Adding/Subtracting Fractions
Simplifying Fractions
ADDING FRACTIONS: MIXED NUMBERS
Adding Fractions
SUBTRACTING FRACTIONS : WITH THE SAME DENOMINATOR
ADDING FRACTIONS : WITH THE SAME DENOMINATORS
Fractions consist of two numbers. The top number is called the numerator. The bottom number is called the denominator.
2
NUMERATOR
DENOMINATOR
To add two fractions with the same denominator,add the numerators and place that sum over the common denominator.
1
2
example:
+
1
2
=
=
2
2
1
ADDING FRACTIONS : WITH DIFFERENT DENOMINATORS
How to Add Fractions with different denominators:
1. Find the Least Common Denominator (LCD) of the fractions
2. Rename the fractions to have the LCD
3. Add the numerators of the fractions
4. Simplify the Fraction (if possible)
example:
1
4
+
1
8
1
=
8
8
+
2
1
=
3
8
Quick Definition: A Mixed Fraction is a
whole number and a fraction combined,
such as 3 .
4
1
To make it easy to add them, just convert to Improper Fractions first.
Adding Mixed Fractions
Convert them to Improper Fractions
Then add them (using Addition of Fractions)
then convert back to Mixed Fractions
Example
1
1
2
+
1
1
3
= ?
=
3
2
+
4
3
=
9
6
+
8
6
=
17
6
=
2
5
6
answer:
To subtract two fractions with the same denominator, subtract the numerators and place that difference over the common denominator.
Example:
5
8

3
8
= ?
(Common Denominator ÷ Denominator) x Numerator = New Numerator
How to Convert Mixed Fraction to Improper Fraction
3
2
3
1. ) divide
2.) add
=
11
3
Example: Find the Sum of 1/4 and 1/8.
1.) Determine the Greatest Common Factor of 4 and 8 which is 4.
2.) Either multiply the denominators and divide by the GCF (4*8=32 then multiply 32 by the GCF 32/4=8)
OR  Divide one of the denominators by the GCF and multiply the answer by the other denominator
(4/4=1 then multiply 1 by the other denominator 1*8=8)
3.) Rename the fractions to use the Least Common Denominator(1/4=2/8  1/8=1/8)
4.) The result is 2/8+ 1/8
5.) Add the numerators and put the sum over the LCD = 3/8
6.) Simplify the fraction if possible. In this case it is not possible.
=
8

5
8
3
=
2
8
Reduce to lowest term.
Answer =
1
4
SUBTRACTING FRACTIONS : WITH DIFFERENT DENOMINATORS
1.)Find the Lowest Common Denominator (LCD) of the fractions
2.)Rename the fractions to have the LCD
3.)Subtract the numerators of the fractions
4.)The difference will be the numerator and the LCD will be the denominator of the answer.
5.)Simplify the Fraction
EXAMPLE:
2
3

1
2
=

=
4
6
3
6
1
6
How to get this:
(Common Denominator ÷ Denominator) x Numerator = New Numerator
Subtracting Mixed Numbers
1.) Make the first numerator larger than the second if it is not.
2.) Subtract the second numerator from the first
3.)Place that difference over the common denominator.
4.)Subtract the integer portions of the two mixed numbers
EXAMPLE:
5
3
7

2
1
2
= ?
=
38 5
7 2

=
76
35

14
14
=
41
14
=
2
13
14
Simplifying Fractions
Simplifying (or reducing) fractions means to make the fraction as simple as possible.
How do I Simplify a Fraction ?
There are two ways to simplify a fraction:
Method 1
Try dividing both the top and bottom of the fraction until you can't go any further (try dividing by 2,3,5,7,... etc).
EXAMPLES:
2
4
÷
1
2
3
6
÷
1
2
2
2
3
3
=
=
56
63
÷
7
7
=
8
9
8
12
÷
4
4
=
2
3
Method 2
Divide both the top and bottom of the fraction by the Greatest Common Factor.
Example:
9
54
=
÷9
÷9
1
6
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Adding/Subtracting Fractions
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