Multiplying Decimals - Big Ideas Learning
English3.3SpanishMultiplying DecimalsWhen multiplying decimals, how do you knowwhere to place the decimal point in the product?1EXAMPLE: Multiplying DecimalsFind 0.2 0.3.2103100.2 0.3 — —Write as fractions.6100Multiply the fractions. —2610Rewrite the denominator as a power of 10. 0.06Rewrite the fraction as a decimal. —So, 0.2 0.3 0.06.2ACTIVITY: Multiplying Decimals Using Powers of 10Work with a partner.a. Copy and complete the table. Use Example 1 as a model.ProblemRewrite asFractionsProductDenominatoras Base 10Rewrite asDecimal0.2 3— —21031—610—16100.60.2 0.3— —210310—6100—26100.060.2 0.030.2 0.0030.2 0.00030.2 0.00003b. Describe the connection between the first and last columns.118Chapter 3Multiplying and Dividing Decimals
EnglishSpanish3ACTIVITY: Multiplying Decimals Using Powers of 10Copy and complete the table. Use Example 1 as a model.Rewrite asFractionsProblem21ProductDenominatoras Base 10Rewrite asDecimal610—16100.6310— —2 0.3—0.2 0.30.02 0.30.002 0.30.0002 0.34. a. What differences do you notice between the tables in Activities 2 and 3?b. What similarities do you notice?5. IN YOUR OWN WORDS When multiplying decimals, how do you knowwhere to place the decimal point in the product? Give examples inyour description.6. Write a general rule for multiplying two decimals. Give examples withyour rule.7. How many products can you find in the circle maze? List each product.Sample: 3 0.3 0.060.0710Use what you learned about multiplying decimals to completeExercises 8 –15 on page 122.Section 3.3Multiplying Decimals119
English3.3SpanishLessonLesson TutorialsThe rule for multiplying two decimals is similar to the rule for multiplyinga decimal by a whole number.Multiplying Decimals by DecimalsWordsMultiply as you would with whole numbers. Then add thenumber of decimal places in the factors. This sum gives youthe number of decimal places in the product.NumbersEXAMPLE14. 7 1 6 0.20.9 4 3 23 decimal places 1 decimal place4 decimal placesMultiplying Decimalsa. Find 4.8 7.2.4.8 7.2963363 4.5 6Estimate 5 7 351 decimal place 1 decimal place2 decimal placesSo, 4.8 7.2 34.56.b. Find 3.1 0.05.3.1 0.0 50.1 5 5Reasonable? 34.56 35Estimate 3 0 01 decimal place 2 decimal places3 decimal placesSo, 3.1 0.05 0.155.Reasonable? 0.155 0Multiply. Use estimation to check your answer.Exercises 8–23120Chapter 3 1. 8.1 5.62. 2.7 9.043. 6.32 0.094. 1.785 0.2Multiplying and Dividing Decimals
EnglishSpanishEXAMPLEEvaluating Expressions2Evaluate the expression 2.4x for the given value of x.a. x 3.95b. x 0.0162.4x 2.4(3.95) Substitute.3.9 5 2.415807909.4 8 02.4x 2.4(0.016) Substitute.0.0 1 6 2.464320.0 3 8 42 decimal places 1 decimal place3 decimal placesSo, 2.4x 9.48 when x 3.95.3 decimal places 1 decimal place4 decimal placesSo, 2.4x 0.0384 when x 0.016.Evaluate the expression 3.5x for the given value of x.Exercises 28–35EXAMPLE5. x 2.416. x 18.47. x 1.0628. x 0.007Real-Life Application3You buy 2.75 pounds of tomatoes. You hand the cashier a 10 bill.How much change will you get back?Tomatoes 1.89/poundGrapes 1.99/poundStep 1: Multiply 1.89 by 2.75.Bananas 0.49/pound1.8 9 2.7 594513233785.1 9 7 52 decimal places 2 decimal places4 decimal placesThe cost of 2.75 pounds of tomatoes is 5.20.Step 2: Subtract 5.20 from 10.10.00 5.204.80So, you will get 4.80 back.9. You buy 2.25 pounds of grapes. You hand the cashier a 5 bill.How much change will you get back?Section 3.3Multiplying Decimals121
EnglishSpanishExercises3.3Help with Homework1. NUMBER SENSE If you know 12 24 288, how can you find 1.2 2.4?Copy the problem and place the decimal point in the product.2.1.7 8 4.987223.9.2 4 0.6 8628324.3.7 5 5.2 2195750How many decimal places are in the product?5. 6.17 8.26. 1.684 10.27. 0.053 2.786) 39 (- 3) 3 (- 9) 4 (- 1)9 (-Multiply. Use estimation to check your product.18.12.0.7 0.20.004 0.99.0.08 0.310.0.007 0.0311.0.0008 0.0913.0.06 0.514.0.0008 0.00415.0.0002 0.0616. 12.4 0.217. 18.6 5.918. 7.91 0.7219. 1.16 3.3520. 6.478 18.2121. 1.064 7.21622. 0.0021 18.223. 6.109 8.40724. ERROR ANALYSIS Describe and correctthe error in the solution. 4.9 3.8186.225. TAKEOUT A Chinese restaurant offers buffet takeout for 4.99 per pound. How much does your takeout meal cost?26. CROPLAND Alabama has about 2.51 million acres of cropland.Florida has about 1.15 times as much cropland as Alabama.How much cropland does Florida have?27. GOLD On a tour of an old gold mine, you find anugget containing 0.82 ounce of gold. Gold is worth 904.62 per ounce. How much is your nugget worth?2 ALGEBRA Evaluate the expression when x 3.7, y 6.19, and z 0.072.12228. 5x29. 8z30. 2.21y31. 0.006x32. xy33. xz34. 3.6y 3.235. 2.7x 3.79Chapter 3Multiplying and Dividing Decimals
EnglishSpanishDescribe the pattern. Find the next three numbers.36. 1, 0.6, 0.36, 0.216, . . .37. 15, 1.5, 0.15, 0.015, . . .38. 0.04, 0.02, 0.01, 0.005, . . .39. 5, 7.5, 11.25, 16.875, . . .Convert the fractions or mixed numbers to decimals. Then multiply.789203540. — —3441. — —116375042. 1 — 3 —44. FOOD You buy 2.6 pounds of apples and 1.475 poundsof peaches. You hand the cashier a 20 bill. How muchchange will you get back?2140162543. 5 — 6 —Apples 1.23/poundPeaches 1.88/pound45. MILEAGE A car can travel 22.36 miles on one gallonof gasoline.a. How far can the car travel on 8.5 gallonsof gasoline?b. A hybrid car can travel 33.1 miles on one gallon of gasoline. How muchfarther can the hybrid car travel on 8.5 gallons of gasoline?46. REASONING Without multiplying, how many decimal places does 3.42 have?3.43? 3.44? Explain your reasoning.47.A rectangular painting has an area of9.52 square feet.a. Draw three different ways in which this can happen.b. The cost of a frame depends on the perimeter of apainting. Which of your drawings from part (a) is theleast expensive to frame? Explain your reasoning.c. The thin black framing costs 1 per foot. The fancyframing costs 5 per foot. Will the fancy framing costfive times as much as the black framing? Explain whyor why not.Divide. SKILLS REVIEW HANDBOOK48. 78 349. 65 1350. 57 1951. 84 1252. MULTIPLE CHOICE How many edges does the rectangularprism at the right have? SKILLS REVIEW HANDBOOKA 4 B 6 C 8 D 12 Section 3.3Multiplying Decimals123
Multiplying Decimals by Decimals Words Multiply as you would with whole numbers. Then add the number of decimal places in the factors. This sum gives you the number of decimal places in the product. Numbers 4. 7 1 6 0.2 0.9 4 3 2 3 decimal places 1 decimal place 4 decimal places EXAMPLE 1 Multip
Adding & Subtracting fractions 28-30 Multiplying Fractions 31-33 Dividing Fractions 34-37 Converting fractions to decimals 38-40 Using your calculator to add, subtract, multiply, divide, reduce fractions and to change fractions to decimals 41-42 DECIMALS 43 Comparing Decimals to fractions 44-46 Reading & Writing Decimals 47-49
Section 3.2 Multiplying Decimals and Whole Numbers 113 Use what you learned about multiplying decimals and whole numbers to complete Exercises 8 –15 on page 116. Game Rules Take turns with y
Exercise Worksheets . Add & Subtract Fractions 11. Add & Subtract Mixed Numbers 12. Multiply Fractions 13. Divide Fractions DECIMALS 14. Decimals to Fractions 15. Add & Subtract Decimals 16. Multiply Decimals 17. Divide Decimals . Worksheet #3 Multiplying Whole Numbers 46 x 72 205 x 34 493 x 67 800 x 30 376 x 18 776 x 98 2309 x 278 79,248 x .
Multiplying Decimals Practice Answers will be sent to me. 1.Make the game on the PPT on Teams and play with a family member or friend. Keep the game to practice your skills with multiplying decimals Activity: 1. Common Core Worksheet Multiplying and Dividing Decimals by Powers of 10 Activ
Section 3.5: Multiplying Polynomials Objective: Multiply polynomials. Multiplying polynomials can take several different forms based on what we are multiplying. We will first look at multiplying monomials; then we will multiply monomials by polynomials; and finish with multiplying polynomials by polynomials.
2.5 Multiplying Decimals 84 Chapter 2 Fractions and Decimals How can you multiply decimals? Work with a partner. Use a rectangle to fi nd the product. a. 2.7 1.3 Arrange base ten blocks to form a rectangle of length 2.7 units and width 1.3 units.
whole numbers and positive decimals. Order a set of positive whole numbers and decimals. 1-2 Learning Targets: Add and subtract multidigit decimals. Solve real-world problems by adding and subtracting decimals. 1-3 Learning Targets: Multiply multidigit decimals. Sub
1. US Baldrige Excellence Framework 2. European Framework for Quality Management 3. Business Excellence Framework The custodians of these frameworks are members of the Global Excellence Model (GEM) Council along with Confederation of Indian Industry, Japanese Productivity Centre for Socio‐Economic
