Home / United States / Math Classes / 3rd Grade Math / Addition of Multi-Digit Numbers

We use the concept of addition of numbers almost every day in our lives. And in most of these cases, we might have to add multi-digit numbers like 834+319. To add such numbers, we need to be thorough with the steps involved in addition and the terms related to it. We can also simplify addition of multi-digit numbers by making use of the properties of addition. ...Read MoreRead Less

- Definition of Numbers
- What is Addition?
- What are some frequently-used terms in Addition?
- Properties of Addition
- Commutative Property of Addition
- Associative Property of Addition
- Addition using a number line
- Count on strategy
- Make a ten strategy for addition:
- Addition using mental math:
- What is the definition of three-digit addition?
- Use partial sum to add :
- Round to estimate sum :
- Addition of three or more numbers :
- Solved Examples :
- Frequently Asked Questions

A number is an arithmetic value that is used to represent a quantity and to perform calculations. Numericals are written symbols that represent a number, . Example 1, 2, 3… are numbers.

Addition is a concept that entails combining or adding things together. It is a mathematical operation in which we add numbers together.

In addition, you will come across the following terms:

**1. Add** – Combining the numbers with the plus (+) operator.

**2. Addend** – A number or numbers that are added together.

**3. Addition equation** – Statements that prove two things are equal. These two things are usually on the left and right sides of the ‘=’ symbol in the equation.

**4. Equals **– The ‘=’ symbol is used for addition equations.

**5. Total or sum** – This is the result that you get after adding two or more numbers.

The above image gives us an example of addition.

**Commutative Property of Addition**

The sum is unaffected by changing the order of addends.

2 + 3 = 3 + 2

**Associative Property of Addition**Changing the order in which addends are grouped has no effect on the sum.

(4 + 3) + 5 = 4 +(3 + 5)

**Addition Property of Zero**The sum of any number and 0 is that number.

2 + 0 = 2

**Addition using a number line :**

We can add numbers on the number line. There are two ways to add numbers on a number line, ** count on **strategy and

**Count on strategy:**

Begin the addition on the number line with the largest number. With the smallest number in the sum, move right along the number line.

For example: find the value of addition 3 + 13.

1. When using the counting strategy, start with the largest number, which is 13.

2. We can look at 13 + 3 instead of 3 + 13, which only requires 3 jumps.

3. We still arrive at 16 after starting at 13 and counting on 3 jumps.

4. It is easiest to start with the largest number when using this addition strategy because the order of the additions does not matter.

**Make a ten strategy for addition:**

To make a ten from one addend, split the other addend and calculate the sum.

For example: Find the sum of 145 + 48

**Addition using mental math:**

Addition using mental math is the way by which we can find the result of an addition equation easily using mental calculations. If any number is very near to hundreds or thousands, then just round off the number and find an approximate result.

Later, we rebalance by reverse operation on the result to find the correct answer. Otherwise, use compensation to change both numbers and directly find the result.

For example, If we want to find the result of 248 + 327

Then, we can see 248 is very close to 250. We can add 2 to 248 and subtract 2 from 327 and find the result of addition easily.

In three-digit addition, we must sort the numbers into columns based on their place values, such as ones, tens, hundreds, thousands, and so on.

Addition of three-digit numbers is equivalent to adding two-digit numbers, and numbers can be added with or without regrouping (or carrying over).

Let’s take a look at the basic steps in 3-digit addition.

**Step 1:** Arrange the given numbers (addends) so that they fall correctly under the columns of ones, tens, and hundreds, one below the other.

**Step 2:** Add the numbers from right to left, starting with the ones column, then the tens column, and finally the hundreds column.

**Step 3:** The sum of the given numbers is obtained after all the columns have been added.

For example: Find the sum of 634 + 192.

**Step 1:** In the ones column, add the numbers together.4 + 2 = 6 . In one of the columns, write 6.

**Step 2:** In the tens column, add the numbers. 3 + 9 = 12. Carry 1 to the hundreds column and write 2 in the tens column.

**Step 3:** In the hundreds column, add the numbers. This equals 8 because 6 + 1 + 1 (from the carry over). The carryover is added along with the other addends after it is placed in the hundreds column.

Follow the below steps to add the number by using partial sum method:

**Step 1:** Using expanded form, write each number.

**Step 2:** Calculate the partial sums.

**Step 3:** Add all of the partial sums together.

**Example:** Calculate 246 + 508

**Solution:**

**Step 1:** Write 246 and 408 in expanded form.

246 = 200 + 40 + 6

508 = 500 + 8

**Step 2:** Find the partial sums.

246+ 508 = 700 + 40 + 14

**Step 3:** Add the partial sums.

246+ 508 = 754

Addition of three-digit numbers can be done arithmetically. We can follow the step below:

**Step 1:** First, we estimate the result. To estimate the numbers to the nearest hundred.

**Step 2:** Find the sum,

Start adding from ones, then then tens, at last the hundreds. If there are not enough ones or tens to add, then regroup the numbers and repeat the same.

Let’s take 39 + 22 as an example.

The number 39 is closer to 40 than the number 30.

As a result, the number 39 is rounded up to 40.

The number 22 is closer to the number 20 than it is to the number 30.

As a result, the number 22 is rounded down to 20.

For adding three or more numbers we follow the below steps:

**Step 1:** Vertically align the numbers.

**Step 2:** Add the ones first.

**Step 3:** Add the tens now.

**Step 4:** Finally, add the thousands.

Let’s take 132 + 520 + 217 as an example.

**Step 1:** Vertically align the numbers.

**Step 2:** Add the ones first.

2 + 0 + 7 = 9

**Step 3:** Add the tens now.

3 + 2 + 1 = 6

**Step 4:** Finally, add the thousands.

1 + 5 + 2 = 8

Hence, 132 + 520 + 217 = 869

**Example 1:**

Find 355 + 28 by using the count on strategy.

**Solution:**Use the count on strategy. Start at 355. Count on by tens, then by ones.

Hence, 355 + 28 = 383

**Example 2:**

Find 425 + 38 by using the make a ten strategy.

**Solution:**

Use the make a ten strategy. Start at 425. Count on to the nearest ten. Then count on by tens and by ones.

Hence, 425 + 38 = 463.

**Example 3:**

Find the value of 225 + 395. Check whether your answer is reasonable.

**Solution:**

**Step 1:** Estimate. Each addend should be rounded up to the nearest hundred.

The sum is about 600.

**Step 2:** calculate the sum. Begin with the ones, then the tens, and finally the hundreds.

**Step 3:** Check. 620 is close to 600, so the answer is reasonable.

**Example 4:**

Robert plans to hike 700 miles in two months. In the first month, he hikes 453 miles, and in the second month, he hikes 247 miles. Is he able to achieve his target of 700 miles?

**Solution:**

Total mile completed by Robert = sum of miles completed by Robert in the first and second month.

So,

Yes, he is able to get to his target of 700 miles.

**Example 5:**

Calculate 143 + 604

**Solution:**

Step 1: Write 143 and 604 in expanded form.

143 = 100 + 40 + 3

604 = 600 + 4

Step 2: Find the partial sums.

143 + 604 = 700 + 40 + 7

Step 3: Add the partial sums.

143 + 604 = 747

Hence, the required sum is 747.

**Example 6:**

Calculate 250 + 324 + 103.

**Solution:**

Step 1: Vertically align the numbers.

Step 2: Add the ones first.

0 + 4 + 3 = 7

Step 3: Add the tens now.

5 + 2 + 0 = 7

Step 4: Finally, add the thousands.

2 + 3 + 1 = 6

Hence, 250 + 324 + 103 = 677

Frequently Asked Questions on Multi Digit Addition Numbers

:If we add and subtract the same number, from another number then the result remains the same. For example, if we add and subtract 5 to a number 10 then, the result will be 10.

Commutative, associative, distributive, and additive identity are the four major properties of addition.