Adding 3-Digit Numbers
- 3 Digit Addition
- What Are Three-Digit Numbers? – Introduction
- Foundational Steps to Add Three-Digit Numbers
- Step-by-Step Guide to Three-digit Addition with Carrying Over
- Adding Three-Digit Numbers – Common Mistakes
- Adding Three-Digit Numbers – Conclusion
- Adding Three-Digit Numbers – Frequently Asked Questions
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Basics on the topic Adding 3-Digit Numbers
3 Digit Addition
Three-digit numbers are integral in various mathematical calculations and daily applications. If you're looking for resources and strategies for teaching 3 digit addition to help your child or student with 3 digit column addition, you've come to the right place! We offer a variety of tools and tips to make learning 3-digit addition a breeze. Read our educational text about 3 digit number addition, refer to the addition 3 digit numbers video (featuring 3-digit addition no regrouping and 3 digit addition with regrouping) and apply your knowledge by using our 3 digit addition worksheets including 3 digit addition word problems.
What Are Three-Digit Numbers? – Introduction
Three-digit numbers range from 100 to 999.
Three-digit numbers are never smaller than 100 and never greater than 999. Each number has three digits: one in the hundreds place, one in the tens place and one in the ones or units place.
Place value is crucial when working with three-digit numbers, as it informs us of a digit's value. Recognising the hundreds, tens and ones place is vital for performing calculations like addition of 3 digit numbers correctly. Let’s have a look at the number 367 in a place value chart. The digits are placed in the hundreds (H), tens (T) and ones place (O):
Foundational Steps to Add Three-Digit Numbers
Once pupils understand three-digit numbers, they can begin learning how to add them. There are essential steps to simplify the process. Three-digit numbers can be difficult to add, so always use a place value chart or use a standard written method to add three-digit numbers. Look at the following steps on how to solve 3 digit addition.
1. Prepare for your calculation
Write down the numbers in a standard written format, aligning digits according to their place value.
2. Always start with the ones place
Begin by adding the digits in the ones place. If the sum is a two-digit number, write down the digit in the ones place and carry over the ten to the tens place.
Understanding carrying over in addition
When calculating 3 digit column addition with carrying, it is important to understand what we are doing. Carrying over is a fundamental concept when the sum in the ones and tens place is a two-digit number. It involves adding the carried-over number to the sum of the digits in the next place.
3. Move on to adding tens
Once you added the unit digits, move on to adding the digits in the tens place. Do not forget to also add any numbers that you carried over from adding the unit digits. If the sum is a two-digit number, write down the unit and carry over the ten to the hundreds place.
4. Move on to adding hundreds
Once you added the digits in the tens place, move on to adding the digits in the hundreds place. Do not forget to also add any numbers that you carried over from adding the tens digits. If the sum is a two-digit number, write down the sum in the hundreds and thousands place.
Step-by-Step Guide to Three-digit Addition with Carrying Over
Let’s look at the example equation and do it together, step by step. Let’s complete 391 + 139.
1. Prepare for your calculation
Write down the first number 391, and right underneath it 139, in a standard written format. Align digits according to their place value - make sure that 9 is under 1, 3 under 9 and 1 under 3. See the example below:
2. Always start with the ones place
Begin by adding the digits in the ones place. In this case, we will add 9 and 1. As you know, the sum of these two digits is 10. This means that you will have to write down 0 in the ones place and carry 1 ten over.
Understanding Carrying Over in Addition
Carrying over is a fundamental concept when the sum in the ones and tens place is a two-digit number. It involves adding the carried-over number to the sum of the digits in the next place.
3. Move on to adding tens
Once you have added the unit digits, move on to adding the digits in the tens place. Here we will need to add 3 tens and 9 tens. However, let’s not forget that there is one more ten that we carried over from the units place. In this case, 3 plus 9 plus 1 equals 13. As this sum is over 10, we will have to carry over again. See the example below:
4. Move on to adding hundreds
Once you have added the digits in the tens place, move on to adding the digits in the hundreds place. Here we add 1 hundred and 3 hundred, their sum equals 4 hundred. But do not forget to also add the 1 hundred we carried over from the tens column! Write the digit 5 in the hundreds place. Well done, you have added two three-digit numbers and their sum is 530 - five hundred and thirty. Look at the representation below:
Adding Three-Digit Numbers – Common Mistakes
Common errors include forgetting to carry over or carrying over incorrect values. Also, pay attention to zeros in the ones or tens place. It is important to never skip them and always remember to keep them as place value holders. Practice and attention to detail can help avoid these mistakes.
Adding Three-Digit Numbers – Conclusion
Mastering the addition of three-digit numbers is essential for students, as it lays the groundwork for more advanced mathematical concepts and applications. With understanding, practice and the use of available resources, students can efficiently and accurately add three-digit numbers. Consistent practice and engagement with various learning tools and materials will facilitate mastery of this fundamental skill.
The key steps to successful three-digit addition are:
|What to do
|Prepare for your calculation
|Always start with the ones place
|Move on to adding tens
|Move on to adding hundreds
For further 3-digit addition practice, have a look at our addition 3-digit numbers worksheets featuring 3-digit addition word problems. We also have 3 digit addition interactive exercises, 3 digit addition games and 3 digit addition story problems.
Adding Three-Digit Numbers – Frequently Asked Questions
Transcript Adding 3-Digit Numbers
Mr. Squeaks is taking off on the trip of a lifetime! He is going to visit a magical place that his beloved grandpa used to tell him stories about. He’s so excited about this trip and has never travelled this far, so he wants to record every moment in his journal! We can help figure out how far away his destination is by totaling up the distance he travels each day. "Adding Three Digit Numbers Using Column Addition" Let’s look at Mr. Squeaks’ flight log to calculate how far he travelled. To find the total distance, we’ll start with his travel of day one and day two combined. First, set up the problem by writing one hundred and forty-two over one hundred and twenty-six. Make sure to include the addition sign, so we remember the operation. Start with the ones place, what is two plus six? We put the eight directly underneath this place value. Move to the left and look at the tens place. How many tens are there in forty and twenty? There are six tens in the number sixty. Write the digit six in the tens place, directly below the line. Continue moving left to the hundreds place. Even though you see the digit one, these have the value of one hundred. We say one hundred plus one hundred equals two hundred. In the answer, we write a two under the hundreds column. Wow! So far Mr. Squeaks has travelled two hundred and sixty-eight metres! The next day he continues another one hundred and twenty-three metres. Let’s add that to our travel log. For our next problem we have two hundred and sixty-eight add one hundred and twenty-three. We have the eight over the three in the ones place, the six over the two in the tens and the two over the one for the hundreds. Again, we want to go back over to the ones place to start adding. Eight and three more, equals eleven. What error do you notice in this answer? We can not have two digits in one place value. This one would be regrouped to the tens place. There are now three digits to add in the tens column. We add the tens by starting with the numbers that we already have in the problem. Six tens plus two tens makes eight tens and now we add one more group of ten. We have ninety, or nine tens. Since we don’t have to regroup, we move over to add the hundreds place. Two hundred and one hundred equals three hundred. In all, he has gone three hundred and ninety-one metres! Mr. Squeaks is almost to his destination, one more day to travel! On his final day, he adds another one hundred and thirty nine metres. Pause the video and try this one on your own before we go over it. What did you notice about the regrouping when solving this problem? We had to regroup twice, both in the tens and hundreds place. Let’s take a look at how we added up these numbers. Starting at the ones place, one plus nine makes ten. What digit do we write underneath the ones place? Zero because there are zero ones in the number ten. The one moves over to the tens place and is added in with nine and three for a total of thirteen tens. Thirteen tens is the same as having one hundred and three tens, so we regroup again. In the hundreds place we add three hundred and one hundred and one hundred more. The total is five hundred, so we put a five in the hundreds place. Mr Squeaks has travelled five hundred and thirty metres! Remember, in column addition, we line up numbers vertically, or one on top of the other, based on place value. We start by adding with the ones place and move to the left to add the tens and again to add the hundreds. Sometimes we need to regroup into the next place value when our sum is greater than ten. Mr. Squeaks steps off the plane. It was the most beautiful thing he had ever seen! His grandpa would be so proud!
Adding 3-Digit Numbers exercise
What is the place value of the underlined digit?Hints
Put your number in the columns below.
Is the underlined digit in the hundreds, tens or ones column?Solution
If your number has 3 digits it will have a hundreds, tens and ones number.
3 hundreds 0 tens 6 ones
2 hundreds 7 tens 1 one
9 hundreds 8 tens 1 one
Can you identify the mistake?Hints
Ensure the numbers have been placed in the correct column.
As the answer from the tens column is more than 2 digits, we need to carry the tens number over to the hundreds column.Solution
Check each column. Have the numbers been added correctly?
5 + 3 = 8
If you add the column and the answer is greater than 10, you must carry across.
4 + 7 = 11
We need to carry across the tens number of 11 to the hundreds column.
Work out the answer to the calculation by placing the digits into the correct boxes.Hints
Ensure you have put all of the numbers for the calculation in the correct place.
Don't forget, if your answer in the ones or tens column is greater than 9, you need to carry the tens digit of the number across to the next column.Solution
Once the digits are in the correct column:
- Add up the ones column first. 4 + 3 = 7.
- Then your tens column. 4 + 6 = 10. We need to carry across the 1 to the hundreds column.
- Finally, your hundreds column. 1 + 3 + 2 = 6.
Solve the problems using the column method.Hints
Add up the columns:
Starting with your ones first.
Then your tens.
473 + 326 = 799
306 + 291 = 597
651 + 367 = 1018
What's the solution?Hints
Add the digits in the ones column first.
3 + 5 =
Add the digits in the tens column next.
4 + 2 =Solution
Add the digits in the ones column first 3 + 5 = 8
Then add the digits in the tens column 4 + 2 = 6
Finally, add the digits in the hundreds column 2 + 1 = 3
243 + 125 = 368
Solve the answers to the problems.Hints
Set your calculation out into the grid method. Making sure all digits are in the correct column.Solution
Set your calculation out using the grid method shown in the video.
Add the digits in each column. Make sure you add them up in the correct order.
Ones: 2 + 4 = 6
Tens: 6 + 4 = 10 We need to carry across the 1 to the hundreds column
Hundreds: 1 + 3 + 2 = 6
The answer: 606