Simplifying Fractions

1
Simplifying Fractions A ratio is a comparison of
two numbers by division. A ratio can expressed
in several ways. The expressions below all
represent the same ratio. 2 to 3
2 3 2/3 2 3 A
ratio is most often written as a fraction in
simplest form. A fraction is in simplest form
when the GCF of the numerator and denominator is
1. Mrs. Leavell inherited 1200 acres, and the
farm is 1500 acres today. So the ratio is
1200/1500.
2

• First find the GCF of the numerator and
  denominator.
• 2 x 2 x 2 x 2 x 3 x 5 x 5
• 2 x 2 x 3 x 5 x 5 x5
• The GCF of 1200 and 1500 is
• 2 x 2 x 3 x 5 x 5 or 300

3

• Now divide the numerator and denominator by 300
  to write the fraction in simplest form.
• 1200 300 4
• 300 5
• Since the GCF of 4 and 5 is 1, the fraction 4/5
  is in simplest form.
• Write 12/40 in simplest form.
• 12 4 3
• 40 4 10

4
Connection to Algebra Simplify 16 x²y³ 2 x
2 x 2 x 2 x x y y y 12 x y³
2 x 2 x 3 x y y y 4x 3
5
Write each fraction in simplest form. If the
fraction is already in simplest form, write
simplified. 2/ 14 1/7 17/20 simplified
6
34/38 17/19 20/53 simplified 12x/15y 4x / 5y
7
xyz³/ x²y z³/x 296/375 Simplified 18h²d/54d h²/3