Multiplying & Dividing Fractions

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

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

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

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 = = =

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 = = =

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

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

Answer the following questions in your notebooks 1 2 4 3 2 5 4

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

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

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!

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

This is an example of a reciprocal fraction 2 1 This is an example of a reciprocal fraction

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

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

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

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

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

Answer this question using a drawing and algorithm

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 =

2 7 3 4 ÷ Find the reciprocal of second fraction Multiply 4 8 21 Multiply 2 x 4 = 7 3

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 =

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

Word Problems

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.

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.

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