January 23, 2012 Warm-Up GCF Word Problem Simplifying Fractions Exit Ticket

Warm-Up: Monday, January 23, 2012 Question: List three equivalent fractions Ex: 3/4 = 6/8

You have 120 red beads, 100 white beads, and 45 blue beads. You want to use all the beads to make bracelets that have red, white, and blue beads on each. What is the greatest number of matching bracelets you can make? Example 1: Word Problem

Example 1 Continued 1 Understand the Problem Rewrite the question as a statement. Find the greatest number of matching bracelets you can make. List the important information: There are 120 red beads, 100 white beads, and 45 blue beads. Each bracelet must have the same number of red, white, and blue beads. The answer will be the GCF of 120, 100, and 45.

2 Make a Plan You can list the prime factors of 120, 100, and 45 to find the GCF. Solve = 2 · 2 · 2 · 3 · = 2 · 2 · 5 · 5 45 = 3 · 3 · 5 The GCF of 120, 100, and 45 is 5. You can make 5 bracelets. Example 1 Continued

Look Back 4 If you make 5 bracelets, each one will have 24 red beads, 20 white beads, and 9 blue beads, with nothing left over. Example 1 Continued

4-2 Simplifying Fractions Vocabulary Equivalent fractions are fractions that have the same value. Ex: 4/12 = 1/3 To find an equivalent fraction, you can multiply or divide the numerator and denominator by the same nonzero number.

4-2 Simplifying Fractions Example 1 3/12 = /4 Divide 3/12 by 3/3 (because 12 ÷ 3 is 4) 3/12 ÷ 3/3 = 1/4

Example 2: On Your Own A. 5/7 = /21 B.12/16 = 6/ 4-2 Simplifying Fractions

Example 2: On Your Own A. 5/7 = /21 Multiply by 3/3 5 x 3 = 15 15/21 B.12/16 = 6/ Divide by 2/2 16 ÷ 2 = 8 6/8

4-2 Simplifying Fractions Vocabulary A fraction is in simplest form when the GCF of the numerator and denominator is 1. There are two methods you can use to write a fraction in simplest form: 1.Divide by the common factors 2.Divide by the GCF

4-2 Simplifying Fractions Example 3 Write 18/24 in simplest form. Method 1: Divide by common factors A common factor of 18 and 24 is 2 -> Divide by 2/2 to get 9/12 A common factor of 9 and 12 is 3 -> Divide by 3/3 to get 3/4

4-2 Simplifying Fractions Example 3 Write 18/24 in simplest form. Method 2: Divide by the GCF Factors of 18: 1, 2, 3, 6, 9, 18 Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 The GCF of 18 and 24 is 6. Divide 18/24 by 6/6 -> 3/4

4-2 Simplifying Fractions Example 4: On Your Own A.9/15 B.36/60

4-2 Simplifying Fractions Example 4: On Your Own Method 1 A. 9/15 A common factor of 9 and 15 is 3 -> Divide by 3/3 to get 3/5 B.36/60 A common factor of 36 and 60 is 6 -> Divide by 6/6 to get 6/10 A common factor of 6 and 10 is 2 -> Divide by 2/2 to get 3/5

4-2 Simplifying Fractions Example 4: On Your Own Method 2: Divide by the GCF A. 9/15 Factors of 9: 1, 3, 9 Factors of 15: 1, 3, 5, 15 The GCF of 18 and 24 is 3. Divide 9/15 by 3/3 -> 3/5

4-2 Simplifying Fractions Example 4: On Your Own Method 2: Divide by the GCF A. 36/60 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 The GCF of 36 and 60 is 12. Divide 36/60 by 12/12 -> 3/5

4-2 Simplifying Fractions Exit Ticket 1.Write 18/24 in the simplest form. State which method you used. 2. Write two fractions equivalent to 4/10.