Multiplying Fractions and Mixed Numbers LESSON 3-4 Problem of the Day (For help, go to Lesson 2-4.) 1. Vocabulary Review In an improper fraction, how does the numerator compare to the denominator? Write each mixed number as an improper fraction. 2. 2 3. 6 4. 1 5. 4 3 5 1 2 2 3 3 4 Check Skills You’ll Need 3-4

Multiplying Fractions and Mixed Numbers LESSON 3-4 Problem of the Day Solutions 1. The numerator is greater than the denominator. 2. 2 = = 3. 6 = = 4. 1 = = 5. 4 = = 3 5 (5  2) + 3 13 1 2 (2  6) + 1 13 2 3 (3  1) + 2 5 3 4 (4  4) + 3 19 3-4

Any questions about the homework? Lesson 3-4, page 138, #s 1-10 Confused about question 4? See the next slide!

Another explanation of area models Source: http://en.wikiversity.org/wiki/Primary_mathematics/Fractions

Follow these steps to multiply fractions and mixed numbers Multiplying Fractions and Mixed Numbers LESSON 3-4 Steps to follow Follow these steps to multiply fractions and mixed numbers Write the mixed numbers as improper fractions, if necessary Multiply numerator and denominators Simplify, if necessary } } OR cross-cancel } common factors Algebra:

Multiplying Fractions and Mixed Numbers LESSON 3-4 Additional Examples – Multiplying fractions Find • . 1 9 3 4 1 9 3 4 • 0 • , or 0 Estimate Multiply the numerators. Multiply the denominators. 1 9 3 4 • = 1 • 3 9 • 4 Find the two products. = 3 36 = Simplify. 1 12 Check for Reasonableness The answer, , is close to the estimate, 0. The answer is reasonable. 1 12 Quick Check 3-4

Multiplying Fractions and Mixed Numbers LESSON 3-4 Additional Examples – Multiplying by a whole number What is of 12? 2 3 Write 12 as . (Why?) 2 3 12 1 = • 2 3 • 12 = • 2 3 12 1 4 Simplify before multiplying. 8 1 = Multiply the numerators. Multiply the denominators. = 8 Simplify. Quick Check 3-4

Multiplying Fractions and Mixed Numbers LESSON 3-4 Problem of the Day – Multiplying by a whole number 1 2 In 2002, a disc jockey broadcast her show for 27 h each week. How many hours did she broadcast that year? 1,430 h 3-4

Multiplying Fractions and Mixed Numbers LESSON 3-4 Additional Examples – Multiplying mixed numbers Quick Check Find 5 • 3 . 1 2 1 3 5 • 3 6 • 3, or 18 1 2 3 Estimate Write the mixed numbers as improper fractions. 5 • 3 = • 1 2 3 11 10 = 11 • 10 2 • 3 Multiply the numerators. Multiply the denominators. = 110 6 55 3 Simplify. = 18 1 3 Write as a mixed number. Check for Reasonableness The answer, 18 , is close to the estimate, 18. The answer is reasonable. 1 3 3-4

Multiplying Fractions and Mixed Numbers LESSON 3-4 Lesson Quiz Find each product. 1. • 2. of 48 3. 4 • 2 4. 3 • 5 3 5 10 12 5 8 1 2 30 1 2 2 10 1 4 1 3 9 10 17 1 3 3-4

Multiplying Fractions and Mixed Numbers LESSON 3-4 Additional Examples – Word problems The length of a track around a field is ¼ mi. You jog 3½ times around the track. How far did you jog? A poster measures 38 cm across. If a photocopy machine is used to make a copy that is 3/5 of the original size, what is the width of the copy? The population of Sweden is about times as great as the population of Denmark. Find the population of Sweden if the population of Denmark is about 5,190,000. 7/8 mi 22 and 4/5ths cm About 8,760,000

Multiplying Fractions and Mixed Numbers LESSON 3-4 Homework Lesson 3-4: p. 138 – 139: #s 15-43, odds Checkpoint Quiz 1: p. 134: # 1 – 10 all Friday: Quiz on 3-1 to 3-4