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Friday, March 24, 2023

Division as The Inverse of Multiplication


In division because the inverse of multiplication, let a and b be two complete numbers. Dividing a by b means discovering an entire quantity which when multiplied by b provides a and we writea ÷ b = c.

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

For instance: 

Divide 28 by 7 means discovering an entire quantity which when multiplied by 7 provides 28. Clearly, such a quantity is 4. So, we write 28 ÷ 7 = 4.


Equally, now 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 Truth 24 ÷ 4 = 6 

Multiplication truth = 6 × 4 = 24 

                                or

                             4 × 6 = 24

Multiplication Truth 6 × 3 = 18 

Division Truth = 18 ÷ 3 = 6 

                           or

                      18 ÷ 6 = 3

Notice:

If a and b are two complete numbers, then a ÷ b can be expressed as a/b.

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

(frac{a}{b}) = c   or   a = b × c.

Questions and Solutions on Division as The Inverse of Multiplication:

I. Write division information: One has been carried out for you.

(i)

× 8 = 48

___________________

48 ÷ 6 = 8

48 ÷ 8 = 6

(ii)

× 5 = 45

___________________

…..  ÷ ….. = …..

…..  ÷ ….. = …..

(iii)

12 × 7 = 84

___________________

…..  ÷ ….. = …..

…..  ÷ ….. = …..

(iv)

14 × 4 = 56

___________________

…..  ÷ ….. = …..

…..  ÷ ….. = …..

(v)

16 × 2 = 32

___________________

…..  ÷ ….. = …..

…..  ÷ ….. = …..

(vi)

× 9 = 54

___________________

…..  ÷ ….. = …..

…..  ÷ ….. = …..

Reply:

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 Information: One has been carried out for you.

(i)

27 ÷ 9 = 3

___________________

3 × 9 = 27

9 × 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

___________________

…..  × ….. = …..

…..  × ….. = …..

Reply:

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

● Entire Numbers

The Quantity Zero

Properties of Entire Numbers

Successor and Predecessor

Illustration of Entire Numbers on Quantity Line

Properties of Addition

Properties of Subtraction

Properties of Multiplication

Properties of Division

Division as The Inverse of Multiplication

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