Addition and Subtraction Relationship (Grade 2)
Addition and subtraction are opposite operations. What addition puts together, subtraction takes apart. They are like two sides of the same coin.
In Class 2, you learn how addition can be used to check subtraction, and how subtraction can undo addition. This is called the inverse relationship.
What is Addition and Subtraction Relationship - Class 2 Maths (Subtraction)?
Inverse operations are operations that undo each other. Addition and subtraction are inverse operations.
If 8 + 5 = 13, then 13 − 5 = 8 and 13 − 8 = 5
This means: if you know one addition fact, you automatically know two subtraction facts.
A group of related addition and subtraction facts is called a fact family.
Types and Properties
Fact Family Example:
For the numbers 6, 9, and 15:
- 6 + 9 = 15 (addition)
- 9 + 6 = 15 (addition — order changed)
- 15 − 9 = 6 (subtraction)
- 15 − 6 = 9 (subtraction)
All four facts use the same three numbers.
Solved Examples
Example 1: Check Subtraction with Addition
Question: Check if 17 − 9 = 8 is correct.
Think:
- If 17 − 9 = 8, then 8 + 9 should equal 17
- 8 + 9 = 17 ✓
Answer: Yes, the subtraction is correct.
Example 2: Write the Fact Family
Question: Write the fact family for 7, 5, and 12.
Think:
- 7 + 5 = 12
- 5 + 7 = 12
- 12 − 5 = 7
- 12 − 7 = 5
Answer: The fact family is: 7 + 5 = 12, 5 + 7 = 12, 12 − 5 = 7, 12 − 7 = 5
Example 3: Find the Missing Number
Question: 14 − ___ = 6. Use addition to find the missing number.
Think:
- 6 + ___ = 14
- 14 − 6 = 8
Answer: 14 − 8 = 6
Example 4: Word Problem — Stickers
Question: Ria had some stickers. She gave 9 stickers to Meera and has 15 left. How many did she start with?
Think:
- ___ − 9 = 15
- Use addition: 15 + 9 = 24
Answer: Ria started with 24 stickers.
Example 5: Word Problem — Marbles
Question: Arjun has 20 marbles. He gives some to Dev and has 12 left. How many did he give? Check your answer.
Think:
- 20 − ___ = 12
- 20 − 12 = 8
- Check: 12 + 8 = 20 ✓
Answer: Arjun gave 8 marbles to Dev.
Example 6: Addition Undoes Subtraction
Question: Aman starts with 30. He subtracts 11. Then he adds 11 back. What number does he have?
Think:
- 30 − 11 = 19
- 19 + 11 = 30
- Adding back the same number returns to the start
Answer: Aman has 30 again. Addition undid the subtraction.
Example 7: Two-Digit Fact Family
Question: Write a fact family using 25, 38, and 63.
Think:
- 25 + 38 = 63
- 38 + 25 = 63
- 63 − 38 = 25
- 63 − 25 = 38
Answer: 25 + 38 = 63, 38 + 25 = 63, 63 − 38 = 25, 63 − 25 = 38
Key Points to Remember
- Addition and subtraction are inverse (opposite) operations.
- You can check subtraction using addition: if a − b = c, then c + b should equal a.
- A fact family has 4 related facts using the same 3 numbers.
- If you know one fact in the family, you can find all the others.
- Adding and subtracting the same number cancels out — you return to where you started.
Practice Problems
- Check if 23 − 15 = 8 is correct using addition.
- Write the fact family for 8, 6, and 14.
- Find the missing number: ___ − 7 = 18
- Priya has 35 beads. She uses some for a necklace and has 20 left. How many did she use?
- If 45 + 27 = 72, what is 72 − 27?
- Dev subtracts 16 from 50 and gets 34. How can he check this answer?
Frequently Asked Questions
Q1. What is the relationship between addition and subtraction?
They are inverse (opposite) operations. Addition puts numbers together; subtraction takes them apart. If 7 + 5 = 12, then 12 − 5 = 7.
Q2. What is a fact family?
A fact family is a group of 4 related addition and subtraction facts that use the same 3 numbers. Example: 3 + 8 = 11, 8 + 3 = 11, 11 − 3 = 8, 11 − 8 = 3.
Q3. How do I check subtraction using addition?
Take the answer and add the number you subtracted. If you get back the original number, your subtraction is correct. Example: 20 − 7 = 13. Check: 13 + 7 = 20. Correct!
Q4. Can I check addition using subtraction?
Yes. If 15 + 8 = 23, check by subtracting: 23 − 8 = 15. If you get back 15, the addition is correct.
Q5. Why are fact families useful?
Knowing one fact gives you three more for free. If you remember 6 + 7 = 13, you also know 13 − 7 = 6 and 13 − 6 = 7.
Q6. What happens when a number has a double?
For doubles like 5 + 5 = 10, the fact family has only 2 different facts: 5 + 5 = 10 and 10 − 5 = 5. Both subtraction facts are the same.
