Operations with Fractions

1
Operations with Fractions
2
Adding and Subtracting Fractions
3
Rewrite the problem with equivalent fractions

• List the multiples of both denominators.
• Find the least common multiple (LCM).
• Write new fractions with the LCM as the new
  denominator.
• Find the factor you multiply by to get from your
  original denominator to your new denominator.
• Use that same factor, and multiply it by your
  original numerator to get a new numerator.
• Finally add and/or subtract from left to right as
  normal.

4
WHAT DOES THAT MEAN?
Lets illustrate the steps with an example.
3
1

4
6
5
3
1

4
6
9
2
x 3
x 2

12
12
11
Multiples of 4 4, 8, 12, 16, 20
12
Multiples of 6 6, 12, 18, 24, 30
6
Example 2
9
2
10, 20, 30, 40, 50
5, 10, 15, 20, 25
5
10
5
x 1
x 2
9
4

10
10
10
1

2
7
Example 3

•  

8
Example 4 improper fractions

•  

9
Practice

• ½ 1/3
• 1/5 ¼
• 5/6 1/5
• 4/7 1/3

10
Homework Time!
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Multiplying With Fractions
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Just Follow These Easy Steps!

• Multiply the numerators and write down the answer
  as your new numerator.
• Multiply the denominators and write down the
  answer as your new denominator.
• Simplify.

13
Example 1
5
3
15
x

32
8
4
There are no common factors for 15 and 32, so
this fraction cannot be simplified.
14
Example 2
3
2
6
1
x


9
36
6
4
This fraction can be reduced. Divide the
numerator and denominator by the GCF, which is 6.
15
Multiplying by a Whole Number
If you want to multiply a fraction by a whole
number, turn your whole number into a fraction by
placing a 1 as the denominator. If your answer is
improper, divide the bottom into the top.
4
20
80
16
x


5
5
1
16
Another Example
15
1
5
15
x


6
1
6
2
15 and 6 have a GCF of 3.
Five halves is improper, so we divide the bottom
into the top.
2
2
5
4
2
1
2
1
17
Practice
18
Multiplying Fractions 1

• Must simplify

•  

•  

19
Homework Time!
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Review Multiplying Fractions

•  

21
Dividing Fractions
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To Divide Fractions

• Rewrite the first fraction.
• Change the division sign to a multiplication
  sign.
• Flip the second fraction upside down.
• Multiply.

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Reciprocal

• When you flip the second fraction, you are
  writing that fractions reciprocal.

3
5
5
3
24
Example 1
1
1
2
3
Rewrite
1
2
2
x

1
3
3
25
Example 2
4
4
5
9
Rewrite
36
4
9
4
1
x


4
5
5
20
26
Example 3
12
3
5
1
Rewrite
60
12
5
20
x


1
3
3
27
Example 4
1
2
6
1
Rewrite
1
1
1
x

6
2
12
28
Homework Time