EXAMPLE 1 Writing a Fraction in Simplest Form

History

One of the Czech Republic’s royal coronation jewels is the St. Wenceslas crown. It was made around 1345 and is decorated with 44 spinels, 30 emeralds, 22 pearls, 19 sapphires, and 1 ruby. Write the fraction of jewels in the crown that are emeralds in simplest form.

EXAMPLE 1 Writing a Fraction in Simplest Form

SOLUTION

Write the fraction of jewels in the crown that are emeralds. Then simplify.

Number of emeralds Total number of jewels in the crown

30116

=

EXAMPLE 1 Writing a Fraction in Simplest Form

Write the fraction of jewels in the crown that are emeralds. Then simplify.

METHOD 1

Find and use the GCF of 30 and 116.

116 = 22 29

30 = 2 3 5

EXAMPLE 1 Writing a Fraction in Simplest Form

The GCF of 30 and 116 is 2.

30116

Divide numerator and denominator by GCF.

1558

= Simplify.

= 30 2116 2

EXAMPLE 1 Writing a Fraction in Simplest Form

Use prime factorization.

METHOD 2

30116

= 2 3 52 2 29

Write prime factorizations.

Divide out common factor.

1558

Simplify.

=2 3 5

2 2 29

1

1

The fraction of jewels that are emeralds is .

ANSWER

1558

GUIDED PRACTICE for Example 1

Use the information from Example 1. Write the fraction of jewels in the crown that are the given jewel. Simplify if possible.

1. Pearls

GUIDED PRACTICE for Example 1

The fraction of jewels that are pearl is .1158

ANSWER

GUIDED PRACTICE for Example 1

Use the information from Example 1. Write the fraction of jewels in the crown that are the given jewel. Simplify if possible.

2. Sapphires

GUIDED PRACTICE for Example 1

The fraction of jewels that are sapphires is19116

ANSWER

GUIDED PRACTICE for Example 1

Use the information from Example 1. Write the fraction of jewels in the crown that are the given jewel. Simplify if possible.

3. Spinels

GUIDED PRACTICE for Example 1

1129

The fraction of jewels that are spinels is

ANSWER