Definition and Fact Family Examples of Related Facts
You have 5 chocolates. And, your best friend gives you 5 more. Now, how many chocolates do you have? Ten. Very Good! But, what if your sister asks you to give her 5 chocolates? Sharing is caring. Right? So, you give her 5 chocolates. Now, how many chocolates do you have? 5, right? Good. That means if you add 5 with 5, you get 10 as a result. And, when you subtract 5 from 10, you will get 5. These are called related facts.
In this article, you will learn about ‘related facts’ along with examples.
Related Facts
Related Facts
Related Facts are the Mathematical facts that derive the relationship between two different inverse operations such as addition and subtraction, and multiplication and division. These are the basic Mathematical expressions that are made up of three numbers.
Related Facts of Addition and Subtraction
To understand the related facts of addition and subtraction, we will consider the following example:
4 + 6 = 10
6 + 4 = 10
10 - 4 = 6
10 - 6 = 4
Addition and subtraction are the inverse operations. In the above-given expressions, 4, 6, and 10 are the three numbers used. These numbers are related to each other using the ‘+’ or ‘-’ and ‘=’. In the first two examples, we perform the operation called addition. And, if we swap the numbers, we get the same result, that is 10. Also, in the last two equations, we subtract either 4 or 6 from the ‘10’, we get 6 or 4, respectively.
In addition and subtraction, related facts tell us that if we add one number, then subtract the same from the obtained result, they cancel each other.
For example, adding 6 with 4 gives the result of 10, and if we subtract 6 from 10, we will get 4. These types of facts are called the ‘related facts’. The point to be considered is that adding 6 with 4 gives the result of 10 whereas adding 4 with 6 gives the result of 10. This is called the commutative property of addition which is a ‘related fact’ of addition.
Relationship of Multiplication and Division
Like addition and subtraction, multiplication and division are also inverse operations, which cancel each other.
To understand the related facts of multiplication and division, we will consider the following example:
6 x 2 = 12
2 x 6 = 12
12 ÷ 2 = 6
12 ÷ 6 = 2
A related fact about multiplication and division is that if we multiply a number by x (say), and then divide the result by x, then we will get the same number.
Conclusion
By a given fact or a set of three numbers, we can write a total of four related facts. In addition, we can write three more facts using it. Similarly, we can write a total of four facts if a set of three numbers is of multiplication and division.
FAQs on Related Facts in Math Explained for Students
1. What are related facts in maths?
Related facts are number sentences that use the same three or four numbers to show how operations are connected. In basic arithmetic, they usually link addition and subtraction or multiplication and division.
- Example (addition and subtraction): 3 + 5 = 8, 5 + 3 = 8, 8 − 3 = 5, 8 − 5 = 3
- Example (multiplication and division): 4 × 6 = 24, 6 × 4 = 24, 24 ÷ 6 = 4, 24 ÷ 4 = 6
2. What is a fact family in maths?
A fact family is a group of related facts that use the same numbers to form addition and subtraction or multiplication and division equations.
- Addition/subtraction fact family uses 3 numbers.
- Multiplication/division fact family also uses 3 numbers.
- Example: For 7, 2, and 9 → 7 + 2 = 9, 2 + 7 = 9, 9 − 7 = 2, 9 − 2 = 7
3. How do you write related facts for addition and subtraction?
To write related facts for addition and subtraction, use three numbers and form two addition and two subtraction equations.
- Step 1: Choose three related numbers (e.g., 4, 9, 13).
- Step 2: Write two addition facts: 4 + 9 = 13, 9 + 4 = 13.
- Step 3: Write two subtraction facts: 13 − 4 = 9, 13 − 9 = 4.
4. How do you write related facts for multiplication and division?
To write related facts for multiplication and division, use three numbers to create two multiplication and two division equations.
- Step 1: Choose three related numbers (e.g., 5, 8, 40).
- Step 2: Write two multiplication facts: 5 × 8 = 40, 8 × 5 = 40.
- Step 3: Write two division facts: 40 ÷ 5 = 8, 40 ÷ 8 = 5.
5. Why are related facts important in maths?
Related facts are important because they help students understand the connection between inverse operations like addition and subtraction or multiplication and division.
- Improve mental maths skills.
- Strengthen number sense.
- Help check answers for accuracy.
- Build a foundation for algebra and equations.
6. What is the difference between related facts and inverse operations?
Related facts are sets of equations using the same numbers, while inverse operations are pairs of operations that undo each other.
- Inverse operations: Addition and subtraction, multiplication and division.
- Related facts: 6 + 4 = 10 and 10 − 6 = 4 are part of the same fact family.
7. Can you give an example of related facts with three numbers?
An example of related facts using three numbers is 2, 9, and 11.
- 2 + 9 = 11
- 9 + 2 = 11
- 11 − 2 = 9
- 11 − 9 = 2
8. How can related facts help check your answer?
Related facts help check your answer by using the inverse operation to confirm the result.
- Example: If 15 ÷ 3 = 5, check by multiplying: 5 × 3 = 15.
- If the inverse calculation gives the original number, the answer is correct.
9. Are related facts used in algebra?
Yes, related facts are used in algebra because they help solve equations using inverse operations.
- Example: If x + 7 = 12, subtract 7 from both sides.
- 12 − 7 = 5, so x = 5.
10. What are common mistakes when working with related facts?
A common mistake when working with related facts is using numbers that do not belong to the same fact family.
- Mixing unrelated numbers (e.g., 3, 5, 9).
- Forgetting to reverse the operation correctly.
- Incorrect division when checking multiplication.
