## 4.6 Division involving 0 and 1.

Some rules for division involving 0 and 1.

**Example:**

- 8 ÷ 8 = 1
- 15 ÷ 1 = 15
- 0 ÷ 249 = 0
- 25 ÷ 0 cannot be done

**4.6.1 Division involving 0.**

### Dividing 0 by a number:

0 divided by any number (except 0) is 0.

**Example1:**

If there are no cookies in the cookie jar and four people want to share them, how many cookies would each person get?

Find 0 ÷ 4.

**Solution:**

4 times of what number equals 0?

4 x 0 = 0

So, 0 ÷ 4 = 0.

**Example 2:**

If there are no pens in the box and five girls want to share them, how many pens would each girl get?

Find 0 ÷ 5.

**Solution:**

5 times of what number equals 0?

5 x 0 = 0

So, 0 ÷ 5 = 0.

### Dividing by zero:

Illustrated figure for dividing by zero is undefined.

**Example1:**

4 chocolates are there among **zero** people, how much does each person get?

Find 4 ÷ 0.

**Solution:**

0 times of what number equals 4?

There is no such number

So, 4 ÷ 0. Cannot be done.

Each person cannot get anything.

**Example2:**

6 tennis bats are there among **zero** people, how much does each person get?

Find 6 ÷ 0.

**Solution:**

0 times of what number equals 6?

There is no such number

So, 6 ÷ 0. Cannot be done.

**4.6.2 Division involving 1.**

### 1 as a quotient:

Any number (except 0) divided by itself is 1.

**Example1:**

Find 6 ÷ 6.

6 times of what number equals 6?

6 x 1 = 6.

So, 6 ÷ 6 =1.

**Example2:**

### Any number divided by 1 is itself.

**Example1:**

Yvonne has 3 apples. She puts 1 apple in each plate. How many plates did Yvonne used?

Find 3 ÷ 1.

**Solution:**

What number of times 1 is 3?

3 x 1 = 3.

So, 3 ÷ 1 =3.

Yvonne used 3 plates.

## Exercise:

1. Solve the multiplication equation to find each quotient.

a. Find 7 ÷ 7.

7 x _____ =7.

So, 7 ÷ 7 =_____.

b. Find 9 ÷ 9.

9 x _____ = 9.

So, 9 ÷ 9 =_____.

2.Find each quotient.

a. 0 ÷ 6 =________.

b. 6 ÷ 1 =________.

c. 5 ÷ 5 =________.

3. Solve the multiplication equation to find each quotient.

Find 0 ÷ 8.

8 x _____ =0.

So, 0 ÷ 8 =_____.

4. Find 7 divided by 1.

5. Find 24 ÷ 0.

6. How can you tell, without dividing that 24 ÷ 24 = 1?

7. Find each quotient.

a.

b.

8. Martin has 2 laptops. He puts 1 laptop in a bag. How many bags did Martin use?

9. Neil wrote 9 invitations. He put 1 invitation in each mail box on the street. How many mail boxes got invitations?

10. Alone bought 3 ice -creams. She gave 3 ice creams to 1 friend. How many ice creams her friend got?

### Concept map :

### What have we learned:

- Understand division involving 0 and 1.
- Understand dividing 0 by a number:
- Understand dividing by zero is undefined.
- Identify the rules for division involving 0 and 1.
- Identify the rule that any number (except 0) divided itself is 1.

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