Addition and Subtraction Fact Families
A fact family is a group of related addition and subtraction facts that use the same three numbers. If you know one fact, you can find the other three.
Fact families show that addition and subtraction are connected — they are opposite operations.
What is Addition and Subtraction Fact Families - Class 2 Maths (Subtraction (Grade 2))?
A fact family is a set of 4 related number sentences using the same 3 numbers.
Example: The numbers 3, 5, and 8 make this fact family:
- 3 + 5 = 8
- 5 + 3 = 8
- 8 − 3 = 5
- 8 − 5 = 3
The biggest number (8) is always the sum in addition and the starting number in subtraction.
Solved Examples
Example 1: Example 1: Fact family for 7, 9, 16
Question: Write the fact family for 7, 9, and 16.
Think:
- The biggest number is 16
- 7 + 9 = 16
- 9 + 7 = 16
- 16 − 7 = 9
- 16 − 9 = 7
Answer: The fact family is: 7 + 9 = 16, 9 + 7 = 16, 16 − 7 = 9, 16 − 9 = 7.
Example 2: Example 2: Find the missing number
Question: 14 + 23 = 37. Use this to find 37 − 14.
Think:
- 14 + 23 = 37 is in the fact family
- So 37 − 14 = the other number = 23
Answer: 37 − 14 = 23.
Example 3: Example 3: Ria’s bangles
Question: Ria has 12 red bangles and 15 green bangles. That is 27 bangles in all. Write the fact family.
Think:
- Numbers: 12, 15, 27
- 12 + 15 = 27
- 15 + 12 = 27
- 27 − 12 = 15
- 27 − 15 = 12
Answer: 12 + 15 = 27, 15 + 12 = 27, 27 − 12 = 15, 27 − 15 = 12.
Example 4: Example 4: Doubles fact family
Question: Write the fact family for 8, 8, 16.
Think:
- 8 + 8 = 16
- 16 − 8 = 8
- Since both addends are the same, only 2 unique facts exist (not 4)
Answer: 8 + 8 = 16 and 16 − 8 = 8. (Only 2 facts because both addends are equal.)
Example 5: Example 5: Fill in the blank
Question: 45 − 19 = 26. What is 26 + 19?
Think:
- This is the same fact family: 19, 26, 45
- 26 + 19 = 45
Answer: 26 + 19 = 45.
Example 6: Example 6: Aman’s toys
Question: Aman has 34 toy cars and 28 toy trucks. Total = 62 toys. If he loses all his trucks, how many toys remain?
Think:
- Fact family: 34, 28, 62
- 62 − 28 = 34 (the toy cars remain)
Answer: Aman has 34 toys remaining.
Example 7: Example 7: Check your subtraction
Question: Meera says 53 − 27 = 26. Is she correct?
Think:
- Use addition to check: 26 + 27 = 53 ✓
- This matches the fact family
Answer: Yes, Meera is correct. 53 − 27 = 26 because 26 + 27 = 53.
Key Points to Remember
- A fact family has 4 related facts (2 addition + 2 subtraction) using the same 3 numbers.
- The largest number is always the sum (in addition) or the starting number (in subtraction).
- If both addends are the same (doubles), the fact family has only 2 unique facts.
- Use fact families to check answers: if 24 + 18 = 42, then 42 − 18 must be 24.
- Addition and subtraction are inverse (opposite) operations.
Practice Problems
- Write the fact family for 5, 8, and 13.
- If 36 + 29 = 65, what is 65 − 36?
- Write the fact family for 10, 10, and 20.
- Aditi has 45 beads. 18 are red and 27 are blue. Write the fact family.
- Use a fact family to check: is 71 − 35 = 36?
- Write all four facts for the numbers 22, 39, and 61.
Frequently Asked Questions
Q1. What is a fact family?
A fact family is a group of 4 related addition and subtraction facts that use the same three numbers. Example: 6 + 8 = 14, 8 + 6 = 14, 14 − 6 = 8, 14 − 8 = 6.
Q2. How many facts are in a fact family?
Usually 4 (two addition, two subtraction). If both addends are the same (like 7 + 7 = 14), there are only 2 unique facts.
Q3. How do fact families help with subtraction?
If you know an addition fact, you automatically know the related subtraction facts. Knowing 8 + 5 = 13 means you know 13 − 8 = 5 and 13 − 5 = 8.
Q4. How do I find the biggest number in a fact family?
Add the two smaller numbers. Their sum is the biggest number. For 12 and 9, the biggest number is 12 + 9 = 21.
Q5. Can fact families use 2-digit numbers?
Yes. Fact families work with any numbers. Example: 35 + 47 = 82, 47 + 35 = 82, 82 − 35 = 47, 82 − 47 = 35.
Q6. Why are addition and subtraction called inverse operations?
Because they undo each other. Adding 5 and then subtracting 5 brings you back to the same number. They are like opposites.
