What is a Fact Family for 20?

S0-SA1-1358

Grade Level:

Pre-School – Class 2

All domains without exception

Definition

What is it?

A fact family for a number like 20 is a set of four related math facts using three numbers. These three numbers show how addition and subtraction (or multiplication and division) are connected. For 20, we'll focus on addition and subtraction.

Simple Example

Quick Example

Imagine you have 20 ladoos. If your friend gives you 5 more, you have 25. But if you started with 15 ladoos and got 5 more, you'd have 20. The numbers 15, 5, and 20 form a fact family because 15 + 5 = 20, 5 + 15 = 20, 20 - 5 = 15, and 20 - 15 = 5.

Worked Example

Step-by-Step

Let's find the fact family for 20 using the numbers 12 and 8.

Step 1: Identify the three numbers. Our numbers are 12, 8, and 20.
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Step 2: Write the first addition fact. Add the two smaller numbers to get the largest number: 12 + 8 = 20.
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Step 3: Write the second addition fact. Reverse the order of the two smaller numbers: 8 + 12 = 20.
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Step 4: Write the first subtraction fact. Start with the largest number and subtract one of the smaller numbers: 20 - 8 = 12.
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Step 5: Write the second subtraction fact. Start with the largest number and subtract the other smaller number: 20 - 12 = 8.
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Answer: The fact family for 20 using 12 and 8 is: 12 + 8 = 20, 8 + 12 = 20, 20 - 8 = 12, and 20 - 12 = 8.

Why It Matters

Understanding fact families helps you see how numbers are connected and makes solving math problems much faster. This skill is super useful in daily life, like when you're calculating change after buying groceries or splitting costs with friends. It's a foundational skill for careers in finance, accounting, and even game development!

Common Mistakes

MISTAKE: Using four different numbers instead of three unique numbers. | CORRECTION: Always use only three specific numbers to form a fact family. For example, if the numbers are 5, 15, and 20, stick to just these three.

MISTAKE: Mixing up addition and subtraction operations, or writing facts that don't make sense. For example, 5 - 20 = 15. | CORRECTION: Remember that the largest number is always the sum in addition and the starting number in subtraction.

MISTAKE: Forgetting one of the four facts in the family. | CORRECTION: Always write two addition facts (if the two smaller numbers are different) and two subtraction facts to complete the family.

Practice Questions

Try It Yourself

QUESTION: Write the fact family for 20 using the numbers 10 and 10. | ANSWER: 10 + 10 = 20, 20 - 10 = 10 (Note: Since the two smaller numbers are the same, there are only two unique facts in this special case.)

QUESTION: If you have 20 rupees and spend 7 rupees on a chai, how many rupees are left? Write the fact family that includes 7, 13, and 20. | ANSWER: 13 rupees left. Fact family: 7 + 13 = 20, 13 + 7 = 20, 20 - 7 = 13, 20 - 13 = 7.

QUESTION: A cricket team scored 20 runs in an over. If 6 runs came from boundaries, how many runs came from singles and doubles? What are the four facts in the fact family for 20 using these numbers? | ANSWER: 14 runs came from singles and doubles. Fact family: 6 + 14 = 20, 14 + 6 = 20, 20 - 6 = 14, 20 - 14 = 6.

MCQ

Quick Quiz

Which of these is NOT part of the fact family for 20 using the numbers 18, 2, and 20?

18 + 2 = 20

20 - 18 = 2

2 + 20 = 18

20 - 2 = 18

The Correct Answer Is:

Option C (2 + 20 = 18) is incorrect because adding 2 and 20 gives 22, not 18. Also, in addition, the sum should be the largest number, which is 20 in this family.

Real World Connection

In the Real World

When a shopkeeper gives you change after you buy something, they are often using fact families in their head without even realizing it! For example, if a bill is 70 rupees and you pay 100 rupees, the shopkeeper quickly calculates 100 - 70 = 30. This is one part of the fact family for 100 (using 70, 30, and 100).

Key Vocabulary

Key Terms

FACT FAMILY: A set of 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 | SUM: The result of an addition problem | DIFFERENCE: The result of a subtraction problem

What's Next

What to Learn Next

Great job understanding fact families! Now that you know how addition and subtraction are linked, you can explore fact families for multiplication and division. This will show you even more amazing connections between numbers!