Multiplication and Division Using a Table with Examples

Key Concepts

1. Use multiplication table for division.
2. Relation between multiplication and division
3. Missing factor equation using multiplication table
4. Tally charts
5. Fact family for division

Relation between Multiplication and Division:

• Addition is the process of combining a number of individual items together to form a new total.
• Multiplication is the process of using repeated addition and combining the total number of        items that make up equal-sized groups.
  Dividend = Divisor x Quotient + Remainder
  Division is the inverse of Multiplication
  5 × 3 = 15
  15 ÷ 3 = 5
  15 ÷ 5 = 3
  Dividend ÷ Divisor = Quotient

Missing Factor Equation:

If we want to know about the missing factor, first we need to understand factor and product definitions.

Product:- The answer we get when we multiply two or more factors.

Factor:-    A number multiplied by another number to get a product.

If factor times factor equals product, and the opposite of multiplying is dividing, then we can say,

For Example:

18 ÷ 3 = ?

Solution:

Think, 3 × ? = 18

Three times of what number is 18?

3 × 6 = 18

So, 18 ÷ 3 = 6

Use of multiplication table for division

Write a missing factor equation and then use the multiplication table to find 15 ÷ 3.

Solution:

Step 1:  Here one factor is 3, find the 3 in the first column of  this multiplication table.

Step 2:  And product is 15. Follow the row the 3 is in until you come to 15.

Step 3:  Look straight up to the top of that column of the table. The number on the top of the column is 5. So, the missing factor is 5.

                3 × 5 = 15

                15 ÷ 3 = 5

Example:

Write the missing factor equation and use the multiplication table to solve the division problem.

12 ÷ 3 = ?

Solution:

Here, one factor is 3

product is 12

We find 12 in the row 3

So, 12 is the intersection point of 3 and 4

Another factor is 4      

3 × 4 = 12              12 ÷ 3 = 4

Missing Numbers in the table

We can find the missing factors by using multiplication or division

2 × 8 = 16

2 × 5 = 10

2 × 4 = 8

9 × 5 = 45

4 × 8 = 32

4 × 4 = 16

7 × 8 = 56

7 × 5 = 35

7 × 4 = 28

Example:

 Find the value that makes the equation correct. Use a multiplication table to help.

24 ÷ 6 = ____

24 = 6 × ____

Solution:

Here, one factor is 6 

product is 24

By using the table, we can find 6 in the column of the table.

We move forward until we get 24.

Look in that row, we find the other factor is 4.

24 ÷ 6 = 4

6 × 4 = 24

Example:

Find the missing factor and the products.

Solution:

2 × 8 = 16

2 × 5 = 10

2 × 7 = 14

5 × 8 = 40

5 × 7 =35

6 × 5 = 30

9 × 8 = 72

9 × 7 = 63

Tally Chart

A tally chart is a simple way of recording and counting frequencies. Each occurrence is shown by a tally mark.

How to draw Tally Marks:

•   The occurrence of each information is marked by a vertical line ‘|’
•   Every fifth tally is recorded by striking through the previous four vertical lines as ‘||||’
•   This makes up counting the tallies easy. 

Example:

• Count the objects given below and prepare the table. 

Let us create a tally chart for the above data.

This looks much easier to read.

Fact family

Factors – The numbers being multiplied.

                    3 × 7 = 21

Inverse Operation –  An opposite operation that undoes another.

                                        3 × 7 = 21                21 ÷ 7 = 3

Example:  What are the four 4 members of the fact family  of 4 × 8 = 32 ?

4 × 8 = 32

8 × 4 = 32

32 ÷ 8 = 4

32 ÷ 4 = 8

What have we learnt:

•  Division is inverse of multiplication.
•  Dividend ÷ Divisor = Quotient
•  If factor times factor equals product, and the opposite of multiplying is dividing.
•  Product / factor = Missing Factor
•  We can find the missing factors by using multiplication or division.
•  A tally chart is a simple way of recording and counting frequencies.
•  Each occurrence is shown by a tally mark.
•  An opposite operation that undoes another is called Inverse Operation.