What is a Number Family (of 15)?

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Grade Level:

Pre-School – Class 2

All domains without exception

Definition

What is it?

A Number Family (of a specific number, like 15) is a group of related math facts using addition and subtraction with the same three numbers. It shows how these three numbers are connected through these operations. For example, a number family of 15 uses three numbers that can be added or subtracted to make 15.

Simple Example

Quick Example

Imagine you have 15 ladoos. If you eat 10 ladoos, you have 5 left. This means 10 + 5 = 15, and 15 - 10 = 5. Also, if you had 5 ladoos and someone gave you 10 more, you would have 15. So, the numbers 10, 5, and 15 form a number family.

Worked Example

Step-by-Step

Let's find the Number Family of 15 using the numbers 7, 8, and 15.

Step 1: Identify the three numbers involved: 7, 8, and 15. Notice that 7 + 8 = 15.
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Step 2: Write the first addition fact. Since 7 and 8 add up to 15, the first fact is 7 + 8 = 15.
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Step 3: Write the second addition fact. You can swap the numbers being added, so 8 + 7 = 15 is the second fact.
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Step 4: Write the first subtraction fact. Start with the largest number (15) and subtract one of the smaller numbers (7). So, 15 - 7 = 8.
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Step 5: Write the second subtraction fact. Again, start with the largest number (15) and subtract the other smaller number (8). So, 15 - 8 = 7.
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Answer: The Number Family of 15 for the numbers 7, 8, and 15 consists of these four facts: 7 + 8 = 15, 8 + 7 = 15, 15 - 7 = 8, and 15 - 8 = 7.

Why It Matters

Understanding number families helps you see the relationship between addition and subtraction, making mental math much faster. This skill is crucial for careers like shopkeepers managing inventory, engineers calculating measurements, or even data analysts who need to quickly process numerical information.

Common Mistakes

MISTAKE: Not including all four facts (two addition, two subtraction) in the family. | CORRECTION: Remember that a complete number family always has four facts, showing both ways to add and both ways to subtract using the same three numbers.

MISTAKE: Using numbers that don't actually form an addition/subtraction relationship for the given total. For example, saying 6, 4, and 15 form a family of 15. | CORRECTION: Always check that the two smaller numbers add up to the largest number, and that the largest number minus one smaller number equals the other smaller number.

MISTAKE: Confusing the 'total' number for the family. For example, trying to make a family of 10 when the numbers given are 5, 10, and 15. | CORRECTION: The 'total' number (like 15 in 'Number Family of 15') is always the largest number in that specific family, and it's the result of the addition.

Practice Questions

Try It Yourself

QUESTION: Write the Number Family of 12 using the numbers 5, 7, and 12. | ANSWER: 5 + 7 = 12, 7 + 5 = 12, 12 - 5 = 7, 12 - 7 = 5

QUESTION: If you know that 9 + 6 = 15, what are the other three facts in this Number Family of 15? | ANSWER: 6 + 9 = 15, 15 - 9 = 6, 15 - 6 = 9

QUESTION: Your friend says the numbers 4, 11, and 15 form a Number Family of 15. Is this correct? If yes, write all four facts. If no, explain why. | ANSWER: Yes, it is correct. The four facts are: 4 + 11 = 15, 11 + 4 = 15, 15 - 4 = 11, 15 - 11 = 4.

MCQ

Quick Quiz

Which set of facts correctly forms a Number Family of 15 using the numbers 6, 9, and 15?

6 + 9 = 15, 9 + 6 = 15, 15 - 6 = 9, 15 - 9 = 6

6 + 9 = 15, 9 + 6 = 15, 15 - 9 = 6, 6 - 9 = 15

6 + 15 = 9, 9 + 6 = 15, 15 - 9 = 6, 15 - 6 = 9

6 + 9 = 15, 9 + 15 = 6, 15 - 6 = 9, 15 - 9 = 6

The Correct Answer Is:

Option A correctly lists all four facts (two addition and two subtraction) that show the relationship between 6, 9, and 15. The other options contain incorrect addition or subtraction statements.

Real World Connection

In the Real World

When a cricket team needs to score 15 runs to win, and they already have 8 runs, a commentator quickly knows they need 7 more (15 - 8 = 7). This quick mental calculation uses the idea of a number family (8, 7, 15) to understand how the runs scored, runs needed, and total target are related.

Key Vocabulary

Key Terms

ADDITION: Combining two or more numbers to find a total | SUBTRACTION: Taking one number away from another to find the difference | FACT FAMILY: Another name for a Number Family | RELATIONSHIP: How numbers are connected to each other through operations

What's Next

What to Learn Next

Next, you can explore Number Families with multiplication and division! It's the same idea but with different operations. Mastering these families will make solving more complex problems, like those in algebra, much easier.