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# Fact Families

## Fact FamilyDefinition

A fact family is a group of math facts consisting of three numbers where you can create mathematical sentences. Moreover, it shows the relationship existing among these three numbers.

Knowing the concept of fact families will help children to learn the concepts of four fundamental operations: addition, subtraction, multiplication, and division.

## Addition and Subtraction Fact Family

Under addition and subtraction, you can be able to create four mathematical sentences: two addition and two subtraction sentences using three numbers.

For example, we have a fact family which consists of three numbers 1, 2, and 3. With this, we can create four mathematical sentences. These are the following:

1 + 2 = 3
2 + 1 = 3

Subtraction:
3 – 1 = 2
3 – 2= 1

### Fact family triangle

In the given triangle below, we have three numbers of a fact family being placed in each corner. By using the fact family triangle, you will be able to see how addition and subtraction family works. Moreover, this is a helpful tool to build mental arithmetic skills. Note that only the numbers in the triangle can be used to create the mathematical sentences.

The triangle contains the numbers in a fact family. Use the numbers to fill in the box.

In the given figure, write four different facts based on the given fact family.

Now, let us look into some tricks and strategies for addition facts.

Here’s a trick or strategy to add a number with 8. For instance, 8 wants to become a 10. For this to happen, it will take two from the other number (from 4). Thus, 8 becomes 10, and only 2 is left.

Observe that from 8 + 4, it becomes 10 + 2, and this gives us a sum of 12.

Now, let’s try adding 8 and 7. Consider that 8 wants to be a full 10. So, 8 takes 2 from 7. Therefore, 8 becomes 10, and only 5 is left.

Observe that from 8 + 7, it becomes 10 + 5, and this gives us a sum of 15.

Here’s a trick or strategy to add a number with 9. For instance, 9 is added to 4. However, 9 is not happy. He wants to become a full 10.

In that case, 1 is taken away from the other number (from 8) to make 9 a full 10.

Therefore, we have 10 and 3, so 10 + 3 is 13.

Now, let’s try adding 9 and 8. Consider that 9 wants to be a full 10. So, 9 takes 1 from 8. Therefore, 9 becomes 10, and only 7 is left. So, we have 10 + 7 = 17.

Let us solve some word-problems related to addition and subtraction family.

Sample Problem 1:

Tom has 5 blue marbles while Ryan has 6 yellow marbles. How many marbles do they have in all?

Solution:

Answer: Therefore, Tom and Ryan have 11 marbles in total.

Sample Problem 2:

Mom bought 8 apples from a store. She gave 3 apples to my sister. How many apples does Mom have?

Solution:

Observe that there are 8 apples below.

Giving away the 3 apples,

The mathematical sentence would be:

8 – 3 =5

Hence, Mom has only 5 apples left.

Now, let us take a closer look about multiplication and division fact family.

## Multiplication and Division Fact Family

Same with addition and subtraction fact family, you can be able to create four mathematical sentences: two multiplication and two division sentences using three numbers.

For example, we have a fact family which consists of three numbers 2, 4, and 8. With this, we can create four mathematical sentences. These are the following:

Multiplication:
24=8
42=8

Division:
84=2
82=4

Now, let us verify if we 3, 9, and 27 is a fact family by using a fact family triangle. By using the fact family triangle, you will be able to see how multiplication and division fact family works. Note that only the numbers in the triangle can be used to create the mathematical sentences.

Fact family of 3, 9, 27

Let’s have more examples about multiplication and division family.

The triangle contains the numbers in a fact family. Use the numbers to fill in the box.

Let us solve some word-problems related to multiplication and division fact family.

Sample Problem 1:

Lisa baked chocolate cookies for her friends. If she has three friends coming over and she made five cookies for each one of them, how many chocolate cookies did she make?

Solution:

The mathematical sentence that represents the problem is:  5 x 3 =15

Hence, Lisa has baked 15 chocolate cookies for her friends.

Sample Problem 2:

Kenneth has 18 pencils. He wants to give his pencils equally to his 6 classmates. How many ballpens does each of his classmates get?

Solution:

The mathematical sentence that represents the problem is:  18÷6=3

Therefore, each of his classmates will get 3 pencils.

## Remember

• Fact Family is a set of four related addition and subtraction facts or multiplication and division facts that use the same three numbers.
• A family triangle group families of related math facts, and this serves as a helpful tool to build mental arithmetic skills.
• There are some strategies in adding numbers with 8 or 9. When a number is added to 8, you need to take 2 away from the other number to make 8 a full 10. Then, add 10 and the new number (which is two less than the number) to get the sum. This is also the same with adding a number to 9. Take 1 from the other number to make 9 a full 10. Then, add 10 and the new number (which is one less than the number) to get the sum.

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• "Fact Families". Helping with Math, https://helpingwithmath.com/fact-families/. Accessed 13 September, 2024.