Simplifying and Comparing
Fractions
5.4
Simplifying Fractions
• A fraction is “simplified” when its numerator
and denominator have a GCF of 1
To Simplify Fractions
• Divide the numerator and denominator by the
GCF
Example Simplify:
12
20
• What is the GCF of 12 and 20?
• 4
12  4
20  4

3
5
Simplify
4
10
• What is the GCF between 4 and 10?
• 2
42
10  2
2
5
Simplifying With Variables
• Divide numbers by GCF
• List the variables out
• Cancel out the variables
Simplify:
5x
3
15 x
15 x x x
15  x
3
xx
x
3
3
2
2
Simplify: 28 m n
3
4
42 m n
28  m  m  n  n  n
42  m  m  m  m  n
2n
2
3m
2
Comparing Fractions Using a Number
Line
• Graph the fractions on the number line
• The number to the left is the smaller number
Graph and Order from Least to
Greatest
15
18
,
3
7
,
7
3
,
8
9
Comparing Fractions
• Get the same denominator (LCD)
– Find the LCM of the denominators
• Make an Equivalent fraction
– Multiply each the fraction (numerator and
denominator) by number to make the LCM
• Once the denominators are the same compare
the numerators
Compare Using <, > or =
2 3
,
5 7
Compare Using <, > or =
4 2
,
9 6
Heart Method to Compare Fractions
• Multiply the diagonals, bring down and
compare the products
Use the heart method to compare
1 1
,
4 5
Use the heart method to compare
11
16
,
5
8
Homework
Page 236 (16-42) even