Subtraction as inverse of addition, conceptual understanding
Elementary Foundations • K-5
Subtraction is the opposite of addition. When you take away some objects from a group, or when you find the difference between two amounts, you are subtracting. Understanding how subtraction and addition are connected makes both operations easier.
Subtraction answers three kinds of questions:
We call 9 the minuend (what you start with), 4 the subtrahend (what you take away), and 5 the difference (what is left).
Addition and subtraction are inverse operations -- they undo each other. This is one of the most powerful ideas in math. Every addition fact has a matching subtraction fact:
Addition Facts
Subtraction Facts
These four facts together are called a fact family. If you know one fact, you can figure out all the others!
Instead of subtracting, ask: "9 plus what equals 15?"
Think: 9 + 1 = 10, and 10 + 5 = 15. That is 1 + 5 = 6 more.
So 15 - 9 = 6.
Start at 12 and count back 4:
So 12 - 4 = 8.
Because subtraction and addition are inverses, you can always check subtraction with addition. If you found that 73 - 28 = 45, verify by adding: 45 + 28 = 73. It works!
Unlike addition, the order in subtraction does matter. 8 - 3 is not the same as 3 - 8. Always subtract the smaller amount from the larger one (at this level). Also, when borrowing in column subtraction, remember to reduce the tens digit by 1.
If a subtraction problem feels hard, turn it into an addition question. For 14 - 8, think: "8 + ? = 14." Start at 8 and count up: 9, 10, 11, 12, 13, 14 -- that is 6 jumps. So 14 - 8 = 6.
1. Write the fact family for 4, 7, and 11.
4 + 7 = 11
7 + 4 = 11
11 - 7 = 4
11 - 4 = 7
2. Solve by counting back: 14 - 5 = ?
Start at 14, count back 5: 13, 12, 11, 10, 9. The answer is 9.
3. Use addition to solve: 16 - 7 = ?
Think: 7 + ? = 16. Count up from 7: 7 + 3 = 10, 10 + 6 = 16. That is 3 + 6 = 9. So 16 - 7 = 9.
4. Subtract: 82 - 35 = ?
82 - 30 = 52. Then 52 - 5 = 47. The answer is 47. Check: 47 + 35 = 82.
5. Maria had 50 stickers. She gave 23 to her friend. How many does she have left?
50 - 23: First, 50 - 20 = 30. Then 30 - 3 = 27. Maria has 27 stickers left.
Summary: Subtraction means taking away, finding a difference, or finding a missing part. Addition and subtraction are inverse operations -- they undo each other and belong to the same fact families. You can always check subtraction by adding. Key strategies include counting back and thinking addition.