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 = Total number of jewels in the crown Number of emeralds

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 = 116 ÷ 2 30 ÷ 2 Divide numerator and denominator by GCF. 2 = = Simplify. = 58 15

Example 1 Writing a Fraction in Simplest Form MEHTOD 2 Use prime factorization Write prime factorizations. = ANSWER The fraction of jewels that are emeralds is Divide out common factor and simplify. = = 15 58

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

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

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 ANSWER 25 9 ANSWER 25 4 for Examples 1, 2, and 3

Guided Practice for Examples 1, 2, and 3 Tell whether the fractions are equivalent ANSWER equivalent ANSWER not equivalent ANSWER not equivalent ANSWER equivalent 24 4, , , ,

Guided Practice for Examples 1, 2, and 3 Write two fractions that are equivalent to the given fraction ANSWER , ANSWER , ANSWER, ANSWER,