1. Multiplying & Dividing Fractions

2. What is the connection between adding and multiplication?
Lets Review
Can you state as a multiplication question?
= 5 x 4
= 20
5 x 4 = 20

3. Fractions and multiplication
What is the sum? =
3 5
Can you restate this addition question as a multiplication question?
1 5 ×3=
3 5

4. What’s the rule? 1 5 3 1 3 5 3 can be stated as
Therefore we can write x =
In your groups, discuss what the rule will be for multiplying 2 fractions together
Rule: Multiply the numerators and then multiply the denominators.
Simplify as needed (lowest terms) 3 1 1 5 3 1 3 5

5. Try these:
1 x 2
5 x 3 2 15
1 5 × 2 3 = = 6 12
3 x 2
4 x 3 1 2
3 4 × 2 3 = = =

6. 1 x 2
5 x 3 2 15
1 5 × 2 3 = =
3 x 2
4 x 3 6 12 1 2
3 4 × 2 3 = = =

7. Mixed Numbers to improper Fractions
1. Multiply the denominator by the whole number
2. Add the product to the numerator

8. Multiplying mixed numbers
Step one: Convert the mixed numbers to improper fractions = =
Step two: Multiply the improper fractions = =

9. Answer the following questions in your notebooks1 2 4 3 2 5 4

10. What is the connection between multiplication and division?
3 x 2 = 6
6 ÷ 3 = 2 and 6 ÷ 2 = 3

11. How many ways can you re-write this division question using multiplication?
8 ÷ 2 = 4
4 x 2 = 8
8 x = 4 1 2

12. Re-state this division question using multiplication
10÷2=5
5×2=10
10× 1 2 =5
What conclusion can we make about 10÷2 and 10× 1 2 ?
Since they both equal 5, they both must be the same!

13. Since 10÷2 = 10× 1 2 ,
how are 2 and connected? 2 1
2 as a fraction?

14. This is an example of a reciprocal fraction2 1
This is an example of a reciprocal fraction

15. Reciprocal Fractions 10 5 2 5 5 2 5 10 1 2 2 3 3 2 2 3 7 7 3 5 6 6 5

16. Let’s Review - Division2 1 2 3 4 5 6 7 8 9 10 ÷
How many 1/5’s
are there in 2? 10

17. 2 2 2 10 1 5 We can also rewrite this question using multiplication ÷
We can also rewrite this
question using multiplication 5 1 2 2 10 ÷ x =

18. 2 2 We can also rewrite this question using multiplication 1 5 5 1 10 5 1 2 2 ÷ 10 x =
algorithm
What’s the rule?
Find the reciprocal of the second
fraction and then multiply straight across

19. For the following questions, solve them using both a diagram and the mathematical algorithm
6 ÷ 1 2
4 ÷ 1 3
5 ÷ 1 6

20. Answer this question using a drawing and algorithm

21. When we are dividing two fractions,
we do the same thing 2 5 ÷ 1 4
Find the reciprocal of second fraction
Multiply
Reciprocal of 1 = 4 4 1
2 x 4 =
5 1 8 5 1 3 5
Multiply =

22. 2 7 3 4 ÷ Find the reciprocal of second fraction Multiply 48 21
Multiply
2 x 4 =
7 3

23. Mixed Numbers 2 3 1 2 Convert the mixed numbers÷
Convert the mixed numbers
into improper fractions 5 2 11 3 ÷ 5 2 3 11
Find the reciprocal of the second fraction and then multiply 15 22 x =

24. 77 114 1. Convert the mixed numbers into improper fractions
2. Find the reciprocal of the second fraction and then multiply 77
114

25. Word Problems

26. A group of friends buys 3 pizzas to share equally
A group of friends buys 3 pizzas to share equally. Each friend receives 3 of a pizza. 8
Show different ways to find the total number of friends in the group.

28. A student says that when you divide two numbers, the quotient is always less than the dividend.
Is this true?
Use examples to explain your answer.

29. Challenge question
Write 3 division questions that have a quotient of 3 5