2.3 Simplest Form of a Fraction
Learning Objectives:
1. Write fractions in simplest or lowest form.
2. Determine wheth
er two fractions are equivalent: simplify and cross
products.
3. Solve application
s by writing fractions in simplest or lowest form.
4. Key Vocabulary: equivalent fractions, simplest form, lowest form, simplifying, cross products, equality
of fractions.
Writing Fractions in Simplest or Lowest Form
A.
Simplest Form of a Fraction—A fraction is written in simplest form or lowest terms when the numerator
and the denominator have no common factors other than 1.
W
riting a Fraction in Simplest Form
—To write a fraction in simplest form is to write the prime
f
actorization
of the numerator and the denominator and then
divide both by all common factors.
E
xample 1.
Write each fraction in simplest or lowest form.
30
1
.
45
39
2.
51
138
3
.
42
B.
Determinin Whether Two Fractions Are Equivalent
g
Two ways to Determine Whether Two Fractions Are Equivalent
1.
Simplifying:
2. Cross Product Rule:
Example 2. Determine whether the pair of fractions is equivalent by simplifying.
12
21
and
20
35