Relationship Between Addition and Subtraction
Addition and subtraction are like two sides of the same coin. When we add, we put things together. When we subtract, we take things away. These two operations are opposite of each other.
If you know an addition fact, you can find a subtraction fact from it. This is called the relationship between addition and subtraction. Learning this helps children in Class 1 solve problems faster and check their answers.
What is Relationship Between Addition and Subtraction - Class 1 Maths (Subtraction (Grade 1))?
Addition means putting numbers together to get a bigger number. Subtraction means taking away from a number to get a smaller number.
They are inverse operations — one undoes the other. If 3 + 4 = 7, then 7 − 4 = 3 and 7 − 3 = 4.
Types and Properties
A fact family is a group of addition and subtraction facts that use the same three numbers.
For the numbers 2, 5, and 7:
| Addition Facts | Subtraction Facts |
|---|---|
| 2 + 5 = 7 | 7 − 5 = 2 |
| 5 + 2 = 7 | 7 − 2 = 5 |
How Addition Undoes Subtraction
If Ria takes away 3 from 8 and gets 5, she can check by adding: 5 + 3 = 8. It matches! So her answer is correct.
How Subtraction Undoes Addition
If Aman adds 4 + 6 = 10, he can check by subtracting: 10 − 6 = 4. It matches!
Solved Examples
Example 1: Example 1: Write the Fact Family
Question: Write the fact family for 3, 5, and 8.
Think:
- 3 + 5 = 8
- 5 + 3 = 8
- 8 − 3 = 5
- 8 − 5 = 3
Answer: The fact family has 4 facts using the numbers 3, 5, and 8.
Example 2: Example 2: Find the Missing Number
Question: 6 + ___ = 9. Use subtraction to find the missing number.
Think:
- We know 6 + ? = 9
- Subtract: 9 − 6 = 3
Answer: The missing number is 3.
Example 3: Example 3: Check an Addition Using Subtraction
Question: Priya says 4 + 5 = 9. Check her answer using subtraction.
Think:
- If 4 + 5 = 9, then 9 − 5 should give 4
- 9 − 5 = 4 ✓
Answer: Priya is correct.
Example 4: Example 4: Check a Subtraction Using Addition
Question: Dev says 10 − 4 = 6. Check his answer using addition.
Think:
- If 10 − 4 = 6, then 6 + 4 should give 10
- 6 + 4 = 10 ✓
Answer: Dev is correct.
Example 5: Example 5: Word Problem — Addition to Subtraction
Question: Meera has 7 bangles. She gives 2 to her friend. How many are left?
Think:
- Total bangles = 7
- She gives away 2 → we subtract
- 7 − 2 = 5
Check: 5 + 2 = 7 ✓
Answer: Meera has 5 bangles left.
Example 6: Example 6: Word Problem — Subtraction to Addition
Question: Arjun had some marbles. He got 3 more and now has 8. How many did he have before?
Think:
- ? + 3 = 8
- Subtract: 8 − 3 = 5
Answer: Arjun had 5 marbles before.
Example 7: Example 7: Complete the Fact Family
Question: 4 + 2 = 6. Write three more facts from this.
Think:
- 2 + 4 = 6 (addition — change order)
- 6 − 2 = 4 (subtraction)
- 6 − 4 = 2 (subtraction)
Answer: The three other facts are 2 + 4 = 6, 6 − 2 = 4, and 6 − 4 = 2.
Real-World Applications
Where do we use this?
- Checking answers: After adding, subtract to check. After subtracting, add to check.
- Shopping: If Kavi pays ₹10 for a ₹6 toy, the change is 10 − 6 = 4. Check: 6 + 4 = 10.
- Sharing: If 9 sweets are shared and 4 are left, you gave away 9 − 4 = 5. Check: 5 + 4 = 9.
Key Points to Remember
- Addition and subtraction are opposite operations — one undoes the other.
- A fact family uses the same 3 numbers to make 2 addition and 2 subtraction facts.
- To find a missing number in addition, use subtraction.
- To check subtraction, add the answer and the number you took away — you should get the starting number.
- To check addition, subtract one part from the total — you should get the other part.
Practice Problems
- Write the fact family for 2, 6, and 8.
- If 5 + 4 = 9, write the two subtraction facts.
- Find the missing number: 7 + ___ = 10.
- Aditi had 9 pencils. She gave 3 away. How many are left? Check your answer using addition.
- Rahul says 8 − 5 = 4. Use addition to check if he is right.
- Complete: If 12 − 7 = 5, then 5 + 7 = ___.
Frequently Asked Questions
Q1. What is the relationship between addition and subtraction?
Addition and subtraction are opposite operations. Addition puts numbers together, and subtraction takes them apart. If you know 3 + 5 = 8, you also know 8 − 5 = 3 and 8 − 3 = 5.
Q2. What is a fact family?
A fact family is a set of 4 number sentences (2 addition and 2 subtraction) that use the same three numbers. For example, 2, 3, and 5 give: 2+3=5, 3+2=5, 5−2=3, 5−3=2.
Q3. How can subtraction help me check addition?
After adding two numbers to get a sum, subtract one of the numbers from the sum. If you get the other number back, your addition was correct. For example, 6+3=9, check: 9−3=6.
Q4. How can addition help me check subtraction?
After subtracting, add the answer to the number you took away. If you get the starting number, your subtraction was correct. For example, 10−4=6, check: 6+4=10.
Q5. Why should I learn fact families?
Fact families help you solve problems faster. If you forget a subtraction fact, you can think of the related addition fact to find the answer.
Q6. Can fact families have only 2 facts instead of 4?
Yes. When a number is added to itself (a double), the fact family has only 2 unique facts. For example, 4+4=8 gives: 4+4=8 and 8−4=4.
Q7. What is the easiest way to find a missing number?
Use the opposite operation. If the problem is addition with a missing part, subtract. If the problem is subtraction with a missing part, add. For example, ___ + 5 = 12 means 12 − 5 = 7.
