What is a Fact Family for 12?

S0-SA1-0382

Grade Level:

Pre-School – Class 2

All domains without exception

Definition

What is it?

A fact family for a number like 12 is a group of four related math facts using the same three numbers. These facts show how addition and subtraction are inverse operations. For example, if you know 5 + 7 = 12, you can also find three other related facts.

Simple Example

Quick Example

Imagine you have 12 ladoos. If you give 5 ladoos to your friend, you are left with 7. This means 5 + 7 = 12 and 12 - 5 = 7. You can also think of it as giving 7 ladoos to your friend, leaving you with 5 (7 + 5 = 12 and 12 - 7 = 5). These four sentences form a fact family for 12 using the numbers 5, 7, and 12.

Worked Example

Step-by-Step

Let's find the fact family for 12 using the numbers 4, 8, and 12.

1. Start with an addition fact: We know that 4 + 8 equals 12.

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2. Write the commutative addition fact: Since 4 + 8 = 12, then 8 + 4 must also equal 12.

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3. Write a subtraction fact: If we start with the total (12) and take away one part (4), we get the other part (8). So, 12 - 4 = 8.

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4. Write the other subtraction fact: Similarly, if we start with 12 and take away 8, we get 4. So, 12 - 8 = 4.

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Answer: The fact family for 12 using 4, 8, and 12 is: 4 + 8 = 12, 8 + 4 = 12, 12 - 4 = 8, and 12 - 8 = 4.

Why It Matters

Understanding fact families helps you see the relationship between addition and subtraction, which is super useful for solving problems quickly. This skill is a building block for algebra and is used by accountants to balance books or by shopkeepers to calculate change efficiently. It makes mental math much easier!

Common Mistakes

MISTAKE: Using four different numbers in the fact family. | CORRECTION: A fact family always uses the same three numbers for all four facts.

MISTAKE: Not including two addition and two subtraction facts. | CORRECTION: Every complete fact family must have two addition statements and two subtraction statements (unless the two smaller numbers are identical, like 6, 6, 12).

MISTAKE: Mixing up the total (sum) with the parts in subtraction. | CORRECTION: In subtraction, always start with the largest number (the total) and subtract one of the smaller numbers to get the other smaller number.

Practice Questions

Try It Yourself

QUESTION: What are the four facts in the fact family for 12 using the numbers 3, 9, and 12? | ANSWER: 3 + 9 = 12, 9 + 3 = 12, 12 - 3 = 9, 12 - 9 = 3

QUESTION: If you know that 7 + 5 = 12, what are the other three facts in this fact family? | ANSWER: 5 + 7 = 12, 12 - 7 = 5, 12 - 5 = 7

QUESTION: A vegetable vendor sold 6 kg of potatoes and 6 kg of onions, making a total of 12 kg of vegetables. Write the complete fact family for this situation. | ANSWER: 6 + 6 = 12, 12 - 6 = 6 (Note: In this special case, there are only two unique facts because the two parts are the same)

MCQ

Quick Quiz

Which set of facts forms a complete fact family for 12 using the numbers 5, 7, and 12?

5 + 7 = 12, 7 + 5 = 12, 12 - 5 = 7

5 + 7 = 12, 7 + 5 = 12, 12 - 5 = 7, 12 - 7 = 5

5 + 7 = 12, 12 - 7 = 5, 12 + 5 = 17

5 + 7 = 12, 7 - 5 = 2, 12 - 7 = 5

The Correct Answer Is:

Option B includes two addition facts and two subtraction facts using only the numbers 5, 7, and 12, which is the definition of a complete fact family. Other options are missing facts or use incorrect numbers/operations.

Real World Connection

In the Real World

When a cashier gives you change after you buy a snack, they often use fact families without even thinking. If your bill is Rs 7 and you give Rs 12, they know 12 - 7 = 5, so they return Rs 5. This quick mental calculation is an everyday use of fact families.

Key Vocabulary

Key Terms

Fact Family: A group of four related math facts using three numbers | Addition: Combining two or more numbers to find a total | Subtraction: Taking one number away from another to find the difference | Inverse Operations: Operations that undo each other (like addition and subtraction)

What's Next

What to Learn Next

Great job understanding fact families for addition and subtraction! Next, you can explore multiplication and division fact families. They work in a similar way and will further strengthen your number sense and problem-solving skills.