1. 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.

2. 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 30 116 =

3. 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 = 2 2 29 30 = 2 3 5

4. EXAMPLE 1 Writing a Fraction in Simplest Form The GCF of 30 and 116 is 2. 30 116 Divide numerator and denominator by GCF. 15 58 = Simplify. = 30 2 116 2

5. EXAMPLE 1 Writing a Fraction in Simplest Form Use prime factorization. METHOD 2 30 116 = 2 3 5 2 2 29 Write prime factorizations. Divide out common factor. 15 58 Simplify. = 2 3 5 2 2 29 1 1 The fraction of jewels that are emeralds is. ANSWER 15 58

6. 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

7. GUIDED PRACTICE for Example 1 The fraction of jewels that are pearl is. 11 58 ANSWER

8. 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

9. GUIDED PRACTICE for Example 1 The fraction of jewels that are sapphires is 19 116 ANSWER

10. 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

11. GUIDED PRACTICE for Example 1 11 29 The fraction of jewels that are spinels is ANSWER