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Dividing of Fractions
by Carol Edelstein
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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.
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General Division PracticeWhen 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
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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. Let’s look at how we can solve these problems…
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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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So, 3 ÷ ¼ = 12.
If you start with 3, you will have 12 groups of 1/4 .
1 2
3 4
5 6
7 11
10
12
9
8
Dividing a Whole Number by a Fraction
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
So, 5 ÷ 1/3 = 15.If you start with 5, you will have 15 groups of 1/3 .
What is 5 ÷ 1/3?
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?
Isn’t 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
x12
41
Basically, in order to divide fractions we will have to multiply.
12
14
÷ =
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Dividing a Fraction by a Fraction
x12
41
From this point, the problem can be solved in the way that you did for multiplying fractions.
12=
21
= 2
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How to Divide Fractions
• Step 1 – Convert whole numbers and mixed numbers to improper fractions.
÷4
31
1÷43 =1
This example is from a prior slide.
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How to Divide Fractions
• Step 2 – Keep your first fraction.
÷4
31
1 = 31
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How to Divide Fractions
• Step 3 – Change the operation to multiplication.
÷4
31
1 = 31 x
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How to Divide Fractions
• Step 4 – Flip the second fraction.
÷
431
1 = 31 x
14
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How to Divide Fractions
• Step 5 – Multiply the numerators, then multiple the denominators.
x 131
4 = 121
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How to Divide Fractions
• Step 6 – Simplify (if possible).
x 131
4 = 121 =12
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Dividing Fractions – An Example
29
34 =÷
Since both are fractions, now you can Keep (1st fraction), Change (the operation to multiplication), and Flip (2nd Fraction)…
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Now, Multiply and Simplify
92
34 = 27
8 8)273x
243
38
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Dividing Fractions
29
34 =÷ 3 3
8
So,
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Dividing Fractions – Another Example
28
13
=÷2Convert to improper fraction
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28
73 =÷ 8
273 x
KeepChange
Flip
Dividing Fractions
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Now, Multiply and Simplify
82
73 = 56
6 6)569x
542
26
9 26
÷ 22
=9 13÷
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Dividing Fractions
28 =÷ 9 1
3
So, 132
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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!