 # How Multiplication and Division are Related? | Relationship between Multiplication and Division with Examples

Multiplication and division are closely related. They are basic arithmetic operations and we know that division is an inverse operation of multiplication. Multiplication means adding equal parts to form a group whereas division is the split of those equal parts from a group. So, Multiplication and Division are related to each other. Here we will check the main differences between division and multiplication. Also, look at the examples on the relationship between multiplication and division.

## Difference Between Division & Multiplication

Below mentioned are the main differences between multiplication and division.

Multiplication Division
It means adding equal groups It means subtracting equal parts from a group
It is denoted by x It is denoted by /, ÷
The parts are multiplier, multiplicand, and product The parts are dividend, divisor, quotient and remainder
The result of the multiplication is the product. The result of division is the quotient.
Example is 6 x 2 = 12 Example is 12 ÷ 6 = 2
6 is the multiplicand, 2 is the multiplier and 12 is the product. 12 is the dividend, 6 is the divisor, 2 is the quotient and 0 is the remainder.
The formula is multiplicand x multiplier = product. Formula is dividend ÷ divisor = quotient + remainder

### How Multiplication and Division are Related?

Multiplication and division are inverse operations. The division is backwards of multiplication. The examples of how division and multiplicated are related in the following sections.

A box has 24 mangoes. Divide those mangoes into 6 groups of equal parts. How many mangoes are there in each group?
24 divided by 6 gives the number of mangoes in each group.
24 ÷ 6 = ? Therefore, each group has 4 mangoes.
There are 6 groups and each group has 4 mangoes. Find how many mangoes are there in total?
The number of mangoes = 4 x 6 = 24
In both the questions, division fact is 24 ÷ 6 = 4 and the multiplication fact is 4 x 6 = 24
Therefore, multiplication fact and division fact shows the relationship between the multiplication and division operations.

### Multiplication Division Relationship Examples

Example 1:
Write the division fact and multiplication fact? Solution:
The image has a total of 15 apples.
Each row has 5 apples.
Let us consider, each row as a group.
Then, division fact = 15 ÷ 3 because the number of apples is 15 and the number of groups is 3
15 ÷ 3 = 5
The number 5 represents the number of apples in each group.
Multiplication fact is 5 x 3 because each group has 5 apples and the number of groups is 3.
5 x 3 = 15
The division fact and multiplication fact shows the relation between them.

Example 2:
Write the division fact and multiplication fact? Find the relation between division and multiplication?
Solution:
The image has 8 groups and each group has 3 bananas.
The multiplication fact gives the total number of bananas.
Multiplication fact is 8 x 3 = 24
The division fact is 24 ÷ 8 = 3
The division fact here gives the number of bananas in each group.
So, multiplication and division are opposite to each other.

Example 3:
Write the multiplication fact for the following.
(i) 28 ÷ 4
(ii) 15 ÷ 3
(iii) 21 ÷ 7
Solution:
(i) The division fact is 28 ÷ 4
28 ÷ 4 = 7
The multiplication fact is 7 x 4 = 28
(ii) The division fact is 15 ÷ 3
15 ÷ 3 = 5
The multiplication fact is 5 x 3 = 15
(iii) The division fact is 21 ÷ 7
21 ÷ 7 = 3
The multiplication fact is 7 x 3 = 21

Example 4:
Write the division fact for the following.
(i) 5 x 4
(ii) 8 x 7
(iii) 9 x 3
Solution:
(i) The multiplication fact is 5 x 4
5 x 4 = 20
The division fact is 20 ÷ 4 = 5
(ii) The multiplication fact is 8 x 7
8 x 7 = 56
The division fact is 56 ÷ 7 = 8
(iii) The multiplication fact is 9 x 3
9 x 3 = 27
The division fact is 27 ÷ 3 = 9

### FAQs on Relation Between Multiplication and Division

1. What is multiplication and division fact?
The division facts are division number sentences related to the tables. And multiplication fact has the same numbers as the division fact but not in the same order it involves multiplication calculation.

2. Write division and multiplication facts for 6, 3 and 18?
We can write 2 multiplication facts and 2 division facts for a set of three numbers.
Multiplication facts are 6 x 3 = 18, 3 x 6 = 18
Division facts are 18 ÷ 3 = 6, 18 ÷ 6 = 3.

3. How are multiplication and division related?
Yes, division and multiplication are related to each other. We can say that division is an inverse operation of multiplication. The multiplication of two numbers gives the product. When you divide the product by any of the two numbers the result will be another number.

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