What is a Fact Family for 18?

S0-SA1-1317

Grade Level:

Pre-School – Class 2

All domains without exception

Definition

What is it?

A fact family for a number like 18 is a group of related math facts using the same three numbers. It shows how addition and subtraction (or multiplication and division) are connected. For 18, we usually look at how three numbers relate to make 18 through addition and subtraction.

Simple Example

Quick Example

Imagine you have 18 laddoos. If you give 10 laddoos to your friend and keep 8 for yourself, that's 10 + 8 = 18. This also means if you started with 18 and ate 8, you'd have 10 left (18 - 8 = 10). And if you ate 10, you'd have 8 left (18 - 10 = 8). The numbers 10, 8, and 18 form a fact family.

Worked Example

Step-by-Step

Let's find a fact family for 18 using the numbers 7 and 11.

1. **Identify the three numbers:** We have 7, 11, and 18.
2. **Form the first addition fact:** Add the two smaller numbers to get the largest number. 7 + 11 = 18.
3. **Form the second addition fact:** Change the order of the smaller numbers (Commutative Property). 11 + 7 = 18.
4. **Form the first subtraction fact:** Start with the largest number and subtract one of the smaller numbers. 18 - 7 = 11.
5. **Form the second subtraction fact:** Start with the largest number and subtract the other smaller number. 18 - 11 = 7.

So, the fact family for 18 using 7 and 11 is: 7 + 11 = 18, 11 + 7 = 18, 18 - 7 = 11, and 18 - 11 = 7.

Why It Matters

Understanding fact families helps you see the relationship between addition and subtraction, which is crucial for mental math and problem-solving. This skill is used by engineers to balance equations, by shopkeepers to calculate change quickly, and even by scientists to verify their data.

Common Mistakes

MISTAKE: Using only two numbers in a fact family. For example, just writing 9 + 9 = 18. | CORRECTION: A fact family typically uses three distinct numbers (unless two are the same, like 9, 9, 18) to show the full set of relationships. For 18, if you use 9 and 9, the family is 9+9=18, 18-9=9.

MISTAKE: Mixing up the largest number in subtraction. For example, writing 7 - 18 = 11. | CORRECTION: In subtraction for a fact family, the largest number (the sum) must always come first. You can only subtract a smaller number from a larger one in this context.

MISTAKE: Forgetting to write all four facts (two addition, two subtraction). | CORRECTION: A complete fact family for three distinct numbers always has four related equations. Make sure to write both ways for addition and both ways for subtraction.

Practice Questions

Try It Yourself

QUESTION: Write the fact family for 18 using the numbers 6 and 12. | ANSWER: 6 + 12 = 18, 12 + 6 = 18, 18 - 6 = 12, 18 - 12 = 6

QUESTION: If a fact family for 18 includes the number 5, what is the third number, and what are all the facts? | ANSWER: The third number is 13 (because 5 + 13 = 18). The facts are: 5 + 13 = 18, 13 + 5 = 18, 18 - 5 = 13, 18 - 13 = 5

QUESTION: Your mom bought 18 oranges. She used some for juice and 7 were left. Write the fact family that shows how many oranges she used. | ANSWER: The numbers are 7, 11 (18 - 7 = 11), and 18. The fact family is: 7 + 11 = 18, 11 + 7 = 18, 18 - 7 = 11, 18 - 11 = 7. She used 11 oranges.

MCQ

Quick Quiz

Which set of numbers forms a fact family for 18?

2018-03-06T00:00:00.000Z

2018-08-10T00:00:00.000Z

2018-09-02T00:00:00.000Z

18, 2, 9

The Correct Answer Is:

Option B (8, 10, 18) forms a fact family because 8 + 10 = 18, 10 + 8 = 18, 18 - 8 = 10, and 18 - 10 = 8. The other options do not add up to 18 correctly.

Real World Connection

In the Real World

When a cricket team needs 18 runs to win, and they score 6 runs in one over, they still need 12 more. This 'runs needed' scenario (6 + 12 = 18, 18 - 6 = 12) is a real-life fact family. Similarly, when you calculate how much change you'll get back from a Rs. 18 bill after buying something for Rs. 7, you're using a fact family concept (18 - 7 = 11).

Key Vocabulary

Key Terms

Fact Family: A group of related math facts using the same three numbers | Sum: The result of adding two or more numbers | Difference: The result of subtracting one number from another | Addends: The numbers that are added together in an addition problem

What's Next

What to Learn Next

Great job understanding fact families for addition and subtraction! Next, you can explore fact families for multiplication and division. These concepts build on the same idea of related operations and will make you even stronger in mental math.