# Adding 3 Digit Numbers Using Standard Algorithm

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Adding 3 Digit Numbers Using Standard Algorithm
CCSS.MATH.CONTENT.4.NBT.B.4

## Basics on the topicAdding 3 Digit Numbers Using Standard Algorithm

Three-digit numbers are integral in various mathematical calculations and daily applications. If you're looking for resources and strategies to help your child or student with three-digit addition, you've come to the right place! We offer a variety of tools and tips to make learning three-digit addition a breeze. Read our educational text about three-digit numbers, refer to the three-digit addition video and apply your knowledge by using our 3 digit addition math worksheets.

## 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. Recognizing the hundreds, tens, and ones place is vital for performing calculations like addition with three digits 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):

H T O
3 6 7

## 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.

Write down the numbers in a standard written format, aligning digits according to their place value.

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 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:

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 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 unit's 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 added the digits in the tens place, move on to adding the digits in the hundreds place. Here we 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:

Step # What to do
3 Move on to adding tens
4 Move on to adding hundreds

What are some common mistakes made while adding three-digit numbers? Common mistakes include not carrying over correctly, misaligning place values, and miscalculating the sums in each place value.

Why is understanding ‘carrying over’ important? Carrying over is crucial as it affects the sums in the tens and hundreds places, leading to accurate results in three-digit addition.

Can three-digit addition be done mentally? How? With practice, students can mentally add three-digit numbers by visualizing the numbers, breaking them down, and adding each place value separately.

How to check if the addition of three-digit numbers is correct? Students can use subtraction or calculators to verify their answers, or cross-check with peers or teachers.

What if there are more than two numbers to add? When adding multiple three-digit numbers, organize them in columns, ensuring each place value is aligned, then add each column starting from the right.

How is subtraction of three-digit numbers related to addition? Understanding addition helps in mastering subtraction as the two operations are inversely related; knowledge of carrying over in addition is applied similarly in borrowing during subtraction.

## Adding 3 Digit Numbers Using Standard Algorithm exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Adding 3 Digit Numbers Using Standard Algorithm .
• ### 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 place.

3 0 6 Tens

3 hundreds 0 tens 6 ones

2 7 1 Hundreds

2 hundreds 7 tens 1 one

9 8 1 Ones

9 hundreds 8 tens 1 one

• ### Can you find the mistake in the solution?

Hints

Make sure the answers have been placed in the correct columns.

Since the answer from the tens column is more than 2 digits, we need to carry the tens number over to the hundreds column.

Solution

For the ones place: 3 + 5 = 8

For the tens place: 4 + 7 = 11

We need to regroup the digit in the tens place to the hundreds column. So you are left with a 1 in the tens place.

For the hundreds place: 1 + 2 + 2 = 5

500 + 10 + 8 = 518

• ### Solve the equation by placing the digits into the correct boxes.

Hints

First, make sure you have put all of the digits for the number you're adding in the correct place.

Start by adding the ones, then the tens, and lastly the hundreds place.

Don't forget if your answer in the ones or tens column is greater than 9, you need to regroup the digit in the tens of the number to the next column.

Solution

Once the digits are in the correct column:

• Add the ones column first. 4 + 3 = 7.
• Then add the tens column. 4 + 6 = 10. We need to regroup the 1 to the hundreds column. So we're left with a 0 in the tens column.
• Finally add the hundreds column. 1 + 3 + 2 = 6.

• ### Solve the equations.

Hints

For this example, looking at the answer in the tens column, the 1 in 12 needs to be regrouped to the hundreds column. Then, the hundreds column will be 1 + 7 + 6.

Are there any that need to be regrouped for these equations above?

Start adding the ones place first.

Solution

473 + 326 = 799

306 + 291 = 597

651 + 367 = 1,018

• ### 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 equations.

Hints

Put the numbers on top of each other in the place value chart. Make sure all digits are in the correct column.

Solution

Put the numbers on top of each other in the place value chart.

Add the digits in each column, starting with the ones, then tens, and lastly, hundreds.

For 362 + 244:

Add the ones: 2 + 4 = 6

Then add the tens: 6 + 4 = 10 We need to regroup the 1 to the hundreds column.

Lastly, add the hundreds: 1 + 3 + 2 = 6

362 + 244 = 606

______________________________

For the rest of the equations:

271 + 149 = 420

745 + 639 = 1384

549 + 207 = 756

365 + 256 = 621