Learn ZOE Math Online Activity: 3-Digit Addition

You deposited $254 in your bank account yesterday, and another $157 today. How much money did you deposit in total? This problem is just a piece of cake. Just add $254 and $157 to get $411. This addition problem seems very simple, but imagine teaching this to your 6-year-old son or daughter. Now that’s a real problem.

Many parents have a hard time explaining simple arithmetic like 3-digit addition to their kids because for some adults the skill is so basic that it actually becomes challenging to break down the process for young children. So here’s a deep dive on how to teach 3-Digit Addition to young children.

What is 3-Digit Addition?

The addition means finding the total or sum of two or more numbers by combining them. 3-digit numbers are, well, numbers with 3 digits from 100 to 999. 3-Digit Addition means finding the sum of two or more 3-digit numbers. In this article, we will focus on the addition of two 3-digit numbers with and without regrouping.

In order for your child to understand how this works, he or she should understand the concept of place values. This will help him/her line up the numbers when adding vertically and understand the concept of regrouping.

Quick Revisit: Place Values

A place value tells you the value of a digit is in a number. For example, 321, 1 is in the ones place. Take a look at the table below.

Number Places Table Chart From Ones to Hundred Millions

In the table, the number is 987,654,321 and the place value of each digit. Identifying the place value of a digit is important when adding vertically. You observe place value so that you can line up the numbers correctly. For example, we want to solve 136+13. The expression when solved vertically must be written in a way that similar place values line up.

Lining up the numbers properly is an important part of solving the problem. It makes sure that numbers are combined correctly, and it helps you understand how the regrouping works, which we’ll get into later.

Sample 3 digit addition. Hundreds and Tens

3-Digit Addition Without Regrouping

3-digit addition won’t be very hard as long as you know how to add two-digit numbers. Let’s start by finding the sum of 145+132.

  • Step 1: Write the numbers vertically. Remember to line up the digits based on their place values. 5 and 2 must be on the ones column, 4, and 3 on the tens column, 1 and 1 on the hundreds column.
Addition of hundreds and hundreds
  • Step 2: Add starting from the right column. Many students start from the left which is not the best practice. Adding starting from the left is problematic because once regrouping is needed, the addition process will go wrong. Encourage your child to add numbers starting from the right (ones place).

Starting from the ones place,

Ones :  5+2=7
Tens : 4+3=7
Hundreds :1+1=2

Sample of 3 digit addition 145 + 132 = 277


Next, we will discuss the case where we have to regroup digits.

3-Digit Addition Without Regrouping

Suppose we want to add these numbers:


  • Step 1: Line up the numbers vertically according to the place value.
3 Digit addition without regrouping
  • Step 2: Starting from the ones place, add 4 and 9.


Each place holder has one digit. Since we cannot write 13 in the ones place, we need to regroup. Remember the place value of digits? The place value of 1 in 13 is tens. It means that in 13, there is 1 ten (10) and 3 ones (3). We write 3 on the ones place and regroup 1 by carrying it over the tens column.

3 digit addition with remainder in tens
  • Step 3: Add the digits in the tens place: 1, 4, and 7.


Now we got 12. Since the digits form the tens place, it actually means that we added 10, 40, and 70, thus


The place value of 1 in 120 is hundreds (100) so it means there is 1 must be regrouped to the hundreds column. We write 2 in the tens column because there are 2 tens in 120.

3 digit addition with remainder in tens and hundreds
  • Step 4: Add the digits in the hundreds place: 1, 3, and 5.


3 digit addition with remainder in tens and hundreds sample.

Therefore, 344+579=923.

Sometimes even the most basic concepts in Math can be challenging to teach. But like most things, Math topics are connected, preparing you for the next skill. Place value is not only about learning to read and write numbers. It is also the foundation of the four basic operations of Math.

Learn ZOE Math Online Activity: 3-Digit Addition
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Learn ZOE Math Online Activity: 3-Digit Addition
Understanding the concept of place values will help your child line up the numbers when adding vertically and understand the concept of regrouping.
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Learn ZOE
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