### Key Concepts

- Use multiplication table for division.
- Relation between multiplication and division
- Missing factor equation using multiplication table
- Tally charts
- 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.