Addition & Subtraction
Master the fundamental operations with whole numbers
What You'll Learn
Understanding Addition
Addition combines two or more quantities to find their total or sum. It's one of the four fundamental arithmetic operations.
Key Addition Terminology
Addends
Numbers being added
5 + 3 → 5 and 3
Sum
Result of addition
5 + 3 = 8
Plus Sign (+)
Indicates addition
a + b
Properties of Addition
Commutative Property
Order doesn't matter
5 + 3 = 3 + 5 = 8
Associative Property
Grouping doesn't matter
(2 + 3) + 4 = 2 + (3 + 4) = 9
Identity Property
Adding zero gives the same number
7 + 0 = 7
Addition Strategies
Column Addition (Standard Algorithm)
Align numbers by place value and add from right to left:
345 + 278 ----- 623
Ones: 5 + 8 = 13 (write 3, carry 1)
Tens: 4 + 7 + 1 = 12 (write 2, carry 1)
Hundreds: 3 + 2 + 1 = 6
Mental Math Strategies
Making 10
8 + 7 = 8 + 2 + 5 = 10 + 5 = 15
Counting On
9 + 4: Start at 9, count 10, 11, 12, 13
Doubles Plus One
6 + 7 = 6 + 6 + 1 = 12 + 1 = 13
Breaking Apart
47 + 38 = 40 + 30 + 7 + 8 = 70 + 15 = 85
Understanding Subtraction
Subtraction is the inverse operation of addition. It represents taking away, finding the difference, or determining how much more one quantity is than another.
Key Subtraction Terminology
Minuend
Number being subtracted from
8 - 3 → 8
Subtrahend
Number being subtracted
8 - 3 → 3
Difference
Result of subtraction
8 - 3 = 5
Important Properties
Non-Commutative
Order DOES matter in subtraction
8 - 3 = 5 but 3 - 8 = -5
Relationship to Addition
Subtraction can be checked using addition
If 8 - 3 = 5, then 5 + 3 = 8 ✓
Subtraction Strategies
Standard Algorithm with Regrouping (Borrowing)
When the digit being subtracted is larger, regroup from the next place value:
523 - 267 ----- 256
Ones: Can't do 3 - 7, regroup: 13 - 7 = 6
Tens: 1 - 6 (after regrouping), regroup: 11 - 6 = 5
Hundreds: 4 - 2 = 2
Mental Subtraction Strategies
Counting Back
12 - 3: Start at 12, count 11, 10, 9
Counting Up
20 - 17: From 17 to 20 is 3
Using Benchmarks
73 - 48 = 73 - 50 + 2 = 23 + 2 = 25
Compensation
82 - 39 = 82 - 40 + 1 = 42 + 1 = 43
Word Problems
Problem 1: Library Books
A school library had 2,456 books. They received a donation of 789 books and purchased another 234 books. How many books does the library have now?
2,456 + 789 + 234 = 3,479 books
Problem 2: Stickers
A teacher had 1,250 stickers. She gave out 467 stickers during the first semester and 389 during the second semester. How many stickers does she have left?
1,250 - 467 - 389 = 394 stickers
Problem 3: Assembly
The morning assembly had 845 students. Later, 167 more arrived. If 234 students left early for a field trip, how many remained?
845 + 167 - 234 = 778 students
Practice Problems
Test your understanding
Addition Practice
1. 234 + 567 = ? ▼
801
2. 1,289 + 3,456 = ? ▼
4,745
3. 45 + 38 + 27 = ? ▼
110
Subtraction Practice
1. 892 - 467 = ? ▼
425
2. 5,000 - 2,348 = ? ▼
2,652
3. 704 - 389 = ? ▼
315
Common Mistakes to Avoid
- • Alignment Errors: Always align numbers by place value
- • Regrouping Mistakes: Remember to reduce the next place value when borrowing
- • Carrying Errors: Don't forget to add carried digits in addition
- • Sign Confusion: Pay attention to whether you're adding or subtracting
- • Estimation: Always estimate to check if your answer is reasonable
Key Takeaways
- ✓ Addition is commutative and associative; subtraction is not
- ✓ Always align digits by place value for column addition/subtraction
- ✓ Use mental math strategies like "making 10" to calculate quickly
- ✓ Check subtraction by adding: difference + subtrahend = minuend
- ✓ Always estimate to verify your answers are reasonable
Related Lessons
Ready for Multiplication?
You've mastered addition and subtraction! Continue to learn multiplication.
