Learning Target: I can divide fractions using models and reciprocals.


 
Divide Fractions



Dividing Fractions

You can divide fractions by using an equation.

Dividing by a fraction is the same as multiplying by its reciprocal.


You can also divide fractions by using a model.

A visual model like fractions strips can help you determine how many of one fraction fits into another.


 

 


Example 1

James is preparing buffalo chicken wings.  He has cups of hot sauce.  Each chicken wing needs   cup of hot sauce.  How many chicken wings can James cover with the hot sauce he has?

 


Think --

I need to divide the cups of sauce by the cup used by each wing.

 

Solve --

Divide. 



Way 1: Multiply by the reciprocal.

Since reciprocals are multiplicative inverses, you can use reciprocals to divide fractions.

Rewrite as a multiplication problem, using the reciprocal of the divisor.

    

 

 

Simplify by using cancelling common factors.

Then multiply.


  x

 


Way 2: Use models.


Use fraction strips to model   in sixteenths.

 

How many divide into, or are in ?

 

 

 

Count the number of groups of .

 

 There are 4 groups of in .




James can top 4 chicken wings with hot sauce.

 

 

 

 

Let's Practice Together

Find each quotient.  Write each quotient in simplest form.

1.         

 

 

 

 

 

 

 

2.        

 

 

 

 

 

 

 

3.        

 

 

 

 

 

 

 

Your Turn

4.      

 

 

 

 

 

 

 

5.        

 

 

 

 

 

 

 

6.      

 

 

 

 

 

Find a value for n  that makes each equation true.

 

7.         

 

 

 

 

 

 

8.         

 

 

 

 

 

 

9.     

 

 

 

 

 

 

10.         





Check for Understanding

1.  How many 3/4-inch pieces of string can be cut from a strand 12 inches long?

 

 

 








 











Answers

1.  3/2 or 11/2

2.  3/2 or 11/2

3.  20

4.  20/3 or 6 2/3

5.  7/32

6.  6/5 or 11/5

7.  1/5

8.  4/9

9.  5/6

10.  18

Check for Understanding

1.  16