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 = 8

48 ÷ 8 = 6

(ii)

9 × 5 = 45

___________________

.....  ÷ ..... = .....

.....  ÷ ..... = .....

(iii)

12 × 7 = 84

___________________

.....  ÷ ..... = .....

.....  ÷ ..... = .....

(iv)

14 × 4 = 56

___________________

.....  ÷ ..... = .....

.....  ÷ ..... = .....

(v)

16 × 2 = 32

___________________

.....  ÷ ..... = .....

.....  ÷ ..... = .....

(vi)

6 × 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

● 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




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.



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.




Share this page: What’s this?

Recent Articles

RSS

  1. Worksheet on Mixed Addition and Subtraction | Questions on Addition

    Jan 12, 25 02:14 PM

    In worksheet on mixed addition and subtraction the questions involve both addition and subtraction together; all grade students can practice the questions on addition and subtraction together.

    Read More

  2. Estimating Sums and Differences | Estimations | Practical Calculations

    Jan 12, 25 02:02 PM

    Estimating Difference
    For estimating sums and differences in the number we use the rounded numbers for estimations to its nearest tens, hundred, and thousand. In many practical calculations, only an approximation is requir…

    Read More

  3. Combination of Addition and Subtraction | Mixed Addition & Subtraction

    Jan 12, 25 01:36 PM

    Add and Sub
    We will discuss here about the combination of addition and subtraction. The rules which can be used to solve the sums involving addition (+) and subtraction (-) together are: I: First add

    Read More

  4. Checking Subtraction using Addition |Use Addition to Check Subtraction

    Jan 12, 25 01:13 PM

    Checking Subtraction using Addition Worksheet
    We can check subtraction by adding the difference to the smaller number. Since the sum of difference and smaller number is equal to the larger number, subtraction is correct.

    Read More

  5. Worksheet on Subtraction of 4-Digit Numbers|Subtracting 4-Digit Number

    Jan 12, 25 09:04 AM

    Worksheet on Subtraction of 4-Digit Numbers
    Practice the questions given in the worksheet on subtraction of 4-digit numbers. Here we will subtract two 4-digit numbers (without borrowing and with borrowing) to find the difference between them.

    Read More