have you practised yet? After watching the video, you can also find more interactive exercises, worksheets and more activities for 3-digit subtraction in expanded form.
Transcript Three digit Subtraction with Regrouping - Expanded Form
Mr. Squeaks and Imani are ready to play on their devices but nothing will load! "Did we run out of data, Imani?" "Let's check our devices to see if there's any left." However, they are having trouble subtracting from three digit numbers. Let's help Imani and Mr. Squeaks solve their equations by learning "Three Digit Subtraction with Regrouping - Expanded Form". Expanded form is a way to write a number that emphasises the VALUE each digit holds. In a subtraction equation, we can write each number in expanded form to make regrouping easier. Let's check Mr. Squeaks' data usage to practice. It says he has eight hundred and fifty megabytes of data and he has used ninety-nine. How much data is left? First, write eight hundred and fifty, and ninety-nine in expanded form with the larger number on top. We'll put separation lines in place of the addition signs, so we don't confuse ourselves as we subtract. Then, subtract the ones column: zero minus nine. Since there is not enough to subtract from, regroup a ten from the tens place. Now subtract ten minus nine. Write the difference, one, below. Then, subtract the tens column, forty minus ninety. Since there is not enough to subtract from, regroup one hundred from the hundreds place and subtract, one hundred and forty minus ninety. Write the difference, fifty, below. Subtract the hundreds column, seven hundred minus zero, and write the difference, seven hundred, below. Finally, add the numbers back together to get our answer, seven hundred and fifty-one. Hmm, Mr. Squeaks should have seven hundred and fifty one megabytes of data left. Now, Imani checks their data usage. It says Imani has three hundred megabytes of data and has used two hundred and ninety-nine..how much DATA is left? What should we do first?
First, write three hundred minus two hundred and ninety-nine in expanded form like THIS. Do you know our next step? Next, subtract the ones column, but we cannot take nine away from zero, so regroup a ten from the tens place and subtract. But there is nothing we can borrow since there is ZERO there. Where can we regroup from? We can regroup one hundred from the hundreds column. Now that there is a hundred to borrow from in the tens place, we can take a ten to regroup for the ones place. Where should we subtract now? The ones place. Ten minus nine is one and we write the difference, here. Then, we move to the tens place and subtract ninety from nintety to get zero. Finally, subtract the hundreds place: two hundred minus two hundred equals zero. What is our very last step? Find the answer by adding the numbers together, one! Hmm, Imani still has one megabyte of data left! Before we solve the data dilemma, let's summarise! Remember, we can write each number in a subtraction equation using expanded form to make regrouping easier. First, subtract the ones column. If there is not enough to subtract from, regroup a ten from the tens place and subtract. Write the difference below. Then, move to the tens and the hundreds place repeating this process as necessary. Finally, find the answer by adding the numbers back together. "I just don't get it, Imani. We should BOTH have enough data left to keep playing."
"Umm, Mr. Squeaks, I think I forgot to unplug my bed..." "...and plug IN the wifi."
Three digit Subtraction with Regrouping - Expanded Form exercise
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What is expanded form?
HintsNumbers can be written using expanded form.
Here is a number in expanded form. You can see each digit's value is shown.
SolutionExpanded form is a way to write a number that emphasises the value each digit holds. In a subtraction equation, this makes regrouping easier.
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Which number is correctly written in expanded form?
HintsCompare this correctly expanded number to the options you have to choose from.
Remember, the value of each digit should be emphasised. If a number is in the hundreds, the first digit should be in the hundreds in the expanded form.
SolutionThe correctly expanded 321 is 300 + 20 + 1. The value of each digit is clear.
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How much data does Mr. Squeaks have left after phone calls?
HintsRemember, you may need to regroup from the tens or hundreds column to be able to subtract correctly.
You will have to regroup from the tens column to solve this problem.
SolutionThe correct answer is 643 megabytes of data.
In the ones place we cannot subtract 7 from 0, so we need to regroup a ten from the tens column. 10 -7 = 3.
Since we regrouped from the tens column to subtract in the ones column, we have 40 minus zero, which is 40.
Finally, 800 minus 200 is 600, leaving us with the final answer of 643.
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How much data did Imani use watching videos online?
HintsBegin by writing out the subtraction equation in expanded form.
As we cannot take 5 ones from 0, what do we need to do?
We need to regroup one of the tens from 50 to the ones column, and change the 50 to 40 in the tens column.
Can we subtract 60 from 40? No, we need to regroup one of the hundreds into the tens column.
SolutionThe correct answer is 385 megabytes.
We cannot subtract 5 from 0 to regroup a ten from the tens column. 10 - 5 = 5.
We then need to regroup a hundred to the tens column to make 140 - 60 = 80.
Then, we solve 700 - 400 = 300.
Finally, combine the numbers 300 + 80 + 5 to get 385.
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How much data is left?
HintsIn this problem you don't have to regroup any numbers, just subtract the numbers provided.
Remember to start from the ones column and move to the tens place, then the hundreds place.
SolutionNewton has 233 megabytes of data left. Since this problem didn't require any regrouping, you could just subtract each of the expanded numbers individually.
In the ones place, 5 minus 2 is 3. In the tens place, 50 minus 20 is 30. Lastly, in the hundreds place, 400 minus 200 is 200. Then recombine the digits to get the answer.
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How much data is left for Mr. Squeaks?
HintsThe equation that we need to solve is 751 - 70.
Write the equation out, placing the larger number on the top and using expanded form.
Do you need to regroup anthing here?
SolutionMr. Squeaks has 681 megabytes of data left.
To find the answer: No regrouping is needed in the ones column to subtract 0 from 1.
We do need to regroup in the tens column from the hundreds column. 150 - 70 = 80.
Finally, we have 600 - 0 = 600.
