Addition & Subtraction Fundamentals
Master the building blocks of all mathematics — from basic adding to advanced mental math tricks.
What Are Addition and Subtraction?
Addition combines quantities together. When you have 3 apples and get 5 more, you have 3 + 5 = 8 apples. The numbers being added are called addends, and the result is the sum.
Subtraction finds the difference between quantities. If you have 8 apples and eat 3, you have 8 - 3 = 5 remaining. The first number is the minuend, the number subtracted is the subtrahend, and the result is the difference.
Understanding Place Value
Place value is the foundation. In the number 4,573:
- 4 is in the thousands place (4,000)
- 5 is in the hundreds place (500)
- 7 is in the tens place (70)
- 3 is in the ones place (3)
When adding or subtracting, always line up numbers by their place value and work from right to left.
Addition with Carrying (Regrouping)
When digits in a column add up to 10 or more, you carry to the next column.
Example 1: 47 + 38
Step 1: Add the ones column: 7 + 8 = 15. Write 5, carry 1.
Step 2: Add the tens column: 4 + 3 + 1 (carried) = 8.
Answer: 85
Example 2: 679 + 543
Step 1: Ones: 9 + 3 = 12. Write 2, carry 1.
Step 2: Tens: 7 + 4 + 1 = 12. Write 2, carry 1.
Step 3: Hundreds: 6 + 5 + 1 = 12. Write 12.
Answer: 1,222
Example 3: 1,487 + 2,935
Step 1: Ones: 7 + 5 = 12 → write 2, carry 1
Step 2: Tens: 8 + 3 + 1 = 12 → write 2, carry 1
Step 3: Hundreds: 4 + 9 + 1 = 14 → write 4, carry 1
Step 4: Thousands: 1 + 2 + 1 = 4
Answer: 4,422
Subtraction with Borrowing
When the top digit is smaller than the bottom digit, you borrow from the next column.
Example 4: 83 - 47
Step 1: Ones: 3 - 7? Can't do it! Borrow 1 from the 8 (making it 7), and the 3 becomes 13.
Step 2: Ones: 13 - 7 = 6
Step 3: Tens: 7 - 4 = 3
Answer: 36
Example 5: 1,000 - 437
This one requires borrowing across zeros! Borrow from the 1 (thousands), chain-borrow through the zeros:
1,000 becomes 0 | 9 | 9 | 10 (after borrowing)
10 - 7 = 3, 9 - 3 = 6, 9 - 4 = 5
Answer: 563
Mental Math Tricks for Addition
Round and Adjust
Instead of 298 + 47, think: 300 + 47 = 347, then subtract 2 = 345
Break Apart Numbers
For 67 + 45: Break 45 into 33 + 12. 67 + 33 = 100, then 100 + 12 = 112
Left to Right Addition
For 456 + 234: Add hundreds first (400+200=600), then tens (50+30=80), then ones (6+4=10). Total: 690
Mental Math Tricks for Subtraction
Add Up Instead
For 73 - 48: How far is 48 from 73? 48 + 2 = 50, 50 + 23 = 73. Total distance: 2 + 23 = 25
Round the Subtrahend
For 500 - 287: 500 - 300 = 200, then add back 13 = 213
Properties of Addition
- Commutative Property: a + b = b + a (order doesn't matter). 3 + 5 = 5 + 3 = 8
- Associative Property: (a + b) + c = a + (b + c) (grouping doesn't matter)
- Identity Property: a + 0 = a (adding zero changes nothing)
Note: Subtraction does NOT have the commutative property. 5 - 3 ≠ 3 - 5.
Checking Your Work
Always verify your answers:
- Addition: Subtract one addend from the sum. If 347 + 568 = 915, then 915 - 568 should equal 347. ✓
- Subtraction: Add the difference to the subtrahend. If 83 - 47 = 36, then 36 + 47 should equal 83. ✓
- Estimation: Round numbers first. 347 + 568 ≈ 350 + 570 = 920. Our answer of 915 is close. ✓
🎯 Try It Yourself
Test your understanding with these practice problems.
1. What is 347 + 568?
💡 Hint: Add ones first: 7+8=15, carry the 1
2. What is 1,003 - 457?
💡 Hint: You'll need to borrow from the thousands
3. What is 99 + 99 + 99?
💡 Hint: Think of it as 3 × 100 - 3
4. What is 500 - 238?
💡 Hint: Try subtracting from 499 and adding 1
5. A store has 1,250 items. They sell 387 and receive 145. How many items now?
💡 Hint: 1250 - 387 + 145
⚠️ Common Mistakes
- ✗Forgetting to carry (regroup) when a column adds to more than 9 — for example, writing 7+8=5 instead of 15 (write 5, carry 1).
- ✗When borrowing in subtraction, forgetting to reduce the digit you borrowed from by 1.
- ✗Starting from the left instead of the right — always start with the ones column.
- ✗Not lining up place values properly, especially with numbers of different lengths (like 47 + 8).
- ✗Mixing up addition and subtraction in word problems — read carefully for 'total', 'sum', 'difference', 'remaining'.
🌍 Real Life Example
Grocery Shopping Budget
You go to the store with $50. You buy bread ($4.29), milk ($3.89), eggs ($5.49), and chicken ($8.75). How much did you spend? $4.29 + $3.89 + $5.49 + $8.75 = $22.42. How much do you have left? $50.00 - $22.42 = $27.58. Addition tells you the total cost, subtraction tells you what remains. This is math you use every single day.
💡 Key Takeaway
Addition and subtraction are inverse operations — one undoes the other. Master carrying (regrouping) for addition and borrowing for subtraction, and you can handle any problem. The key is working right to left, one column at a time.