Fractions and Decimals Lesson 3 Fractions and Decimals Simplifying Fractions

Warm-Up Find the value of 24 ÷ 3. Find the value of 48 ÷ 8. What is the GCF of 28 and 35? What is the GCF of 30 and 45?

Simplifying Fractions Target: Write fractions in simplest form.

Vocabulary Simplest Form: A fraction where the numerator’s and denominator’s only common factor is 1.

Example 1 Use common factors to write in simplest form. A common factor is 2. Divide the numerator and denominator by 2. A common factor is 3. Divide the numerator and denominator by 3. The only common factor is 1. The fraction is in simplest form.

Writing Fractions in Simplest Form Divide the numerator and denominator by common factors until the only common factor is 1. - OR - Divide the numerator and denominator by the greatest common factor (GCF).

Example 2 Use the greatest common factor to write in simplest form. Factors of 10: 1, 2, 5, 10 Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40 The GCF is 10, so divide both the numerator and the denominator by 10. The fraction is in simplest form.

Example 3 Use the graph to determine the fraction of students who chose Track & Field as their favorite sport. Write the answer in simplest form. The fraction will be: Find total surveyed: 20 + 16 + 14 = 50 The fraction is .

Example 3 (continued) Simplify the fraction. Use the common factor method or the GCF method. Two-fifths of the students said Track & Field is their favorite sport.

Exit Problems Write in simplest form.

Communication Prompt What are some reasons fractions might NOT be written in simplest form?