### Dividing Fractions

```Dividing Fractions
CCSS.6.NS.1: Apply and extend previous
understandings multiplication and division to divide
fractions by fractions.
You need your Journal, glue, ruler, highlighter and a
pencil.
Bar Models and Number Lines
Using the problems for 12 ÷ 3 = 4
to create bar models in your Journal.


Create a number line for 10 ÷ 5 = 2.

examples on the board.
PART 1
Apply what you learned about dividing whole numbers
to dividing whole numbers by fractions.



1.
2.
Use a bar diagram to help you understand what it means to divide.
This board is 1 yard (3 feet) long.
Sam wants to divide it equally into 1 foot pieces. What do you
know?
What do you need to find?
Draw a model that represents the length of the board. Draw
lines to separate the board into thirds. Each third represent one
foot.
How many groups of 1 foot are in 3 feet?
Juan is building a set for the school musical. He has a 3-foot
board that he needs to equally divide into ½ foot pieces. How
many pieces will he have after he cuts the board?
What do you know?
 What do you need to find?
1. Draw a model that represents the length of the board. Draw lines
to separate the board into thirds. Each third represent one foot.

2. Divide each foot into halves.
3. Determine how many groups of ½ are in 3. Circle the groups that
are the size of the divisor ½.
½
½
½
½
½
½
Juan is building a set for the school musical. He has a 3-foot
board that he needs to equally divide into ½ foot pieces. How
many pieces will he have after he cuts the board?
3. Determine how many groups of ½ are in 3. Circle the groups that
are the size of the divisor ½.
½
½
½
½
½
½
Conclusion: There are 6 groups of ½ . So, 3 ÷ ½ = 6. (And 3 x 2 = 6.)
Check by multiplying: 6 x ½ = 3.
2
3
Find 4 ÷ .
1.
Draw a model to represent 4.
1
1
1
1
2.
Divide each whole into thirds.
3.
Circle groups of on the model. Think: How many
2
3
2
3
groups of are in 4?
2
3
Find 4 ÷ .
3.
2
3
Circle groups of on the model. Think: How many
2
3
groups of are in 4?
4.
5.
2
3
2
3
There are 6 groups of . So, 4 ÷ = 6.
Check by multiplying: 6 x
2
3
=
12
3
= 4.
1
You try it. Find 3 ÷ .
3
1. Draw a model to represent 3.
2. Divide each whole into _____.
3. Determine how many groups of _____
are in _____. Circle groups of _____
on the model.
4. There are _____ groups of ___. So,
1
3 ÷ = _____.
3
Work with a partner in your group. Draw a bar
model or number line to find each quotient.
1.
2÷
2.
6÷
3.
4÷
4.
3÷
1
4
2
3
1
2
3
4
1
4
1.
2÷ =8
2.
6÷ =9
3.
1
2
4÷ =8
4.
3÷ =4
2
3
3
4
understand what it means to divide fractions?
Discuss this idea in your groups.

The diagrams show the relationship between
the factors and the quotient. The model shows
that a quotient can be greater than the dividend
when the divisor is less than 1.
HOMEWORK

Use the same process for the bar diagram
to create number lines for the following
problems.
1
1. 2 ÷ =
3
1
2. 3÷ =
3
2
3. 4 ÷ =
3
Part 2
Developing the Algorithm.
Vocabulary

Reciprocal: any two numbers with a product of 1.
Number
1
2
2
3

Product
1
2
x2=1
2
3
x2=1
3
Reciprocal
2
3
2
Describe the relationship between the numerator
and denominator of a number and its reciprocal.
Connect to the vocabulary.
Another name for reciprocal is
multiplicative inverse. What are some
words in everyday language that are
similar to reciprocal or inverse?
 Pilots can fly in an inverted position, or
upside down. How can you use the
remember the mathematical meaning of
multiplicative inverse, or reciprocal?

Find Reciprocals

1
2
Dividing 3 by gives the same result as
multiplying 3 by 2, which is the reciprocal
1
of . Any two numbers with a product of
2
1 are called reciprocals.
reciprocals
1
2
3÷ =6
3x2=6
same result
Practice finding the reciprocal.

2
3
Find the reciprocal of .
2
3
3
2
2
3
3
2
Since x = 1, the reciprocal of is .
 Find the reciprocal of each number.

1.
2.
3.
1
8
3
5
2
9
4. 7
5. 1
1
2
Divide by a fraction:
Words: To divide a whole number or a fraction by a
fraction, multiply by its reciprocal (or multiplicative
inverse) of the divisor.
EX.


2
3
5
1
3
2
5÷ = x =
15
2
=7
1
2
Five divided by two thirds means you need to find
how many two thirds are in 5. (part of a whole)
3
8
2
3
3
8
3
2
9
16
÷ = x =
Three eighths divided by two thirds means
you need to find how many two thirds are in
three eighths. (part of a part)

Practice – find the quotients.
1.
5÷
2.
4÷
3
6
7
9
3.
10 ÷
4.
12 ÷
1
5.
8
3
6.
4
1
7.
3
÷
÷
1
2
2
3
÷8
5
6
3
8
2
8. 4 ÷1
3
3
2
9. 2 ÷
4
3
Practice

Complete the practice worksheet
applying what you have learned about
finding quotients to the contextual
problems.
```