## What Is a Fact Family?

A fact family in math is a group of math facts created using three numbers. Numbers also have relationships, just like members of a family. These relations between numbers are well described using fact families.

## Fact Family Definition

A fact family can be defined as a collection of math facts that express the relation between the same set of numbers. It is also known as a “number family” and generally uses three numbers.

It helps to understand basic arithmetic operations (addition, subtraction, multiplication, and division) and solve their problems.

## Fact Family Triangle

**Fact families** are usually represented in the form of a triangle, as shown in the below image. The three numbers forming the **fact family** are written in the three corners (near the vertices) of the triangle.

The operation’s sign connecting the three numbers is usually written in the middle. For the addition **fact family**, the sum of the numbers is usually written at the top vertex, and the numbers being added are written at the vertices at the bottom.

Take a look at the fact family triangle with fact family numbers 2, 5, 7.

**Fact families** can be used for solving basic arithmetic equations involving addition, subtraction, multiplication, and division. Let’s look into two types of fact family** **examples.

## Addition and Subtraction Fact Family

In an **addition and subtraction fact family**, the three numbers will have two addition and two subtraction relationships.

Here, for instance, a **fact family** has been created using the numbers 12, 8, and 4, where 12 is the total number of crayons, out of which 8 are yellow and 4 are red.

The four relationships here are as follows.

- $4 + 8 = 12$
- $8 + 4 = 12$
- $12$ $–$ $8 = 4$
- $12$ $–$ $4 = 8$

Let’s take another example with the numbers 9, 4, and 5. Here, 4 and 5 are parts, while 9 is the whole.

## Multiplication and Division Fact Family

In a **multiplication and division fact family**, the three numbers will have two multiplication and two division relationships.

For instance, let’s consider an art class where 8 students sit at 4 tables in groups of 2. Four relations formed using the numbers 2, 4, 8 are are:

- $4 \times 2 = 8$
- $2 \times 4 = 8$
- $8 \div 4 = 2$
- $8 \div 2 = 4$

Let’s take another example. Here, 4 and 3 are parts, while 12 is the whole.

## Fun Fact!

One exciting thing about fact families is that they represent the inverse relationship between operations.

**Get ready to rap!!**

*Three numbers—it’s a family bond!*

*Just multiply or divide to respond.*

*Or whether you add or subtract,*

*In the end, you get a family of facts!*

## Conclusion

A** fact family** is a fundamental concept that lets the brain think of various arithmetic operations and combinations of numbers. This will help in developing problem-solving skills and enhance analytical thinking capabilities.

## Solved Examples

**Form two addition and subtraction equations for the fact family diagram given below.**

**Solution**: The three numbers 10, 2, and 8 form an **addition and subtraction fact family**. The equations for addition are as follows:

**Addition equations**

- $8 + 2 = 10$
- $2 + 8 = 10$

The equations for subtraction are as follows:

**Subtraction equations**

- $10$ $–$ $2 = 8$
- $10$ $–$ $8 = 2$

**2. Form multiplication and division equations for the fact family triangle given below.**

**Solution:**

**Multiplication equations**

$6 \times 12 = 72$

$12 \times 6 = 72$

**Division equations**

$72 \div 6 = 12$

$72 \div 12 = 6$

**3. Form a fact family triangle with numbers 4, 5, and 20. Write the equations.**

**Solution:**

**Multiplication equations**

$4 \times 5 = 20$

$5 \times 4 = 20$

**Division equations**

$20 \div 4 = 5$

$20 \div 5 = 4$

**4. Complete the fact family triangle and equations for the three numbers: 3, 6 and 9.**

**Solution:**

The equations are as follows:

- $3 + 6 = 9$
- $6 + 3 = 9$
- $9$ $–$ $3 = 6$
- $9$ $–$ $6 = 3$

## Practice Problems

## Fact Family

### What’s the missing relation?

$2 + 8 = 10$

$8 + 2 = 10$

$10 – 2 = 8$

?

This is an

**addition and subtraction fact family**, where two addition sentences are given in the problem statement with one subtraction sentence. The missing subtraction sentence that matches the

**fact family**of three numbers 2, 8, and 10 is $10$ $–$ $8$, equal to 2.

### Which math operation does NOT belong in the family of math facts you can create from the numbers 8, 5, and 13?

8, 5, and 13 form an

**addition and subtraction fact family**, where the possible operations are as follows.

$8 + 5 = 13$

$5 + 8 = 13$

$13$ $–$ $5 = 8$

$13$ $–$ $8 = 5$

The odd one is option b, i.e., $8 \times 5 = 40$, which does not belong to the

**fact family**.

### Find the missing number in the multiplication and division fact family: 2, 20, ?

2,

**10**, and 20 form a

**multiplication and division fact family**where the two possible division operations are $20 \div 10 = 2$ and $20 \div 2 = 10$.

## Frequently Asked Questions

**What are the operations used in forming a fact family?**

Addition, subtraction, multiplication, and division are the operations involved in forming a fact family.

**How can we efficiently teach fact family to children?**

Instead of handing out math worksheets, play a game with your children using fun things like jelly beans. Give jelly beans in a set of three numbers, say 2, 3, and 5. Ask them to create an addition and subtraction fact family using the jelly beans. Repeat for multiplication and division fact family.

**How are fact families and arrays related?**

Arrays are visual representations of a fact family in the form of symmetry. For example, in a fact family of 4, 3, and 12, twelve students are made to stand in 3 rows and 4 columns, forming a $3 \times 4$ array.