Chapter: Addition (Three Digits)

Hello Math Explorer! Get ready to level up your addition skills. In this chapter, we'll learn how to add bigger numbers with up to three digits. Think of it as being able to count huge piles of stickers, video game scores, or anything you can imagine! It's a very important skill, and we'll make it fun and easy to learn. You can do this!


First, A Quick Review: Place Value

Before we add big numbers, let's remember what makes them big! Every digit in a number has a special place. For a three-digit number like 472, it looks like this:

  • 4 is in the Hundreds place (it means 400)
  • 7 is in the Tens place (it means 70)
  • 2 is in the Ones place (it means 2)

Remembering Hundreds, Tens, and Ones (H T O) will make adding super easy!

Key Takeaway

Lining up numbers by their place value (Ones with Ones, Tens with Tens, etc.) is the most important first step in addition!


Adding Three-Digit Numbers (No Carrying)

Let's start with a simple one. This is when the numbers in each column add up to 9 or less. We'll use the column method.

Example: Let's add 152 + 345.

Step 1: Line them up!
Write the numbers on top of each other. Make sure the Ones, Tens, and Hundreds places are lined up perfectly.

$$ \begin{array}{c} & H & T & O \\ & 1 & 5 & 2 \\ + & 3 & 4 & 5 \\ \hline \end{array} $$

Step 2: Add the Ones.
Start from the right side. Add the digits in the Ones column. (2 + 5 = 7)

$$ \begin{array}{c} & 1 & 5 & 2 \\ + & 3 & 4 & 5 \\ \hline & & & 7 \\ \end{array} $$

Step 3: Add the Tens.
Now move to the Tens column. (5 + 4 = 9)

$$ \begin{array}{c} & 1 & 5 & 2 \\ + & 3 & 4 & 5 \\ \hline & & 9 & 7 \\ \end{array} $$

Step 4: Add the Hundreds.
Finally, add the Hundreds column. (1 + 3 = 4)

$$ \begin{array}{c} & 1 & 5 & 2 \\ + & 3 & 4 & 5 \\ \hline & 4 & 9 & 7 \\ \end{array} $$

So, 152 + 345 = 497. See? You did it!


Level Up: Adding with Carrying!

Sometimes, when you add the digits in a column, the answer is 10 or more. What do we do then? We carry! Don't worry, it's like a fun puzzle.

Analogy: The Overflowing Box!
Imagine each place value column is a little box that can only hold 9 items. If you get 10 or more, you have to bundle 10 of them into a group and "carry" that group to the next box on the left (the bigger place value)!

Carrying from the Ones to the Tens

Example: Let's solve 238 + 124.

Step 1: Add the Ones.
(8 + 4 = 12). Uh oh, 12 is too big for the Ones box! 12 is the same as 1 Ten and 2 Ones.
So, we write the 2 in the Ones answer space and carry the small 1 over to the top of the Tens column.

$$ \begin{array}{c} & & \small{1} & \\ & 2 & 3 & 8 \\ + & 1 & 2 & 4 \\ \hline & & & 2 \\ \end{array} $$

Step 2: Add the Tens.
Now add all the digits in the Tens column, including the little number you carried!
(1 + 3 + 2 = 6). Write the 6 in the Tens answer space.

$$ \begin{array}{c} & & \small{1} & \\ & 2 & 3 & 8 \\ + & 1 & 2 & 4 \\ \hline & & 6 & 2 \\ \end{array} $$

Step 3: Add the Hundreds.
(2 + 1 = 3). Write the 3 in the Hundreds answer space.

$$ \begin{array}{c} & & \small{1} & \\ & 2 & 3 & 8 \\ + & 1 & 2 & 4 \\ \hline & 3 & 6 & 2 \\ \end{array} $$

The final answer is 362. Amazing work!

Watch Out! Common Mistake

A common mistake is forgetting to add the little number you carried over. That little number is a superhero! Always remember to include it when you add the next column.


Challenge Mode: Adding Three Numbers!

Guess what? Adding three numbers is just the same as adding two! You just have one more digit in each column to add.

Example: Let's add 142 + 315 + 228.

Step 1: Line them all up and add the Ones.
(2 + 5 + 8 = 15). That's 5 Ones and 1 Ten to carry.

$$ \begin{array}{c} & & \small{1} & \\ & 1 & 4 & 2 \\ & 3 & 1 & 5 \\ + & 2 & 2 & 8 \\ \hline & & & 5 \\ \end{array} $$

Step 2: Add the Tens (don't forget the carry!).
(1 + 4 + 1 + 2 = 8).

$$ \begin{array}{c} & & \small{1} & \\ & 1 & 4 & 2 \\ & 3 & 1 & 5 \\ + & 2 & 2 & 8 \\ \hline & & 8 & 5 \\ \end{array} $$

Step 3: Add the Hundreds.
(1 + 3 + 2 = 6).

$$ \begin{array}{c} & & \small{1} & \\ & 1 & 4 & 2 \\ & 3 & 1 & 5 \\ + & 2 & 2 & 8 \\ \hline & 6 & 8 & 5 \\ \end{array} $$

The total is 685. You are becoming an addition master!

Key Takeaway

Whether you add two or three numbers, the steps are the same: Line Up, Add Ones, Add Tens, Add Hundreds. Always remember to carry when a column adds up to 10 or more!


A Super Smart Math Trick!

Sometimes, you can make addition easier by looking for "number friends" that add up to a nice, round number (like 10 or 100).

Example: Add 1 + 65 + 399.

Hmm, adding 65 + 399 seems a bit tricky. But wait! Look at 1 and 399. They are "number friends"!
Adding 1 + 399 first gives you 400.
Now the problem is just 65 + 400, which is super easy! The answer is 465.

You can change the order you add numbers to make the job faster and easier for yourself!


Putting It All Together: Solving Word Problems

Now let's use our skills to solve a real-life problem!

Problem: A baker made 175 chocolate chip cookies in the morning. In the afternoon, he made 240 more. How many cookies did he make in total?

Step 1: Read and find the numbers.
The numbers are 175 and 240.

Step 2: Look for keywords.
The words "in total" tell us we need to add!

Step 3: Solve it using column addition.

$$ \begin{array}{c} & & \small{1} & \\ & 1 & 7 & 5 \\ + & 2 & 4 & 0 \\ \hline & 4 & 1 & 5 \\ \end{array} $$

Step 4: Write your answer in a sentence.
The baker made 415 cookies in total.

Did You Know?

The plus sign (+) that we use for addition first appeared in a book written in Germany more than 500 years ago, in 1489!