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)

× 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

___________________

.....  ÷ ..... = .....

.....  ÷ ..... = .....

Answer:

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 = 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

___________________

.....  × ..... = .....

.....  × ..... = .....

Answer:

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

You might like these

● Whole Numbers

The Number Zero

Properties of Whole Numbers

Successor and Predecessor

Representation of Whole Numbers on Number Line

Properties of Addition

Properties of Subtraction

Properties of Multiplication

Properties of Division

Division as The Inverse of Multiplication



Numbers Page 

6th Grade Page 

From Division as The Inverse of Multiplication to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?