Division as The Inverse of Multiplication

In division as the inverse of multiplication, let a and b be two whole numbers. Dividing a by b means finding a whole number which when multiplied by b gives a and we writea ÷ b = c.

Thus, a ÷ b = c      or      a = b × c

For example:

Divide 28 by 7 means finding a whole number which when multiplied by 7 gives 28. Clearly, such a number is 4. So, we write 28 ÷ 7 = 4.

Similarly, we have

12 ÷ 4 = 3, since 4 × 3 = 12

35 ÷ 5 = 7, since 5 × 7 = 35

2 ÷ 1 = 2, since 2 × 1 = 2

15 ÷ 15 = 1, since 15 × 1 = 15

42 ÷ 6 = 7, since 6 × 7 = 42

Division by Inverse of Multiplication:

 Division Fact 24 ÷ 4 = 6 → Multiplication fact = 6 × 4 = 24                                  or                              4 × 6 = 24 Multiplication Fact 6 × 3 = 18 → Division Fact = 18 ÷ 3 = 6                             or                       18 ÷ 6 = 3

Note:

If a and b are two whole numbers, then a ÷ b is also expressed as a/b.

Thus, a ÷ b = c   or   a = bc, which can also be written as

$$\frac{a}{b}$$ = c   or   a = b × c.

Questions and Answers on Division as The Inverse of Multiplication:

I. Write division facts: One has been done for you.

 (i) 6 × 8 = 48___________________48 ÷ 6 = 848 ÷ 8 = 6 (ii) 9 × 5 = 45___________________.....  ÷ ..... = ..........  ÷ ..... = .....
 (iii) 12 × 7 = 84___________________.....  ÷ ..... = ..........  ÷ ..... = ..... (iv) 14 × 4 = 56___________________.....  ÷ ..... = ..........  ÷ ..... = .....
 (v) 16 × 2 = 32___________________.....  ÷ ..... = ..........  ÷ ..... = ..... (vi) 6 × 9 = 54___________________.....  ÷ ..... = ..........  ÷ ..... = .....

I. (ii) 45 ÷ 9 = 5;     45 ÷ 5 = 9

(iii) 72 ÷ 12 = 6;      72 ÷ 6 = 12

(iv) 30 ÷ 15 = 2;     30 ÷ 2 = 15

(v) 84 ÷ 12 = 7;      84 ÷ 7 = 12

(vi) 56 ÷ 14 = 4;     56 ÷ 4 = 14

(vii) 32 ÷ 16 = 2;    32 ÷ 2 = 16

(viii) 45 ÷ 9 = 5;     45 ÷ 5 = 9

II. Write Multiplication Facts: One has been done for you.

 (i) 27 ÷ 9 = 3___________________3 × 9 = 279 × 3 = 27 (ii) 45 ÷ 3 = 15___________________.....  × ..... = ..........  × ..... = .....
 (iii) 15 ÷ 3 = 5___________________.....  × ..... = ..........  × ..... = ..... (iv) 12 ÷ 4 = 3___________________.....  × ..... = ..........  × ..... = .....
 (v) 16 ÷ 2 = 8___________________.....  × ..... = ..........  × ..... = ..... (vi) 49 ÷ 7 = 7___________________.....  × ..... = ..........  × ..... = .....
 (vii) 54 ÷ 6 = 9___________________.....  × ..... = ..........  × ..... = ..... (viii) 48 ÷ 8 = 6___________________.....  × ..... = ..........  × ..... = .....

II. (ii) 15 × 3 = 45;     3 × 15 = 45

(iii) 5 × 3 = 15;     3 × 5 = 15

(iv) 3 × 4 = 12;     4 × 3 = 15

(v) 8 × 2 = 16;     2 × 8 = 16

(vi) 7 × 7 = 49;     7 × 7 = 49

(vii) 9 × 6 = 54;     6 × 9 = 54

(viii) 6 × 8 = 48;     8 × 6 = 48

● Whole Numbers

The Number Zero

Properties of Whole Numbers

Successor and Predecessor

Representation of Whole Numbers on Number Line

Properties of Subtraction

Properties of Multiplication

Properties of Division

Division as The Inverse of Multiplication

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