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4-5 Subtracting Mixed Numbers 1

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4-5 Subtracting Mixed Numbers 1 4-5 4-5 Subtracting Mixed Numbers 1. Plan Lesson Preview What You’ll Learn Check Skills You’ll Need For help, go to Lesson 3-5. OBJECTIVE PowerPoint 1 To subtract mixed numbers Write each improper fraction as a mixed number in simplest form. Check Skills You’ll Need OBJECTIVE 3 8 23 To subtract mixed 11 22 3 2 1.2 2.3 3 3. 45 Writing Fractions as numbers with 2 5 20 15 24 Mixed Numbers renaming 4.21 5.21 6. 22 Lesson 3-5: Example 3. Extra 8 2 6 2 10 5 Practice p. 644. ...And Why 7. Explain the steps you used to write 24 as a mixed number in To subtract two weights, 10 as in Example 1 simplest form. Divide 24 by 10. The quotient 2 is the integer of the Lesson Resources mixed number. The remainder 4 is the numerator, and 10 is the 4 2 denominator: 210 . Reduce to 25 . Teaching Resources OBJECTIVE Practice, Reteaching, Enrichment Interactive lesson includes instant self-check, tutorials, and activities. 1 Subtracting Mixed Numbers Reaching All Students Practice Workbook 4-5 To subtract mixed numbers, first you may need to write the fractions with a Spanish Practice Workbook 4-5 Guided Problem Solving 4-5 common denominator. Then subtract the whole numbers and the fraction Hands-On Activities 14 parts separately. Presentation Assistant Plus! 1 EXAMPLE Real-World Problem Solving Transparencies • Check Skills You’ll Need 4-5 3 Lions At birth, one lion cub weighs 3 pounds. Another cub in the same • Problem of the Day 4-5 5 4 litter weighs 2 pounds. How much more does the heavier cub weigh? • Additional Examples 4-5 8 • Student Edition Answers 4-5 3 5 To calculate the difference in weights, find 3 - 2 . • Lesson Quiz 4-5 4 8 3 6 d 3 6 PH Presentation Pro CD-ROM 4-5 3 3 The LCD is 8. Write as . 4 8 4 8 S 5 5 2 2 2 2 Male cubs grow to an adult 8 8 Computer Test Generator CD Subtract the whole numbers. weight of 600 pounds. 1 d 1 Then subtract the fractions. 8 Technology 1 The heavier cub weighs 1 pounds more than the other cub. Resource Pro® CD-ROM 8 Computer Test Generator CD 3 5 Check for Reasonableness Round each mixed number: 3 < 4; 2 < 3. PH Presentation Pro CD-ROM 4 8 - = 1 Then subtract: 4 3 1. The answer 18 is close to the estimate. So, the www.PHSchool.com answer is reasonable. Student Site 3 7 Teacher Web Code: aak-5500 • Check Understanding 1 a. A supporting wedge for a window is 216 inches wide and 28 inches long. • Self-grading Lesson Quiz 11 How much longer is the wedge than it is wide? 16 in. PH SuccessNet Teacher Center b. Reasoning In Example 1, could you use 32 as the common denominator? • Lesson Planner Explain your answer. Yes; answers may vary. Sample: 32 is a common • Resources multiple of 8 and 4, so it is also a common denominator. Plus 190 Chapter 4 Adding and Subtracting Fractions ANT ST C H N I E C K M S E Y T S Ongoing Assessment and Intervention Before the Lesson During the Lesson After the Lesson Diagnose prerequisite skills using: Monitor progress using: Assess knowledge using: • Check Skills You’ll Need • Check Understanding • Lesson Quiz • Additional Examples • Computer Test Generator CD • Test Prep 190 OBJECTIVE 2 Subtracting Mixed Numbers by Renaming 2. Teach Sometimes you need to rename whole numbers or fractions in order to 1 Math Background subtract from them. Here is how to rename 3 4. Subtracting mixed numbers is Need Help? ϭ 1 1 3 5 2 1 1 similar to adding mixed numbers For help writing mixed 4 4 in that whole numbers and numbers as improper 5 fractions, go to Lesson 3-5. 5 2 1 fraction parts are dealt with 1 5 4 3 ϭ 2 separately and the results are 4 4 5 5 2 combined. The new step in 4 subtracting mixed numbers involves renaming. If the fraction 2 EXAMPLE Renaming Whole Numbers being subtracted is greater than 5 the one from which it is being - 2 Find 7 8. subtracted, the fraction from which you are subtracting must Write 7 as a mixed number. Use 8 for the denominator since you must 5 be renamed. This requires also subtract 8. renaming the whole number part 8 d 8 8 of the mixed number. For 7 6 Rename 7 as 6 1 1 5 6 1 , or 6 . 8 8 8 1 2 S instance, in subtracting 4 5 2 2 5, 1 6 5 5 you rename 4 5 as 3 5. First you 2 2 2 2 8 8 subtract the fractions. Then you 3 d Subtract the whole numbers. subtract the whole numbers. 4 8 Then subtract the fractions. 6 2 4 3 5 2 2 5 5 15 2 1 1 3 Check Understanding 2 Find each difference. a. 5 - 3 1 b. 10 - 4 5 3 3 4 4 Teaching Notes Inclusion 3 EXAMPLE Renaming Mixed Numbers You may need to review how to 2 find the LCD (Least Common Distance (miles) Biology In one hour, a bee can fly 53 miles and a moth can fly Denominator) of two fractions. 1 Moth 11 6 miles. How much farther can the moth fly in one hour? 1 1 EXAMPLE Error Prevention 116 1 2 1 2 1 To answer the question, find 11 - 5 . Since , , rename 11 . 6 3 6 3 6 Guide students to begin with the 2 I fractions’ column when they 5 3 1 2 Estimate 11 2 5 < 11 2 6 5 5 subtract mixed numbers. In Bee Difference 6 3 Example 1 no renaming is 1 7 1 1 7 11 10 d Rename 11 as 10 151 10 . required; but in problems that 6 6 6 6 6 S do require renaming, subtracting d The LCD is 6. Write 2 as 4. the whole numbers first can cause 2 4 3 6 2 5 2 5 3 6 errors. 3 d Subtract. 3. Answers may vary. 5 5 2 EXAMPLE Teaching Tip 6 Sample: If the Call attention to Check benchmark of the 1 d Simplify. first fraction is less 5 5 Understanding 2b. Review that 2 0 than the benchmark 1 10 is the same as 10 4. Ask: Check for Reasonableness The answer 5 is close to the estimate of 5. 4 of the second 2 How do you rename 10? 9 4 fraction, then rename 1 PowerPoint before subtracting. The moth can fly 5 2 miles farther than the bee. Additional Examples Check Understanding 3 Number Sense How can you use benchmarks to tell whether you will have 1 to rename before subtracting? See above left. 1 A black bear is about 5 4 ft long. An Alaskan brown bear 1 is about 7 2 ft long. How much 4-5 Subtracting Mixed Numbers 191 longer is an Alaskan brown 1 bear than a black bear? 2 4 ft 2 1 Reaching All Students 2 Find 9 2 13. 7 3 3 A two-week-old panda bear Below Level Have students rename Advanced Learners Match up E, F, Inclusion 3 mixed numbers as improper fractions. G, and H to the digits 1, 2, 5, and 8 See note on page 191. weighed 4 pound. At age 2 = 3 2 5 to solve this mystery problem. Visual Learners one-month, the cub weighed 13 3 1 3 5 3 3 G F 9 2 10 pounds. How many pounds H 2 F 5 6 E ≠ 5, F ≠ 1, See note on page 192. 14 = 9 1 4 5 13 E G 10 did it gain? 111 lb 9 9 9 9 2 1 9 G ≠ 2, H ≠ 8 20 5 = 6 5 11 8 5 2 12 5 6 10 16 6 1 6 5 6 191 Visual Learners More Than One Way For the More Than One Way 1 feature, have students make a Suppose you caught two fish. The first one is 48 inches long. The second drawing to help them visualize 1 one is 2 inches long. How much longer is the first fish? the problem situation. Then work 4 through both solution methods Leon’s Method using colors to illustrate each step. For instance, have volunteers write 1 1 1 I need to subtract the lengths. Since , , I will rename 4 . the subtraction on the board or 8 4 8 an overhead transparency and use 1 9 1 1 9 4 3 d Rename 4 as 3 151 3 . a color to circle the denominators. 8 S 8 8 8 8 Then have students use another 1 2 1 2 2 2 2 4 d The LCD is 8. Write as . color to circle the numerators that 4 8 4 8 will be subtracted, and a third 7 1 d Find the difference. color for the number that has 8 been renamed. 7 The first fish is 1 8 inches longer than the second one. Closure Lauren’s Method • When do you have to rename when you are subtracting mixed I need to subtract the lengths. I will change both mixed numbers? when the fraction being subtracted is greater numbers to improper fractions with the same denominator. than the one from which it is 1 1 33 9 d 4 -=-2 Write as improper fractions. being subtracted 8 4 8 4 • Explain how you would rename =-33 18 d Rename as equivalent fractions 1 1 8 8 with a like denominator.
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