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# 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.

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