1. Lesson 4.3
Special Quotients

2. Set the Purpose
You have learned that multiplication and division have an inverse relationship. Today, you are going to use multiplication facts to understand some special division rules.

3. Connect
You have learned that in math, sharing equally is one meaning of division.
Think of a situation where you might need to share 4 objects equally among 4 people.

4. Example
Sharing 4 snacks with 4 friends

5. Word Problem
Four friends want to share 4 books. How many books would each friend get?
What number sentence could you use to show this?

6. Word Problem
What if there were 4 books and 1 person? Draw a picture to show how many books 1 person would get.
What number sentence could you use to show this?
What two multiplication sentences are related to these two division sentences?

7. Wrong! What is wrong with this number sentence? 1 ÷ 4 = 4
What does that number sentence mean?

8. Special Quotients How can you divide with 1 and 0?
A sandwich is cut into 8 pieces. How many people can have 1 piece each?
1group of 8

9. Continued…. Dividing by 1
1 x 8 = 8
So, 8 ÷ 1 =
Rule: Any number divided by 1 is itself.

10. Practice!
9 ÷ 1 =
12 ÷ 1 =
1,200 ÷ 1 =

11. 1 as a quotient To find 8 ÷ 8, think 8 times what number equal 8?
8 x 1 = 8
So, 8 ÷ 8 =
Rule: Any number (except 0) divided by itself is 1.

12. Practice!
7 ÷ 7 =
21 ÷ 21 =
3,000 ÷ 3,000 =

13. Dividing 0 by a number
To find 0 ÷ 8, think 8 times what number equals 0?
8 x 0 = 0
So, 0 ÷ 8 =
Rule: 0 divided by any number (except 0) is 0.

14. Practice!
0 ÷ 5 =
0 ÷ 20 =
0 ÷ 100 =

15. Dividing by 0 = NO!!
To find 8 ÷ 0, think 0 times what number equals 8?
You CAN’T!
There is NO such number!
Rule: You cannot divide by 0.
* You cannot divide 8 of something into zero groups.

16. Practice! Explain if it’s > , < , or = 8 ÷ 8 4 ÷ 4 3 ÷ 3 0 ÷ 6
8 ÷ ÷ 4
3 ÷ ÷ 6
0 ÷ ÷ 7

17. Extra Practice

18. Extra Practice

19. Remember! 0 and 1
Any number (except 0) divided by itself is equal to 1. Any number divided by 1 is that number. Zero divided by any number (except 0) is zero. Zero cannot be a divisor.