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.

Relationship between Multiplication and Division

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.

Multiplication Facts Math

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.

Multiplication and Division Relationship

4 × 3 = 12

3 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

Division and Multiplication Relationship

12 ÷ 3 = 4

12 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 ……….. × ……….. = ……….


Answer:

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 ……….. ÷ ……….. = ………. 


Answer:

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    ……….               ……….               ………. 


Answer:

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 = 15

15 ÷ 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

You might like these





3rd Grade Math Lessons

From Terms Used in Division 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?

Recent Articles

  1. Roman Numerals | System of Numbers | Symbol of Roman Numerals |Numbers

    Feb 22, 24 04:21 PM

    List of Roman Numerals Chart
    How to read and write roman numerals? Hundreds of year ago, the Romans had a system of numbers which had only seven symbols. Each symbol had a different value and there was no symbol for 0. The symbol…

    Read More

  2. Worksheet on Roman Numerals |Roman Numerals|Symbols for Roman Numerals

    Feb 22, 24 04:15 PM

    Roman Numbers Table
    Practice the worksheet on roman numerals or numbers. This sheet will encourage the students to practice about the symbols for roman numerals and their values. Write the number for the following: (a) V…

    Read More

  3. Roman Symbols | What are Roman Numbers? | Roman Numeration System

    Feb 22, 24 02:30 PM

    Roman Numbers
    Do we know from where Roman symbols came? In Rome, people wanted to use their own symbols to express various numbers. These symbols, used by Romans, are known as Roman symbols, Romans used only seven…

    Read More

  4. Place Value | Place, Place Value and Face Value | Grouping the Digits

    Feb 19, 24 11:57 PM

    Place-value of a Digit
    The place value of a digit in a number is the value it holds to be at the place in the number. We know about the place value and face value of a digit and we will learn about it in details. We know th…

    Read More

  5. Math Questions Answers | Solved Math Questions and Answers | Free Math

    Feb 19, 24 11:14 PM

    Math Questions Answers
    In math questions answers each questions are solved with explanation. The questions are based from different topics. Care has been taken to solve the questions in such a way that students

    Read More