Dividing of Fractions

1
Dividing of Fractions

• by Carol Edelstein

2
When would you divide fractions?

• One example is when you are trying to figure out
  how many episodes of your favorite ½ hour tv
  program you could watch in the 1 ½ hrs you have
  available.

1½ ½ 3 You could watch 3
episodes.
3
General Division Practice
When you are faced with the division problem 18
divided by 6, think If I have 18 items and I
make groups of 6, how many groups will I have?
18 6 dividend
divisor (start) (what groups look like)
How many groups of 6 items are there?
So, 18 6
3
4
Dividing Fractions Conceptual Understanding

• Like when we divided decimals, when you divide
  two fractions that are between 0 and 1, the
  quotient is going to be larger than at least one
  of your fractions.

½ ½ 1
½ ¾ 2/3
Ok. Lets look at how we can solve these
problems
5
Dividing a Whole Number by a Fraction

• What is 3 ¼ ?

Use your prior knowledge and the illustration
above to figure it out. Think, If I start with
3, how many groups that look like ¼ will I have?

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Dividing a Whole Number by a Fraction
If you start with 3, you will have 12 groups of
1/4 .

• So, 3 ¼ 12.

Can you see how you could manipulate the
fractions to get an answer of 12?
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Dividing a Whole Number by a Fraction
What is 5 1/3?
If you start with 5, you will have 15 groups of
1/3 .

• So, 5 1/3 15.

Can you see how you could manipulate the
fractions to get an answer of 15?
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Dividing a Fraction by a Fraction

• What is 1/2 1/4?

How many groups of 1/4 could you fit in the half
of the rectangle?
2
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Dividing a Fraction by a Fraction

• For the problem 1/2 1/4 , how could you
  get an answer of 2?

Can you see how you could manipulate the
fractions to get an answer of 2?
Isnt ½ x 4 2? Remember that division is
the opposite operation of multiplication, so we
can do the following MULTIPLY. ?
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Dividing a Fraction by a Fraction

Basically, in order to divide fractions we will
have to multiply.
1
1
1
4
x


2
4
2
1
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Dividing a Fraction by a Fraction
From this point, the problem can be solved in the
way that you did for multiplying fractions.

2
2
1
4
x
2


2
1
1
1
12
How to Divide Fractions

• Step 1 Convert whole numbers and mixed numbers
  to improper fractions.

This example is from a prior slide.
1
3
1
3



4
4
1
13
How to Divide Fractions

• Step 2 Keep your first fraction.

3
1
3


4
1
1
14
How to Divide Fractions

• Step 3 Change the operation to multiplication.

3
1
3

x

4
1
1
15
How to Divide Fractions

• Step 4 Flip the second fraction.

3
1
3
4

x

1
4
1
1
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How to Divide Fractions

• Step 5 Multiply the numerators, then multiple
  the denominators.

3
4
12

x
1
1
1
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How to Divide Fractions

• Step 6 Simplify (if possible).

3
4
12


12
x
1
1
1
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Dividing Fractions An Example
2
3


9
4
Since both are fractions, now you can Keep (1st
fraction), Change (the operation to
multiplication), and Flip (2nd Fraction)
19
Now, Multiply and Simplify
3
3
9
3
27
8
x

8)
2
4
8
27
24
3
20
Dividing Fractions
So,
2
3


9
4
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Dividing Fractions Another Example
2
1

2

3
8
Convert to improper fraction
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Dividing Fractions
2
8
7


x
8
2
3
Keep
Change
Flip
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Now, Multiply and Simplify
2
8
7
56
9
6
x

6)
2
3
6
56
54
2
2
1


9
9
2
6
2
3

24
Dividing Fractions
So,
2
1

2

8
3
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Dividing Fractions More Examples
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REVIEW Dividing Fractions Conceptual
Understanding

• Remember, when you divide two fractions that are
  between 0 and 1, the quotient is going to be
  larger than at least one of your fractions.

½ ½ 1
½ ¾ 2/3
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Great job!