What is a Fact Family for 15?

S0-SA1-1314

Grade Level:

Pre-School – Class 2

All domains without exception

Definition

What is it?

A fact family for a number like 15 is a set of four related math facts (two addition and two subtraction) that use the same three numbers. Think of it like a family where everyone is connected! These facts show how addition and subtraction are opposite operations.

Simple Example

Quick Example

Imagine you have 7 laddoo and your friend gives you 8 more. Now you have 15 laddoo. This gives us one fact: 7 + 8 = 15. From this, we can also say 8 + 7 = 15. If you started with 15 laddoo and ate 7, you'd have 8 left (15 - 7 = 8). And if you ate 8, you'd have 7 left (15 - 8 = 7). These four statements form the fact family for 7, 8, and 15.

Worked Example

Step-by-Step

Let's find the fact family for the numbers 6, 9, and 15.

1. Identify the three numbers: 6, 9, and 15. We know that 6 + 9 = 15.
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2. Write the first addition fact: 6 + 9 = 15. (Like having 6 cricket balls and getting 9 more, making 15 in total).
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3. Write the second addition fact by swapping the first two numbers: 9 + 6 = 15. (It doesn't matter if you get 9 balls first then 6, the total is still 15).
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4. Write the first subtraction fact: Start with the largest number (15) and subtract one of the smaller numbers (6): 15 - 6 = 9. (If you had 15 rupees and spent 6, you'd have 9 left).
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5. Write the second subtraction fact: Start with the largest number (15) and subtract the other smaller number (9): 15 - 9 = 6. (If you had 15 rupees and spent 9, you'd have 6 left).
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ANSWER: The fact family for 6, 9, and 15 is: 6 + 9 = 15, 9 + 6 = 15, 15 - 6 = 9, and 15 - 9 = 6.

Why It Matters

Understanding fact families helps you see the relationship between addition and subtraction, which is key for solving more complex math problems later on. It's like building strong foundations! Engineers use these basic number relationships to check calculations, and even game developers need to understand how numbers add and subtract quickly.

Common Mistakes

MISTAKE: Using numbers that don't belong to the family (e.g., for 6, 9, 15, writing 6 + 7 = 13) | CORRECTION: Always use only the three given numbers for all four facts in the family.

MISTAKE: Forgetting that subtraction always starts with the largest number in the family (e.g., for 6, 9, 15, writing 6 - 9 = -3) | CORRECTION: In subtraction facts within a family, the largest number is always the one you start with (the minuend).

MISTAKE: Writing only two facts instead of four (e.g., just 6 + 9 = 15 and 15 - 9 = 6) | CORRECTION: Remember that a complete fact family always has two addition facts and two subtraction facts.

Practice Questions

Try It Yourself

QUESTION: Write the fact family for the numbers 5, 10, and 15. | ANSWER: 5 + 10 = 15, 10 + 5 = 15, 15 - 5 = 10, 15 - 10 = 5

QUESTION: If 7 + 8 = 15 is one fact, what are the other three facts in its family? | ANSWER: 8 + 7 = 15, 15 - 7 = 8, 15 - 8 = 7

QUESTION: My auto-rickshaw fare was 15 rupees. If I paid with a 20-rupee note and got 5 rupees back, what is the fact family relating these three numbers? | ANSWER: 15 + 5 = 20, 5 + 15 = 20, 20 - 15 = 5, 20 - 5 = 15

MCQ

Quick Quiz

Which set of facts correctly represents the fact family for 4, 11, and 15?

4 + 11 = 15, 11 + 4 = 15, 15 - 4 = 11, 15 - 11 = 4

4 + 11 = 15, 11 + 4 = 15, 15 - 4 = 11, 11 - 4 = 7

4 + 11 = 15, 15 - 4 = 11, 15 - 11 = 4, 4 + 15 = 19

4 + 11 = 15, 11 + 4 = 15, 15 - 11 = 4, 15 - 5 = 10

The Correct Answer Is:

Option A correctly lists two addition facts and two subtraction facts using only the numbers 4, 11, and 15. Other options either use incorrect numbers or incorrect operations.

Real World Connection

In the Real World

Imagine you're managing a small 'kirana' store. If you start with 15 packets of biscuits, sell 8 packets, and have 7 left, you're using a fact family! This helps you quickly check your stock: 8 + 7 = 15 (sold + left = total) or 15 - 8 = 7 (total - sold = left). This basic idea is used in inventory management and sales tracking, even in big e-commerce companies like Flipkart or Amazon.

Key Vocabulary

Key Terms

FACT FAMILY: A set of four related math facts (two addition, two subtraction) using the same three numbers | ADDITION: Combining two or more numbers to find a total | SUBTRACTION: Taking one number away from another to find the difference | OPERATION: A mathematical process like addition or subtraction

What's Next

What to Learn Next

Great job understanding fact families! Now that you see how addition and subtraction are linked, you're ready to explore how multiplication and division are also related through their own fact families. This will strengthen your number sense even more!