1. Simplest Form of a Fraction
Section
2.3
Simplest Form of a Fraction

2. Writing Fractions in Simplest Form
Fractions that represent the same portion of a whole are called equivalent fractions.
There are many equivalent forms of a fraction. A special form of a fraction is called simplest form.
Simplest Form of a Fraction
A fraction is written in simplest form or lowest terms when the numerator and denominator have no common factors other than 1.
Objective A 2

3. Examples
Write in simplest form. a. b. c.
Objective A 3

4. Simplest Form Writing a Fraction in Simplest Form
To write a fraction in simplest form, write the prime factorization of the numerator and the denominator and then divide both by all common factors.
Objective A 4

5. Examples
Write in simplest form. a. b. c.
Objective A 5

6. Example
Write in simplest form:

7. Example Determine whether are equivalent. Simplify each fraction.
Since both of the simplified fractions are the same, they are equivalent.
Objective A 7

8. Equality of Fractions
Objective A 8

9. Example Determine whether are equivalent by cross multiplying.
Objective A
Since 22 ≠20, then 9

10. Example
There are 5280 feet in a mile. What fraction of a mile is represented by 2640.
Both 2640 and 5280 have a common factor of 2640.
Objective C
The fraction of a mile represented by 2640 is 1/2.