Welcome, Young Mathematicians!
In this chapter, you’ll learn an exciting new skill called carryover (also called regrouping). When the numbers in a place get too big, we carry some over to the next place. Let’s discover how!
Part 1: Adding Single-Digit Numbers with Carryover
Sometimes when we add two numbers, the answer is bigger than 9. When this happens, we need to carry over!
Understanding Carryover
Think about it like this: You have a box that can only hold 9 candies. If you have more than 9, you need to start a new box of 10!
Example 1: 8 + 5
Let’s solve this step by step:
Step 1: Add the numbers
8 + 5 = 13
Step 2: Break apart 13
13 = 10 + 3
Step 3: Write it down
8
+ 5
---
13
The answer is 13. We had to go past 9, so we got a number in the tens place!
Let’s Practice!
Problem 1: 7 + 6 = ___
Solution:
- 7 + 6 = 13
- Answer: 13
Problem 2: 9 + 4 = ___
Solution:
- 9 + 4 = 13
- Answer: 13
Problem 3: 8 + 7 = ___
Solution:
- 8 + 7 = 15
- Answer: 15
Try These Yourself!
- 6 + 8 = ___
- 9 + 9 = ___
- 7 + 5 = ___
- 8 + 6 = ___
Part 2: Adding Double-Digit and Single-Digit Numbers with Carryover
Now let’s add bigger numbers! We’ll use column addition and write our numbers neatly in columns.
The Column Method
We stack numbers with ones under ones, and tens under tens:
T | O
2 | 7
+ 0 | 6
-------
Example 1: 27 + 6
Step 1: Line up the numbers
Tens | Ones
2 | 7
+ | 6
----------
Step 2: Add the ones column
7 + 6 = 13
That's 1 ten and 3 ones!
Step 3: Carry the 1 to the tens column
¹
2 7
+ 6
------
3
Step 4: Add the tens column
2 + 1 = 3
Step 5: Write the final answer
¹
2 7
+ 6
------
3 3
Answer: 33
Example 2: 48 + 7
Step 1: Add the ones
8 + 7 = 15 (carry the 1)
¹
4 8
+ 7
------
5
Step 2: Add the tens
4 + 1 = 5
Answer: 55
Let’s Practice!
Problem 1: 35 + 8
¹
3 5
+ 8
------
4 3
Answer: 43
Problem 2: 59 + 6
¹
5 9
+ 6
------
6 5
Answer: 65
Try These Yourself!
- 46 + 7 = ___
- 38 + 5 = ___
- 67 + 8 = ___
- 24 + 9 = ___
Part 3: Adding Double-Digit Numbers with Double-Digit Numbers
Now for the grand adventure! Let’s add two double-digit numbers together.
Example 1: 34 + 28
Step 1: Line up by place value
3 4
+ 2 8
------
Step 2: Add the ones column
4 + 8 = 12
That's 1 ten and 2 ones! Carry the 1.
¹
3 4
+ 2 8
------
2
Step 3: Add the tens column
3 + 2 + 1 = 6
¹
3 4
+ 2 8
------
6 2
Answer: 62
Example 2: 47 + 36
Step 1: Add the ones
7 + 6 = 13 (carry the 1)
¹
4 7
+ 3 6
------
3
Step 2: Add the tens
4 + 3 + 1 = 8
Answer: 83
Example 3: 58 + 25
Step 1: Add the ones
8 + 5 = 13 (carry the 1)
¹
5 8
+ 2 5
------
3
Step 2: Add the tens
5 + 2 + 1 = 8
Answer: 83
Let’s Practice!
Problem 1: 45 + 37
¹
4 5
+ 3 7
------
8 2
Answer: 82
Problem 2: 56 + 29
¹
5 6
+ 2 9
------
8 5
Answer: 85
Try These Yourself!
- 38 + 24 = ___
- 49 + 33 = ___
- 67 + 18 = ___
- 55 + 26 = ___
Part 4: Adding Three Double-Digit Numbers
Now for the ultimate challenge! We can add three numbers at once. Here’s an important secret: You can add numbers in any order and get the same answer! This is called the Commutative Property of addition.
Example 1: 23 + 15 + 34
Step 1: Stack all three numbers
2 3
1 5
+ 3 4
------
Step 2: Add the ones column
3 + 5 + 4 = 12
That's 1 ten and 2 ones! Carry the 1.
¹
2 3
1 5
+ 3 4
------
2
Step 3: Add the tens column
2 + 1 + 3 + 1 = 7
¹
2 3
1 5
+ 3 4
------
7 2
Answer: 72
Does Order Matter?
Let’s try adding the same numbers in a different order!
23 + 34 + 15
¹
2 3
3 4
+ 1 5
------
7 2
Answer: 72 (The same!)
34 + 15 + 23
¹
3 4
1 5
+ 2 3
------
7 2
Answer: 72 (Still the same!)
🌟 Important Discovery!
No matter what order you add numbers, you always get the same answer!
This means:
- 5 + 3 = 3 + 5
- 23 + 15 + 34 = 34 + 15 + 23 = 15 + 23 + 34
You can rearrange the numbers to make adding easier!
Example 2: 18 + 25 + 32
Step 1: Add the ones
8 + 5 + 2 = 15 (carry the 1)
¹
1 8
2 5
+ 3 2
------
5
Step 2: Add the tens
1 + 2 + 3 + 1 = 7
Answer: 75
Example 3: 27 + 14 + 29
Step 1: Add the ones
7 + 4 + 9 = 20 (carry the 2)
²
2 7
1 4
+ 2 9
------
0
Step 2: Add the tens
2 + 1 + 2 + 2 = 7
Answer: 70
Smart Adding Tip!
Sometimes you can rearrange numbers to make adding easier:
25 + 38 + 15
Notice that 25 + 15 = 40 (nice and easy!)
So we can think: (25 + 15) + 38 = 40 + 38 = 78
Let’s Practice!
Problem 1: 12 + 24 + 36
¹
1 2
2 4
+ 3 6
------
7 2
Answer: 72
Problem 2: 19 + 23 + 28
²
1 9
2 3
+ 2 8
------
7 0
Answer: 70
Try These Yourself!
- 15 + 22 + 35 = ___
- 28 + 16 + 24 = ___
- 33 + 19 + 28 = ___
- 25 + 25 + 25 = ___
Chapter Review
What We Learned:
- Carryover happens when the sum in a column is 10 or more
- We write the carried number small and above the next column
- We always add the ones column first, then the tens column
- Order doesn’t matter in addition! 15 + 23 = 23 + 15
- When adding three numbers, we can rearrange them to make it easier
Key Steps for Addition with Carryover:
- Line up the numbers by place value (ones under ones, tens under tens)
- Start with the ones column
- If the sum is 10 or more, carry to the next column
- Add the tens column (don’t forget the carried number!)
- Write your answer
Fun Math Fact!
Did you know that the order of addition working the same way (like 5 + 3 = 3 + 5) is a special rule that mathematicians use all the time? It’s called the Commutative Property, and it works for addition and multiplication, but NOT for subtraction or division!
Great job learning about addition with carryover! You’re becoming a real mathematician! 🎉
