Fractions Procedures
Reducing Fractions
 List the factor of numerator and denominator
 Find GCF (Greatest Common Factor)
 Divide numerator and denominator by GCF
Adding/Subtracting Fractions with like
denominators
 Add/Subtract numerators, keep denominator
the same
 If an improper fraction, change to mixed
number
 Look to Simplify/Reduce
Adding/Subtracting Fractions with unlike
denominators
 Rewrite vertically
 Find the Common denominator
 Multiply denominators to find common
denominator OR List the multiples to find
LCM (Least Common Multiple) which is LCD
(Least common denominator)
 Make equivalent fractions using common
denominator
 Add/Subtract numerators, keep denominator
the same
 If an improper fraction, change to mixed
number
 Look to Simplify/Reduce
Adding/Subtracting Mixed numbe rs with unlike
denominators
 Rewrite vertically
 Find the Common denominator
 Multiply denominators to find common
denominator OR List the multiples to find
LCM (Least Common Multiple) which is LCD
(Least common denominator)
 Make equivalent fractions using common
denominator, carry through whole numbers
 Add/Subtract whole numbers & numerators,
keep denominator the same
 If an improper fraction, change to mixed
number, carry through whole number and add
 Look to Simplify/Reduce
12
18
Example:
12
18
12  6 2
1  12 1  18
GCF = 6

18  6 3
2 6 29
3 4 3 6
Example 1:
9
4
5 5 1



10 10 10  5 2
Example 2:
9
5 14
4
2


1 1
10 10 10
10
5
Example1:
4 1

7 9
4 9
7 9
1 7

9 7
36
63
7
63
43
63
7
2
Example1: 3  1
8
3
6 5
7 5
4 7

5 7
7 3
8 3
2 8
1
3 8
21
24
16
1
24
5
2
24
3
30
35
28
35
58
23
1
35
35
5
3
Example 2: 5  3
6
7
5 7
6 7
3 6
3
7 6
5
3
6 4

7 5
Example 2:
35
42
18
3
42
53
8
42
5
8 1
9
11
42
11
42
Multiplying Fractions without cross canceling
 Keep fractions written horizontally
 Multiply numerator times numerator
 Multiply denominator times denominator
 Look to Simplify/Reduce
NOTE: You work with much larger numbers if
you don't cross cancel ahead of time.
Multiplying Fractions with cross canceling
 Keep fractions written horizontally
 Use cross cancel technique, you can cross
cancel (diagonally) and (up and down)
 Look for GCF and divide it into each number
that you are cross canceling
 Multiply what is left, numerator times
numerator and denominator times denominator
 Look to Simplify/Reduce
5 12 60  15 4
 

9 15 135  15 9
Example 1:
6
2
5
 5  12  60
6 6
Example 2:  12     
9
3
9
 9  1  9
1
4
5 12 4
Example 1:  
9 15 9
3
3
4
5
5
12
2
 
   20
6
Example 2:  12      
3
9
 9  1  3
3
NOTE: If you cross cancel correctly, you will never
have to simplify/reduce.
Multiplying Mixed Numbe rs
 Keep fractions written horizontally
 Change mixed numbers to improper fractions
 Refer to multiplying rules to continue
 Look to Simplify/Reduce
Dividing Fractions
 Keep fractions written horizontally
 Change division to multiplication
[COPY DOT FLIP]
You are multiplying by the inverse or
reciprocal
 Refer to multiplying rules to continue
 Look to Simplify/Reduce
Dividing Mixed Numbe rs
 Keep fractions written horizontally
 Change mixed numbers to improper fractions
 Change division to multiplication
[COPY DOT FLIP]
You are multiplying by the inverse or
reciprocal
 Refer to multiplying rules to continue
 Look to Simplify/Reduce
1
1 4 7 11 11
2
Example 1: 2  1     3
3 7 3 7
3
3
1
1
Example 1:
3 6 3 7 7
   
4 7 4 6 8
2
1
3 10 19 10 8 80
23
   
1
Example 1: 3  2 
3
8 3 8
3 19 57
57