Core Focus on Decimals & Fractions Lesson 3.5 Core Focus on Decimals & Fractions Ordering and Comparing Fractions

Warm-Up What do the symbols < and > mean? Find the LCD for . Find the LCD for . < means less than; > means greater than 70 12

Ordering and Comparing Fractions Lesson 3.5 Ordering and Comparing Fractions Compare fractions with like and unlike denominators to find the smallest or largest fraction.

Explore! Which is Larger? Darin, Yolanda and Ivan finished PE class and were thirsty. Darin drank liter of water. Yolanda drank liter of water. Ivan drank liter of water. Step 1 Use fraction tiles to model each fraction in the situation above. Draw a picture of each model. Step 2 Explain how you can tell which student drank the most water by looking at the models. Step 3 List the students in order from who drank the least water to who drank the most water.

Explore! Which is Larger? Darin, Yolanda and Ivan finished PE class and were thirsty. Darin drank liter of water. Yolanda drank liter of water. Ivan drank liter of water. Step 4 Uma ate pound of carrots. Her bother ate pound of carrots. Use the fraction tiles to determine who ate the most carrots. Explain your answer. Step 5 Diana’s hair is foot long. Mikayla’s hair is foot long. Larry’s hair is foot long. List the people in order from shortest hair to longest hair. Step 6 Explain how using fraction tiles can help with ordering and comparing fractions.

Compare and Order Fractions with Unlike Denominators Find the least common denominator (LCD) for the fractions in the set. Write an equivalent fraction for each fraction in the set using the LCD. Compare the numerators.

Example 1 In a recent survey, three-fifths of people liked peanut butter and jam. One-third liked grilled cheese sandwiches. Compare three-fifths and one-third to find which food was most popular. Convert words to numbers. The denominators are 3 and 5. 3: 3, 6, 9, 12, 15, … List multiples of each. 5: 5, 10, 15, 20, 25, … The LCM = 15, so the LCD = 15.

> means “greater than” Example 1 Continued… In a recent survey, three-fifths of people liked peanut butter and jam. One-third liked grilled cheese sandwiches. Compare three-fifths and one-third to find which food was most popular. Make equivalent fractions with denominators of 15. Compare the numerators. Nine is larger than 5. Substitute the original fractions in the comparison. The group that liked peanut butter and jam sandwiches was larger. > means “greater than” < means “less than”

Example 2 List the following fractions from least to greatest: List the fractions that need to be compared. The denominators are 2, 6 and 3. 2: 2, 4, 6, 8, 10 6: 6, 12, 18, 24 3: 3, 6, 9, 12, 15 The LCM = 6, so the LCD = 6. Make equivalent fractions.

Example 2 Continued… List the following fractions from least to greatest: Compare the numerators and put them in order from least to greatest. Substitute the original fractions for each simplified fraction to answer the question.

Example 3 Find a fraction between . Write in simplest form. USING COMMON DENOMINATORS The denominators are 6 and 2. List multiples of each denominator. 6: 6, 12, 18, … 2: 2, 4, 6, 8, … Make equivalent fractions. Compare the fractions. A fraction that would be between is .

Example 3 Cont. How could you use fraction tiles to find a fraction between ? Find the fraction tiles on the chart . Find fraction tiles whose length is between .

Communication Prompt What is the process for ordering three fractions with three different denominators?

Exit Problems > < Compare each pair of fractions. Replace the with <, > or = to make a true sentence. 1. 2. 2. Write the fractions in order from least to greatest. > <