Download Adding or Subtracting Fractions

Rules for Working with Fractions
A fraction is simply a part of a whole number. The number on top of the line is the
numerator; the number below the line is the denominator.
3
4
numerator
denominator
A fraction represents division.
The line means “divided by.”
Fractions may be common or proper (as in
number (as in 1
1
3
3
5
or ), improper (as in or ) or a mixed
2
4
2
4
1
3
or 2 ).
2
4
Converting Fractions to Decimals
Divide the numerator by the denominator.
Example:
3
= 3 ÷ 4 = 0.75
4
Reducing Fractions to Lowest Terms and Increasing to
Higher Terms
There is an infinite number of fractions that have the same value. For example, the
1
2 3 4
fraction
can also be written , , , etc. We create a different form of the fraction
2
4 6 8
1 2 2
by multiplying the numerator and denominator by the same factor. Ex:       .
2 2 4
Notice that the factor that we multiple by has the value of one so the value of the original
fraction remains unchanged. We can also divide numerator and denominator by like
factors to reduce the fraction to lower terms. If we divide by all the common factors the
fraction will be in lowest terms.
Example:
Reducing
20
24
10
which is lower terms.
12
5
If we divide numerator and denominator by 4 we get
which is lowest terms because
6
there are no more common factors.
If we divide numerator and denominator by 2 we get
19
Revised 3/22/12:sw
Practice:
Copy the problem onto another sheet of paper. Show all of your work.
Reduce to lowest terms:
15

1)
25
Increase to higher terms:
1

4)
3
2)
8

28
5)
2

5
3)
6)
12

30
3

8
Adding or Subtracting Fractions
The fractions must have a common denominator (the denominator must be the same
number in the fractions being added or subtracted). After the fractions have common
denominators, the numerators are added or subtracted to solve the problem.
The common denominator can be the value of the denominators multiplied together.
1 1

2 4
multiplied common denominator is 8
1 5
+
8 6
multiplied common denominator is 48
The common denominator can be the lowest number that both denominators will divide
into evenly.
1 1
+
2 4
lowest common denominator is 4
1 5
+
8 6
lowest common denominator is 24
Once we find the lowest common denominator, LCD, we convert each fraction to a new
fraction with the same value by multiplying the numerator and denominator by the same
number. Question: What do I have to multiply each denominator by to get the LCD?
Whatever the factor is, multiply the numerator by it as well.
Completing the addition of fractions:
1 1 2 1 3
   
2 4 4 4 4
Revised 3/22/12:sw
1 5 3 20 23
 


8 6 24 24 24
Practice:
Copy the problem onto another sheet of paper.
Show all of your work.
7)
4 5
+
5 9
8)
5 4

6 5
9)
10)
4 2
5 3
11)
2 1

15 8
12)
14 5
+
15 8
9 7
11 22
Adding & Subtracting Mixed Numbers
Method 1: Convert the mixed number to an improper fraction, then proceed as usual,
finding a common denominator.
1
3
1 9 ?
2
4
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and 9
3 39

(convert mixed
4 4
numbers to improper fractions)
3 39

?
2 4
3 6

(find lowest common denominator)
2 4
6 39 45
1


 11
4 4
4
4
Method 2: Work with the fractions and the whole numbers separately, dealing with the
fractions first.
3
1
7 3 ?
5
10
Revised 3/22/12:sw
7  3  10 and
10 
3 1
6
1
7




(work with fractions and whole numbers separately)
5 10 10 10 10
7
7
 10
10
10
Practice:
Copy the problem onto another sheet of paper. Show all of your work.
13)
2
2
5
+ 1
3
8
14)
8
1
12
–
5
5
6
Multiplying Fractions
Convert any mixed numbers to improper fractions. Then multiply numerators together
and denominators together. Reduce the answer.
 2  3  6 2

   
 3  5  15 5
7
 1  1   3  13  39
4
1  3      
8
 2  4   2  4  8
To avoid having to do extensive reducing in the end, cancel out common factors
 top 

 prior to multiplying.
 bottom 
æ 2 öæ 3 ö
ç ÷ç ÷
è 3 øè 5 ø
3’s cancel each other out, leaving 1’s in their places.
Multiplying then gives
(2)(1) = 2
(1)(5) 5
When the numerator and denominator each have numbers that end in Ø, you can cancel
as many zeros as you find in the number that has the fewest.
100
25000
canceling two zeros out of the top and bottom results in
Practice:
Copy the problem onto another sheet of paper.
1
250
Show all of your work.
Revised 3/22/12:sw
15)
3 5

7 6
16)
16 5

21 8
17)
10 97

27 100
Dividing Fractions
To divide fractions, invert (take the reciprocal of) the divisor (the second number) and
then follow the steps for multiplication.
6 1  6  3  18
4
     
2
7 3  7  1  7
7
Example:
Practice:
Copy the problem onto another sheet of paper.
18) 6 
2
5
19)
4
5
7
Show all of your work.
1 2
20) 3 
8 3
Revised 3/22/12:sw