1. Example 1 Writing a Fraction in Simplest Form One of the Czech Republic’s royal coronation jewels 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. HISTORY Write the fraction of jewels in the crown that are emeralds. Then simplify. SOLUTION = 116 30 Total number of jewels in the crown Number of emeralds

2. Example 1 Writing a Fraction in Simplest Form METHOD 1 Find and use the GCF of 30 and 116. The GCF of 30 and 116 is 2. 116 30 = 116 ÷ 2 30 ÷ 2 Divide numerator and denominator by GCF. 2 = 5 3302 22 2 = 29116 Simplify. = 58 15

3. Example 1 Writing a Fraction in Simplest Form MEHTOD 2 Use prime factorization. 116 30 Write prime factorizations. = 25 3 2292 ANSWER The fraction of jewels that are emeralds is. 58 15 Divide out common factor and simplify. = 1212 5 3 2121 292 = 15 58

4. Example 2 Identifying Equivalent Fractions SOLUTION Write each fraction in simplest form. Tell whether the fractions and are equivalent. 48 18 8 3 is in simplest form. 8 3 48 18 = 48 ÷ 6 18 ÷ 6 = 8 3 ANSWER The fractions have the same simplest form, so they are equivalent.

5. Example 3 Writing Equivalent Fractions Write two fractions that are equivalent to. 10 4 SOLUTION Multiply or divide the numerator and denominator by the same nonzero number. Multiply numerator and denominator by 3. 10 4 = 10  3 4  3 = 30 12 Divide numerator and denominator by 2, a common factor of 4 and 10. 10 4 = 10 ÷ 2 4 ÷ 2 = 5 2 ANSWER The fractions and are equivalent to. 30 12 5 2 10 4

6. Guided Practice Of your 25 classmates, 5 prefer apples, 7 prefer oranges, and 9 prefer bananas. Write the fraction of your classmates who prefer the given fruit in simplest form. 1. Apple 2. Orange 3. Banana 4. Other ANSWER 5 1 25 7 ANSWER 25 9 ANSWER 25 4 for Examples 1, 2, and 3

7. Guided Practice for Examples 1, 2, and 3 Tell whether the fractions are equivalent. 5. 6 1 ANSWER equivalent ANSWER not equivalent ANSWER not equivalent ANSWER equivalent 24 4, 6. 7 3 21 10, 7. 30 24 6 4, 8. 35 15 7 3,

8. Guided Practice for Examples 1, 2, and 3 Write two fractions that are equivalent to the given fraction. 9. 16 8 10. 15 9 11. 12 10 12. 24 21 ANSWER 2 1 32 16, ANSWER 5 3 30 18, ANSWER, 6 5 24 20 ANSWER, 8 7 48 42