Relationship between Multiplication and Division

We know that multiplication is repeated addition and division is repeated subtraction. This means that multiplication and division are inverse operation.

Let us understand this with the following example.

We can say that for each multiplication fact, of two distinct numbers we have two division facts. 2 × 2 gives only one division fact 4 ÷2 = 2.

For example:

Write two division facts for each of the following multiplication facts.

Since, division and multiplication are related, we can check our answer by multiplying quotient and divisor to get the dividend.

 When we multiply, we put together the collections containing same number of objects. 4 × 3 = 123 groups of 4 flowers each put together as a single group of 12 flowers. When we divide, we take away collections containing equal number of objects 12 ÷ 3 = 412 flowers set aside as 3 groups of 4 flowers each.

What do we conclude from the above discussion?

We conclude that multiplication is the reverse process of division.

Let us observe the following examples:

1. 5 × 2 = 10 is a multiplication fact.

From this fact we can write:

(i) 10 ÷ 5 = 2

(ii) 10 ÷ 2 = 5

Thus, for every multiplication fact there are two division facts.

2. 21 ÷ 3 = 7 is a division fact.

From this fact we can write:

(i) 7 × 3 = 21

(ii) 3 × 7 = 21

Thus, for every division fact there are two multiplication facts.

Questions and Answers on Relationship between Multiplication and Division:

I. Write multiplication fact for each division fact.

(i) 56 ÷ 8 = ……….. means ……….. × ……….. = ……….

(ii) 33 ÷ 11 = ……….. means ……….. × ……….. = ……….

(iii) 42 ÷ 6 = ……….. means ……….. × ……….. = ……….

(iv) 28 ÷ 7 = ……….. means ……….. × ……….. = ……….

I. (i) 7, 8 × 7 = 56

(ii) 3, 11 × 3 = 33

(iii) 7, 6 × 7 = 42

(iv) 4, 7 × 4 = 28

II. Write two division facts for each multiplication fact.

(i) 7 × 9 =  ……….. means ……….. ÷ ……….. = ………. and ……….. ÷ ……….. = ……….

(ii) 5 × 4 =  ……….. means ……….. ÷ ……….. = ………. and ……….. ÷ ……….. = ……….

II. (i) 63, 63 ÷ 7 = 9, 63 ÷ 9 = 7

(ii)  20, 20 ÷ 4 = 59, 20 ÷ 5 = 4

III. Using following numbers, write multiplication facts and division facts.

(i) 5, 4, 20        ……….               ……….               ……….

(ii) 6, 9, 54       ……….               ……….               ……….

(iii) 7, 4, 28      ……….               ……….               ……….

(iv) 20, 2, 10    ……….               ……….               ……….

III. (i) 5 × 4 = 20, 20 ÷ 4 = 5, 20 ÷ 5 = 4

(ii) 6 × 9 = 54, 54 ÷ 6 = 9, 54 ÷ 9 = 6

(iii) 7 × 4 = 28, 28 ÷ 7 = 4, 28 ÷ 4 = 7

(iv) 2 × 10 = 20, 20 ÷ 2 = 10, 20 ÷ 10 = 2

IV. Write corresponding division facts for the given multiplication facts. One has been done for you.

 (i) 3 × 5 = 1515 ÷ 3 = 5        15 ÷ 5 = 3 (ii) 7 × 4 = 28
 (iii) 2 × 8 = 16 (iv) 4 × 6 = 24

V. Write the corresponding multiplication facts for the given division facts. One has been done for you.

 Division Facts Multiplication Facts (i) 15 ÷ 3 = 5 3 × 5 = 15           5 × 3 = 15 (ii) 42 ÷ 6 = 7 (iii) 63 ÷ 7 = 9 (iv) 40 ÷ 5 = 8 (v) 54 ÷ 9 = 6

VI. Fill in the empty boxes with quotients by using multiplication facts given alongside. One has been done for you.

 (i) 24 ÷ 4 =     6 4 × 6 = 24
 (ii) 35 ÷ 5 = 5 × 7 = 35
 (iii) 27 ÷ 3 = 3 × 9 = 27
 (iv) 42 ÷ 7 = 7 × 6 = 42
 (v) 16 ÷ 2 = 2 × 8 = 16
 (vi) 40 ÷ 8 = 8 × 5 = 40
 (vii) 70 ÷ 10 = 10 × 7 = 70
 (viii) 63 ÷ 9 = 9 × 7 = 63
 (ix) 72 ÷ 8 = 8 × 9 = 72
 (x) 56 ÷ 8 = 8 × 7 = 56

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