What is a Fact Family for 17?

S0-SA1-1316

Grade Level:

Pre-School – Class 2

All domains without exception

Definition

What is it?

A fact family for a number like 17 is a group of related addition and subtraction sentences that use the same three numbers. Think of it like a small family where everyone is connected by addition and subtraction. For 17, we need two smaller numbers that add up to 17.

Simple Example

Quick Example

Imagine you have 17 laddoos. If you give 10 laddoos to your friend and keep 7 for yourself, then 10 + 7 = 17. This also means 7 + 10 = 17. If you started with 17 laddoos and gave away 10, you're left with 7 (17 - 10 = 7). And if you gave away 7, you'd have 10 left (17 - 7 = 10). These four sentences form a fact family for 17 using the numbers 10, 7, and 17.

Worked Example

Step-by-Step

Let's find a fact family for 17 using the numbers 8 and 9.

Step 1: Identify the three numbers in our family. These are 8, 9, and 17.
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Step 2: Write the first addition sentence. Put the two smaller numbers together to get the largest number. So, 8 + 9 = 17.
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Step 3: Write the second addition sentence. Just swap the order of the two smaller numbers. So, 9 + 8 = 17.
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Step 4: Write the first subtraction sentence. Start with the largest number and subtract one of the smaller numbers. So, 17 - 8 = 9.
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Step 5: Write the second subtraction sentence. Start with the largest number again and subtract the other smaller number. So, 17 - 9 = 8.
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The fact family for 17 using 8 and 9 is: 8 + 9 = 17, 9 + 8 = 17, 17 - 8 = 9, and 17 - 9 = 8.

Why It Matters

Understanding fact families helps you see how numbers are connected and makes mental math much faster. This skill is super useful in everyday life, like calculating change at a shop or splitting bills with friends. It's a foundational concept for careers in finance, data analysis, and even engineering, where quick number sense is key.

Common Mistakes

MISTAKE: Using numbers that don't add up to 17 for the addition facts. For example, saying 5 + 10 = 17. | CORRECTION: Always ensure the two smaller numbers add up to the target number (17 in this case). 5 + 10 = 15, not 17.

MISTAKE: Forgetting to start subtraction sentences with the largest number. For example, writing 8 - 17 = 9. | CORRECTION: In a fact family, subtraction always starts with the largest number (the sum) and subtracts one of the smaller parts.

MISTAKE: Only writing one addition or one subtraction fact. | CORRECTION: A complete fact family for three distinct numbers always has two addition facts and two subtraction facts. If two numbers are the same (e.g., for 16, using 8 and 8), then there will only be one addition and one subtraction fact.

Practice Questions

Try It Yourself

QUESTION: What are the four number sentences in the fact family for 17 using the numbers 6 and 11? | ANSWER: 6 + 11 = 17, 11 + 6 = 17, 17 - 6 = 11, 17 - 11 = 6

QUESTION: If you know that 17 - 5 = 12, what are the other three facts in this fact family? | ANSWER: 17 - 12 = 5, 5 + 12 = 17, 12 + 5 = 17

QUESTION: Your mom gave you Rs. 17. You spent Rs. 9 on a 'samosa' and 'chai'. How much money do you have left? Write the complete fact family for this situation using the numbers involved. | ANSWER: You have Rs. 8 left. Fact Family: 9 + 8 = 17, 8 + 9 = 17, 17 - 9 = 8, 17 - 8 = 9

MCQ

Quick Quiz

Which set of sentences forms a complete fact family for 17 using the numbers 7, 10, and 17?

7 + 10 = 17, 10 + 7 = 17, 17 - 7 = 10

7 + 10 = 17, 10 - 7 = 3, 17 - 10 = 7

7 + 10 = 17, 10 + 7 = 17, 17 - 7 = 10, 17 - 10 = 7

17 + 7 = 24, 17 - 10 = 7, 10 + 7 = 17

The Correct Answer Is:

Option C includes all four correct number sentences (two addition, two subtraction) that connect the numbers 7, 10, and 17. The other options are either incomplete or contain incorrect facts.

Real World Connection

In the Real World

Imagine you're checking your mobile data usage. If you started with 17 GB of data and used 5 GB, you'd have 12 GB left. This is 17 - 5 = 12. You can also think that 5 GB used + 12 GB remaining = 17 GB total. This quick calculation helps you manage your data plan, just like fact families help us understand number relationships instantly.

Key Vocabulary

Key Terms

FACT FAMILY: A group of related addition and subtraction sentences using the same three numbers. | ADDITION: Combining numbers to find a total. | SUBTRACTION: Taking one number away from another to find the difference. | SUM: The result of adding two or more numbers. | DIFFERENCE: The result of subtracting one number from another.

What's Next

What to Learn Next

Great job understanding fact families! Now that you know how numbers relate, you can explore inverse operations for multiplication and division. This will show you how multiplication and division are also connected, just like addition and subtraction are in fact families.