Relation Between Multiplication and Division

What is a fact family?

A fact family can be defined as a group of math facts created using the same set of numbers.

The fact family has relationships between the three numbers involved.

12, 4 and 3 are the fact family. Where 4 and 3 are parts, while 12 is the whole.

Multiplication and Division Fact Family

Parts of division:

4.1.1 Multiplication facts in division

Robert mother arranged cups in shelves. She arranged 18 cups in 3 rows. How many cups did she arrange in each row?

This array can be shown as the relationship between multiplication and division.

Solution:

Multiplication:

3 rows of 6 cups.

3 x 6 = 18 cups.

Division:

18 cups in 3 equal rows.

18 ÷ 3 = 6.

Robert mother arranged 6 cups in each row.

A fact family shows how multiplication and division are related.

Fact family for 3, 6 and 18:

6 cups are arranged in each row.

Example2:

Richard arranged 12 apples in 3 rows on the table. How many apples did he arrange in each row?

Solution:

Multiplication:

3 rows of 4 apples.

3 x 4 = 12 apples.

Division:

12 apples in 3 equal rows.

12 ÷ 3 = 4.

4 apples in each row.

A fact family shows how multiplication and division are related.

Fact family for 3, 4 and 12:

4 apples are arranged in each row.

4.1.2 Divisor, quotient, dividend

Dividend: 

The dividend is the number of objects to be divided.

Divisor:

The divisor is the number by which another number is divided.

Quotient:

The quotient is the answer to a division problem.

Example2:

Ria collected the bird’s images and she arranged them on the chart. There are 32 bird’s images arranged in 4 rows. How many birds did she arrange in each row?

Find 32 ÷ 4?

Solution:

Division:

32 birds in 4 equal rows.

8 bird’s images arranged in each row.

Dividend = 32

Divisor = 4

Quotient = 8.

Example3:

Mercy packed some cookies for her friend. She arranged 25 cookies in 5 rows. How many cookies did she arrange in each row?

Find 25 ÷ 5?

Solution:

Division:

25 cookies in 5 equal rows.

5 cookies are arranged in each row.

Dividend = 25

Divisor = 5

Quotient = 5.

Exercise:

1. Write the fact family for 3, 4 and 12.
2. Write the fact family for 8, 10 and 80.
3. Use the relationship between the multiplication and the division to complete each equation:
   • 2 x _____ =12.
     12 ÷ 2 = _______.
   • 3 x _____ =21
     21÷ 3 = ______.
4. Use the relationship between multiplication and division to complete each equation:
   • 2 x 9 = 18.
     18 ÷ 2 = _____.
   • 3 x 8 = 24.
     24 ÷ 3 =______.
5. Identify the dividend, divisor, quotient and remainder.

6. Susan is selling raffle tickets for 3 dollars. She collects a total of 40 dollars. Find the total number of tickets she sell?

7. 56 people have been invited to a banquet. The caterer is arranging tables. Each table has 8 people. How many tables are needed?      

8. 60 passengers are on the bus. If there are 6 rows of seats on the bus, how many seats are there in each row?

9. Do division and complete the answers in empty spaces.

10. A piece of rope is 81 m long. How many 9 m long pieces can I cut from it?

Concept map:

What have we learned:

• Understand fact family.
• Understand how to use multiplication facts in division.
• Understand how to do division.
• Understand divisor, quotient, dividend.
• Identify divisor, quotient, dividend in the division problem.