TM A world-class program based on top-performing 5B Singapore, Republic of Korea and Hong Kong Coursework Book SCHOLASTIC Name Philippine Edition
About Mathematics (Philippine Edition) Welcome to Scholastic TM Mathematics (Philippine Edition). The program covers the five strands of mathematics across six years/grades: Numbers and Number Sense, Measurement, Geometry, Statistics and Probability, and Patterns and Algebra. This program has been carefully designed to meet the objectives of the Philippine Department of Education Mathematics Curriculum. There are two Coursework Books for each year/grade. Each Coursework Book introduces and develops concepts and skills, as well as provides practice exercises for the consolidation of learning. Instructional Design Each chapter of the Coursework Book provides content and instruction to cover the three phases in learning mathematics: readiness, engagement and mastery. SCHOLASTIC Phase 1: Readin Phase 2: Engagement Phase 3: Mastery Let's Remember ess Learn Practice ChapterWrap-up Review *Let’s Remember Practice after each *Reviews provide offers an Learn provides summative assessment opportunity for and consolidation of systematic recall opportunities for concepts and skills and assessment of formative and learned across various prior knowledge independent practice. topics. in preparation for new learning. Learn introduces new *Chapter Wrap-up at the end of the chapter concepts and builds summarizes the key on concepts and skills learning points of the learned previously. chapter. *Think About It and *Mind Stretcher at the *Create Your Own end of the chapter develop metacognitive allows students to abilities by providing apply knowledge to opportunities for non-routine problems mathematical to develop higher- communication, order thinking skills. reasoning and justification. *Found in the Teacher’s Manual © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Each chapter of the Coursework Book comprises two parts, Lessons and Practices. 1 Lesson focuses on a concept or an aspect of it. Learning Outcomes at Number Bonds In Learn, concepts and the start of each lesson skills are introduced give an overview of the Lesson 1 Telling Number Stories and developed using learning objectives of the concrete-pictorial- the lesson. Learning Outcomes: abstract approach. This • Tell number stories proven, research-based • Make and complete number bonds approach helps students develop deep conceptual Making 5 understanding. Learn Definitions, key ideas There are 5 children. and points to take note 3 are girls. of are highlighted in the 2 are boys. Notes box. SCHOLASTIC 5 3 3 and 2 make 5. whole part 2 part This is a number bond. A number bond is made up of parts and a whole. 14 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6937-2 2 Practice provides opportunities for formative assessment and independent practice. Tasks with icons indicate Practices4 Tasks in each Practice class practice to provide are systematically students with immediate 1. Draw more marbles to show the doubles fact of 5. varied and graded to reinforcement and provide comprehensive enable teachers to check 2. Circle the doubles fact. practice and formative understanding and assessment. identify remediation needs. 3+3=6 4+2=6 3. Look at the picture. Then, circle the correct doubles fact. 10 + 10 = 20 2+2=4 5 + 5 = 10 Tasks without icons indicate 4. Write the doubles fact for each number. The two numbers independent practice for a) 16 = being added must students to attain fluency b) 18 = be the same. and mastery of concepts. 5. Write the doubles fact for each number. a) 14 = b) 20 = 88 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6937-2 iv © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Chapters end with a Problem Solving lesson. Word problems provide a meaningful context for students to apply mathematical knowledge. The focus is on both the strategies and the process of problem solving. A 4-step process guides Lesson 4 Problem Solving students to systematically solve problems and to Word problems apply appropriate Learn problem-solving strategies. Mr. Cruz bought an LED monitor for P5863. He also bought a printer that cost P1965 less than the monitor. How much did the monitor and the printer cost altogether? 1 Understand The monitor cost P5863. The printer cost the problem. P1965 less than the monitor. I need to find how much the monitor and the printer cost altogether. 2 Plan I can simplify the problem. First, I what to do. have to find the cost of the printer. I can draw a bar model to help me. 3 Work out the P 5863 Answer. monitor printer ? P 1965 ? P5863 – P1965 = P3898 The printer cost P3898. SCHOLASTIC P5863 + P3898 = P9761 The monitor and the printer cost P9761 altogether. 4 Check 8 16 15 11 Subtracting the cost of if your answer 97 6 the printer from the total is correct. cost of the monitor and – 3898 the printer, I get P5863. My answer is correct. 58 6 3 1. Understand 2. Plan 3. Answer 4. Check 38 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6941-9 39 Shine G3A_C2_2nd Proofs.indd 38 20/02/17 12:47 PM Features found in the Teacher’s Manual: Let’s Remember WS3.1 Let’s Remember Worksheet WS3.2 Think About It Worksheet Think About It assesses readiness addresses common for new learning. 1. Add 123 and 326. misconceptions 123 and errors and 326 0 is an even number. strengthens mathematical Yen 0 is neither an odd Sam thinking. nor an even number. Who is correct? Explain why. Mind Stretcher ? provides 123 + 326 = First, add the ones. opportunities for 123 students to apply +326 ................................................................................................................................................................................................... knowledge to unusual or complex WS3.3 Think About It Worksheet problem situations. 2. Subtract 435 from 947. Reviews appear after every two Ask a student from each group to present the Guess 1 947 11 101 or three chapters questions they came up with, as well as the answers. to assess and – Have students first find the total distance from 5 550□5□ 5 550□5□ reinforce students’ – Students should change the two numerical understanding of values in the word problem: the distance that Point A to Point E, and from Point E to Point D. 0 0 knowledge gained. Reno jumped, and how much further Eloy Yen 0 0 jumped. 9St0u+d43e357nt=s should be able to ?see that Sam 127. 5 5 – Guide students to use realistic numbers for the – Lead students to conclude9 t4ha7t since 127 5 5 distance Reno jumped. Remind them that the 947 –m4e3t5er=s is less than 353 m–et4er3s, t5his path is Fnirostt, subtract 0 0 the ones. 505 ÷ 5 = 11 Create Your Owndifference between the two distances should 505 ÷ 5 = 101 be less than the distance Reno jumped. Who is correct? Explain why. the path that Joel took. develops higherFor sample answers, go to CW Manual p. 128. order thinking skillsv Blended Learning Programv Guess 2 ................................................................................................................................................................................................... and metacognitiveFrom PR1ME Mathematics Interactive Edition: 3. JS–oheellcyPHooacilvnloeetlcleAsttcWsutot9dsS9eP13nob5.ti2ansfetstCheEwe,brefnearrofalbilmnctadeaPsteorhYdbiensoat.tulEol rtctaoOal PrdwdoissitnnatthnWCac,neoaJrfnrkoodsemh. eet WS3.4 BCMre3a.1teMYinodusr tOrewtcnhWerorksheet Mind stretcher (CB pp. 94–95) HowfmromanPyobinat sCebtoaPll ocinatrdDs. dStouedsenShtseslhlyoculodllbeecta?ble abUThs))eeJ–ontooe,hnnseoeeLmttglhoevsaeeiueavsdtbeedpetdethnarrissteatttiwouihhcswdonatlteiorehotwdsran9nsdsot0ttsawrhpJ9d+tnooa9roo6dpernd0bcrlno3otl+peuo5bnmrm83oloce3kmsbblmu..=ledee.2rmtese3t3.trohs.,awtthrisistienpca–eth2913is359not ability. Go through the problem with students. Use the Learn detailed lesson plan given in the corresponding Write a word problem for this bar model using the words provided. lesson notes to carry out the teaching. ATThhdeeendle,igswoitaslvnientstthhtoee atwedondsrdtpwplaorconebulaemrmeb.ethrse. same. GuSehsesll3y Fill in the missing digits and find the two numbers. 8 Learn +5 Mind stretcher – NexDt,iahave s?tudesntatsmfinpds t1h5e totagl idveistawncaey from Julio ? 990 Point A to Point B, from Point B to Point E, and 1 Understand stickerHs ow many digitsMaareriathere in each ShellyfrosctmioclklPeeocrisntst E to hPboawinstemDba.anSltylucdaerndtss.shoAunldybe able left tAhme yproblem. of the two numbers? twice to see that 135 + 75 + 37 = 247. 78 How many digaitltsoagretmheisrsing? How do I add a 3-digit number – LeaYdarsatudentsgtoamcoenccalurddse that asinltocgee2t4h7er 483 and a 2-digit number? meters is less than 353 meters, this path is not Do I need to regroup? the1p6a3th that Joel btouoyk. 342 erasers Learning Outcome: Guess 4 2 Plan what to do. I can guess and check and • Solve a non-routine problem on length using – Finally, have students find the total distance the strategy of guess and check from Point A to Point B, from Point B to Point work backwards. Answers 181 E, from Point E to Point C, and from Point C to © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6953-2 Materials: Point D. Highlight that 135 + 75 + 60 + 83 = 353. • 1 copy of Mind stretcher (BM5.3) per student – Lead students to conclude that this is the path Teacher's Resources 143 that Joel took.© 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6951-8 3 Work out the Answer. Overview 4. Check if your answer is correct. To add a 3-digit number and a This problem requires students to add two or more – Guide students to see that they can check the 2-digit number, first add the ones. numbers. The strategy introduced here allows students answer by working backwards. Since 353 – 75 – Then, add the tens. to try out different values until they get the correct 60 – 83 = 0, the answer is correct. Lastly, add the hundreds. Chapter Wrap-upanswer. Go through the problem using the 4-step Guess 1 Understand-Plan-Answer-Check process. 1 LoWokS2a.t3thReeovniees.w 1 ends the chapter byDistribute a copy of Mind stretcher (BM5.3) to each Reiterate the following points: 5 + 5 = 10 +5=0 7 student. Have them underline the key information. – Meters and centimeters are both units for length. 1. Write the numbers. 1 + 5 = 10 3 summarizing the keyThis helps them to understand the problem and – We use meters to measure longer lengths and interpret it correctly. centimeters to measure shorter lengths. a) three thousand, five8 hund5red andRtewgeronutpy-thseevoennes. – We write m for meter. b) eight thousand,+four hund5red and six learning points of1. Understand the problem. – We write cm for centimeter. – Have students look at the diagram in Mind – We measure these lines with a ruler: 990 2. Write the numbers in words. the chapter.stretcher (BM5.3). Highlight where Points A and D are. a) 4198 b) 7032 – Tell students that Joel travels a total distance of 353 meters to get from Point A to Point D. 3. Write the numbers. a) 2000 + 400 + 10 = _____ 2. Plan what to do. – We measure these lines with a string and a b) 5903 = 5000 + 900 + _____ – Point out that since there are many possible ways to travel from Point A to Point D, we can ruler: © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6951-8 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6951-8 Teacher's Resources 141 use the guess and check method to find the 144 Teacher's Resources path that adds up to a total distance of 353 4. Fill in the blanks. meters. a) In 1359, the digit 1 is in the _____ place. b) In 6407, the digit _____ is in the tens place. 3. Work out the Answer. c) In 9820, the digit 8 has a value of _____. – Have students suggest other guesses besides those shown on the page. 5. Fill in the circles with > or <. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 a) 2173 2204 b) 4035 435 c) 6735 6753 d) 8292 8294 6. Arrange the numbers in order. Begin with the smallest. 64 Chapter 5 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6951-8 3647 3746 3467 3674
Contents Chapter 8 Decimals SCHOLASTIC 1 2 0.0001 0.0001 0.0001 0.0001 0.0001 Lesson 1: Ten Thousandths 4 Practice 1 5 0.0001 0.0001 0.0001 0.0001 0.0001 Practice 2 7 Practice 3 8 9 Lesson 2: Approximation 11 0.001 Practice 4 12 Practice 5 13 Practice 6 14 Practice 7 19 22 Lesson 3: Addition and Subtraction of Decimals 24 Practice 8 Practice 9 25 Practice 10 27 Practice 11 29 30 Lesson 4: Multiplication by Tens, Hundreds or Thousands 31 Ones Tenths Hundredths Practice 12 33 Practice 13 35 4. ÷ 10 2 ÷ 10 Practice 14 37 .4 2 Lesson 5: Division by Tens, Hundreds or Thousands Practice 15 38 Practice 16 38 Practice 17 40 Lesson 6: Multiplication by 2-digit Whole Numbers 42 Practice 18 43 Practice 19 46 Lesson 7: Multiplication of Decimals 47 Practice 20 48 Practice 21 49 50 Lesson 8: Conversion of Measurements Practice 22 51 Practice 23 52 Practice 24 Lesson 9: Problem Solving Practice 25 vi © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Chapter 9 Percent SCHOLASTIC 54 ? 55 64 s Lesson 1: Percent 57 Practice 1 58 Practice 2 59 Practice 3 60 Practice 4 61 Lesson 2: Expressing Fractions as Percents 64 Practice 5 66 Practice 6 68 Practice 7 70 Lesson 3: Percentage of a Quantity 72 Practice 8 74 Practice 9 75 Practice 10 Practice 11 76 77 Chapter 10 Average 80 83 Lesson 1: Understanding Average 85 Practice 1 86 Practice 2 89 Practice 3 Practice 4 91 Lesson 2: Problem Solving 91 28 eggs Practice 5 92 94 1 s Chapter 11 Rate 96 98 Lesson 1: Rate 101 Practice 1 Practice 2 104 Pentagon Hexagon Practice 3 106 Practice 4 108 Lesson 2: Problem Solving 109 Practice 5 Chapter 12 Polygons Lesson 1: Naming and Describing Polygons Practice 1 Lesson 2: Congruent Polygons Practice 2 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Chapter 13 Area of Triangles and Quadrilaterals 111 A 113 Lesson 1: Area of Triangles 117 B height C Practice 1 118 D Practice 2 119 Practice 3 121 base Practice 4 123 126 Lesson 2: Area of Quadrilaterals Practice 5 Practice 6 Chapter 14 Tessellations SCHOLASTIC 129 130 Lesson 1: Tiling Patterns 132 Practice 1 134 Practice 2 135 139 Lesson 2: Making More Tessellations Practice 3 Practice 4 Chapter 15 Solids 142 B 143 Lesson 1: Identifying Solids 144 Practice 1 147 Practice 2 148 Practice 3 Practice 4 Chapter 16 Volume 150 ? 151 4 cm Lesson 1: Units of Volume 153 Practice 1 154 10 cm Practice 2 155 156 Lesson 2: Volume of a Cuboid and of Liquid 159 Practice 3 161 Practice 4 162 Practice 5 164 166 Lesson 3: Cubes and Cuboids 168 Practice 6 170 Practice 7 Practice 8 Lesson 4: Problem Solving Practice 9 viii © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Chapter 17 Algebra 174 x red x red 176 beads beads Lesson 1: Algebraic Expressions 179 Practice 1 182 x green Practice 2 beads Practice 3 183 Chapter 18 Temperature 186 188 Lesson 1: Measuring Temperatures 191 Practice 1 193 Practice 2 196 Practice 3 Glossary Problem Solving Process SCHOLASTIC © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Decimals Lesson 1 Ten Thousandths Learning Outcomes: • Read and write decimals with 4 decimal places • Interpret decimals with 4 decimal places in terms of tens, ones, tenths, hundredths, thousandths and ten thousandths • Identify the values of digits in decimals with 4 decimal places • Compare and order decimals up to 4 decimal places SCHOLASTIC Reading and writing decimals Learn a) When we divide 1 whole into 10 000 equal parts, each part is 1 or 1 ten thousandth of the whole. 10 000 1 We read the decimal 0.0001 as 10 000 = 0.0001 zero point zero zero zero one. b) 10 ten thousandths is 10 . 0.0001 0.0001 0.0001 0.0001 0.0001 10 000 0.0001 0.0001 0.0001 0.0001 0.0001 10 1 0.001 10 000 = 1000 = 0.001 0.001 is 1 thousandth. So, 10 ten thousandths = 1 thousandth. 3212 We read the decimal 0.3212 as c) 3212 ten thousandths is 10 000 . zero point three two one two. 3212 10 000 = 0.3212 0.3212 is 3 tenths 2 hundredths 1 thousandth 2 ten thousandths. 32 1 2 0.3212 = 10 + 100 + 1000 + 10 000 0.1 0.1 0.1 0.01 0.01 0.001 0.0001 0.0001 3 tenths 2 hundredths 1 thousandth 2 ten thousandths © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 1
Interpreting decimals in terms of tens, ones, tenths, hundredths, thousandths and ten thousandths Learn a) Ones Tenths Hundredths Thousandths Ten Thousandths Tens 3 tens + 1 one + 4 tenths + 5 hundredths + 2 thousandths + 6 ten thousandths = 30 + 1 + 0.4 + 0.05 + 0.002 + 0.0006 = 31.4526 SCHOLASTIC 30 + 1 + 4 + 5 + 2 + 6 10 100 1000 10 000 b) Express 2.5073 in terms of ones, tenths, hundredths, thousandths and ten thousandths. 2.5 0 7 3 0.0003 0.007 0 0.5 2 2.5073 = 2 + 0.5 + 0 + 0.007 + 0.0003 Practices1 1. Fill in the missing decimal. 10 10 0.1 0.01 0.01 0.001 0.0001 0.0001 0.0001 1 thousandth 2 tens 1 tenth 2 hundredths 3 ten thousandths 2 tens 1 tenth 2 hundredths 1 thousandth 3 ten thousandths = 2 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
2. Write the decimal for each of the following. a) 0.0001 0.0001 0.0001 0.0001 0.0001 b) 0.1 0.1 0.01 0.01 0.001 0.001 0.0001 0.0001 0.001 0.0001 0.0001 0.01 0.01 c) 10 11 0.01 0.01 0.001 0.0001 0.0001 11 0.01 3. Fill in the blanks. SCHOLASTIC a) 50 + 2 + 0.3 + 0.005 + 0.0006 = 38 2 b) 1.3825 = 1 + 10 + 100 + 1000 + 4. Fill in the blanks. a) 100 + 8 + 0.3 + 0.02 + 0.009 + 0.0007 = b) 60 + 5 + 0.1 + 0.008 + 0.0004 = c) 2.8745 = 2 + 0.8 + + + 0.0005 d) 0.0568 = 0.05 + e) 79.4131 = 79 + 0.4 + 0.01 + 5. Fill in the missing fractions. a) 20.0918 = 20 + +1+ 1000 16 b) 54.1603 = 54 + 10 + 100 + c) 39.1065 = 30 + 9 + 6 + 1000 + d) 82.0093 = 82 + © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 3
Identifying values of digits Learn Tens Ones Tenths Hundredths Thousandths Ten Thousandths 1 9. 8 0 2 5 In 19.8025: The digit 1 in the tens place stands for 10. Its value is 10. The digit in the tenths place is 8. 19.8025 = 10 + 9 + 0.8 + 0.002 + 0.0005 Its value is 0.8. SCHOLASTIC The digit in the hundredths place is 0. Its value is 0. The digit in the ten thousandths place is 5. Its value is 0.0005. The number 19.8025 has 4 place values after the decimal point —tenths, h undredths, thousandths and ten thousandths. We say that this decimal has 4 decimal places. Practices2 1. Read the table. Then, fill in the blanks. Tens Ones Tenths Hundredths Thousandths Ten Thousandths 5 0.3 1 0 4 a) The digit is in the ones place. b) The value of the digit 4 is . c) The digit 3 stands for . 2. Fill in the blanks. place. Its value is . In 1.4028: a) The digit 0 is in the . b) The value of the digit 2 is c) The digit 8 stands for . Its value is . 4 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Comparing and ordering decimals Learn Compare 12.435, 1.2435 and 12.4355. Align the digits according to their place values. 12.435 can be written as 12.4350. Tens Ones Tenths Hundredths Thousandths Ten Thousandths 12.435 SCHOLASTIC12.4 3 5 1.2435 1 1. 2 4 3 0 12.4355 2. 4 3 5 5 5 First, compare the Next, compare the Then, compare the tens. 0 tens is the ones, tenths, hundredths ten thousandths. 5 ten smallest. So, 1.2435 and thousandths of thousandths is greater is the smallest. 12.435 and 12.4355. than 0 ten thousandths. They are the same. So, 12.4355 is the greatest. Arranging the numbers in order from the smallest, we have: 1.2435, 12.435, 12.4355 (smallest) Practices3 1. Compare 42.0515 and 42.155. Then, fill in the blanks. Tens Ones Tenths Hundredths Thousandths Ten Thousandths 4 2. 0 5 1 4 2. 1 5 5 5 0 is greater than . © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 5
2. Circle the smaller number. a) 3.05, 3.0005 b) 18.1345, 18.1354 c) 93.401, 93.4003 d) 5 101500 , 5 5 10 000 3. Fill in the blanks with greater than, smaller than or equal to. a) 1.9305 is 1.9304. b) 0.025 isSCHOLASTIC 0.0025. c) 4.1009 is 4.108. d) 35.05 is 35.050. e) 100.0001 is 100.001. f) 20.002 is 20 10200 . 4. Arrange the numbers in order. Begin with the greatest. a) 1.45, 1.2245, 1.5, 1.245 b) 0.0018, 0.18, 0.018, 1.0008 c) 57.1265, 57.216, 57.22, 57.126 9.005, 5 , 9.50, 9 10 5 d) 9 100 000 6 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
SCHOLASTICLesson 2 Approximation Learning Outcomes: • Round decimals to 2 decimal places • Divide decimals by 1-digit whole numbers and give the quotients correct to 2 decimal places • Express mixed numbers as decimals correct to 2 decimal places • Round decimals to 3 decimal places Rounding decimals to 2 decimal places Learn a) Round 5.673 to 2 decimal places. 5.673 5.67 5.675 5.68 5.673 is less than halfway between 5.67 and 5.68. It is nearer to 5.67 than to 5.68. 5.673 is 5.67 when rounded to 2 decimal places. 5.673 ≈ 5.67 b) Round 3.147 to 2 decimal places. 3.147 3.14 3.145 3.15 3.147 is more than halfway between 3.14 and 3.15. It is nearer to 3.15 than to 3.14. 3.147 is 3.15 when rounded to 2 decimal places. 3.147 ≈ 3.15 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 7
c) Round 4.205 to 2 decimal places. 4.205 4.20 4.21 4.205 is halfway between 4.20 and 4.21. 4.205 is 4.21 when rounded to 2 decimal places. 4.205 ≈ 4.21 To round a number to 2 decimal places, look at the digit in the thousandths place. If it is 5 or greater than 5, we round up. If it is smaller than 5, we round down. SCHOLASTIC Practices4 1. Round each decimal to 2 decimal places. a) 4.858 4.85 4.855 4.86 4.858 is when rounded to 2 decimal places. b) 10.324 10.32 10.325 10.33 10.324 is when rounded to 2 decimal places. c) 95.005 95.00 95.01 95.005 is when rounded to 2 decimal places. 8 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
2. Round each decimal to 2 decimal places. a) 0.006 ≈ b) 0.064 ≈ c) 1.205 ≈ d) 3.092 ≈ e) 2.498 ≈ f) 5.997 ≈ Rounding quotients to 2 decimal places Learn Find the value of 13.85 ÷ 6 correct to 2 decimal places. 2.3 0 SCHOLASTICAdd zero as a 2 . 3 0 8 ≈ 2.31 Divide to 3 decimal 6 13.850 placeholder and 6 13.850 places. Then, round continue to divide. the answer to 12 12 2 decimal places. 18 18 18 18 5 5 0 0 50 50 48 2 13.85 ÷ 6 ≈ 2.31 Practices5 1. Find the value of 75.02 ÷ 8 correct to 2 decimal places. 8 75.02 Divide to 3 decimal places. Then, round the answer to 2 decimal places. 75.02 ÷ 8 ≈ © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 9
2. Find the value of each of the following correct to 2 decimal places. a) 80 ÷ 7 b) 0.12 ÷ 9 c) 50.32 ÷ 6 d) 64.39 ÷ 4 SCHOLASTIC Expressing mixed numbers as decimals correct to 2 decimal places Learn Express 173 as a decimal correct to 2 decimal places. 137 = 1 + 3 3 = 3 ÷ 7 0 . 4 2 8 ≈ 0.43 7 7 7 3.000 = 1 + (3 ÷ 7) ≈ 0.43 0 ≈ 1.43 30 28 20 14 60 56 4 10 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Practices6 1. Express 156 as a decimal correct to 2 decimal places. 65 5 = 5 ÷ 6 6 165 ≈ SCHOLASTIC 2. Express each mixed number as a decimal correct to 2 decimal places. a) 2 17 b) 3 32 c) 4 95 d) 5 78 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 11
Rounding decimals to 3 decimal places Learn Round 1.2348 to 3 decimal places. 1.2348 1.234 1.2345 1.235 1.2348 is more than halfway between 1.234 and 1.235. It is nearer to 1.235 than to 1.234. 1.2348 is 1.235 when rounded to 3 decimal places.SCHOLASTIC 1.2348 ≈ 1.235 To round a number to 3 decimal places, look at the digit in the ten thousandths place. If it is 5 or greater than 5, we round up. If it is smaller than 5, we round down. Practices7 1. Round 0.1485 to 3 decimal places. 0.1485 0.148 0.149 0.1485 is __________ when rounded to 3 decimal places. 2. Round each decimal to 3 decimal places. a) 0.5436 ≈ b) 5.9874 ≈ c) 0.0017 ≈ d) 0.0005 ≈ e) 7.4208 ≈ f) 1.4002 ≈ 12 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Lesson 3 Addition and Subtraction of Decimals Learning Outcomes: • Add and subtract decimals with and without regrouping • Estimate sums and differences • Solve word problems Adding decimals up to 3 decimal places Learn a) Add 0.003 and 0.005. SCHOLASTIC 0.003 0.001 0.001 0.001 0.005 0.001 0.001 0.001 0.001 0.001 3 thousandths + 5 thousandths 0.003 + 0.005 = 0.008 = 8 thousandths b) Add 0.008 and 0.005. Ones Tenths Hundredths Thousandths Align the decimal points. Then, add the thousandths. 1 0.008 + 0.005 0.013 5 thousandths + 8 thousandths = 13 thousandths = 1 hundredth 3 thousandths 0.005 + 0.008 = 0.013 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 13
c) Add 1.035 and 2.028. Ones Tenths Hundredths Thousandths 1 Add the thousandths. 1 1.035 + 2.028 3 5 thousandths + 8 thousandths = 13 thousandths Regroup the thousandths. 13 thousandths = 1 hundredth 3 thousandths 2 Add the hundredths.SCHOLASTIC 1 1.035 + 2.028 63 3 Add the ones. 1 1.035 + 2.028 There are no tenths in both numbers. Write a ‘0’ in the 3.063 tenths place of the answer. So, 1.035 + 2.028 = 3.063. Practices8 0.001 0.001 0.001 0.001 0.001 1. Add. a) 0.002 + 0.003 = 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 b) 0.008 + 0.006 = 0.008 0.01 + 0.006 14 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
2. Add. b) 0.002 + 0.007 = a) 0.004 + 0.003 = c) 0.007 + 0.009 = d) 0.018 + 0.006 = SCHOLASTIC3. Add. b) 21.325 + 10.91 = a) 3.205 + 5.027 = 21 . 325 Write 10.91 as + 10 . 910 10.910 and align 3 . 2 0 5 the decimal point. + 5.027 4. Add. b) 50.105 + 0.225 = a) 4.023 + 0.008 = c) 12.367 + 0.16 = d) 87.041 + 2.78 = © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 15
Subtracting decimals up to 3 decimal places Learn a) Subtract 0.003 from 0.008. 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.008 – 0.003 = 0.005 8 thousandths – 3 thousandths = 5 thousandths b) Subtract 0.006 from 0.02. 0.01 0.001 0.001 0.001 0.001 0.001 0.01 0.01 0.001 0.001 0.001 0.001 0.001 SCHOLASTIC 1 hundredth = 10 thousandths So, 2 hundredths = 1 hundredth 10 thousandths 2 hundredths – 6 thousandths = 1 hundredth 10 thousandths – 6 thousandths = 1 hundredth 4 thousandths 0.02 – 0.006 = 0.014 c) Subtract 0.035 from 0.1. 0.1 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 1 tenth – 3 hundredths 5 thousandths = 9 hundredths 10 thousandths – 3 hundredths 5 thousandths = 6 hundredths 5 thousandths 0.1 – 0.035 = 0.065 16 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
d) Subtract 0.482 from 3. 1 Subtract the thousandths. Ones Tenths Hundredths Thousandths First, regroup the ones, tenths, hundredths and thousandths. 3 ones = 2 ones 9 tenths Ones Tenths Hundredths Thousandths 9 hundredths 10 thousandths 2 . 9 09 10 3 0 – 0.482 .8 SCHOLASTIC 2 Subtract the hundredths. 2 . 9 09 10 3 0 – 0.482 . 18 3 Subtract the tenths. 2 . 9 09 10 3 0 – 0.482 .518 4 Subtract the ones. 2 . 9 09 10 3 0 – 0.482 2.518 So, 3 – 0.482 = 2.518. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 17
e) Subtract 1.546 from 2.033. Ones Tenths Hundredths Thousandths 1 Subtract the thousandths. First, regroup the hundredths and thousandths. 3 hundredths = 2 hundredths Ones Tenths Hundredths Thousandths 10 thousandths 2 . 0 3213 – 1.546 .7 2 Subtract the hundredths.SCHOLASTIC First, regroup the ones, tenths and hundredths. 2 ones 2 hundredths = 1 one 9 tenths 12 hundredths 1 0 91 3 213 2 . – 1.546 . 87 3 Subtract the tenths. 1 0 91 3 213 2 . – 1.546 .487 4 Subtract the ones. 1 0 91 32 13 2 . – 1.546 0.487 So, 2.033 – 1.546 = 0.487. 18 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Practices9 1. Subtract. a) 0.009 – 0.005 = 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 b) 0.04 – 0.007 = 0.01 0.01 0.01 0.01 0.001 0.001 0.001 0.001 0.001 0.01 0.01 0.01 0.001 0.001 0.001 0.001 0.001 SCHOLASTIC 0 .040 – 0 .007 2. Subtract. b) 0.07 – 0.006 = a) 0.007 – 0.006 = 3. Subtract. 1 tenth = 9 hundredths 10 thousandths 0.1 – 0.082 = 0.1 0 0 – 0 . 0 8 2 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 19
4. Subtract. b) 7 – 0.006 = a) 0.7 – 0.006 = c) 10 – 3.049 = d) 8.976 – 0.403 = SCHOLASTIC e) 6.809 – 0.317 = f) 5.372 – 0.275 = g) 27.021 – 4.628 = h) 32.104 – 13.918 = 20 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Estimating sums and differences Learn a) Estimate the value of 52.64 + 9.365. 52.64 + 9.365 ≈ 53 + 9 Round each decimal to the nearest whole number. = 62 The estimated value of 52.64 + 9.365 is 62. b) Find the actual value of 52.64 + 9.365. 52.64 + 9.365 = 62.005 11 1 Write 52.64 as 52.640. 52 . 640 + 9 . 365 SCHOLASTIC 62 . 005 The estimated value found in a) is 62. My answer here is close to the estimate. So, it is reasonable. c) Estimate the value of 92.158 – 5.62. 92.158 – 5.62 ≈ 92 – 6 = 86 The estimated value of 92.158 – 5.62 is 86. d) Find the actual value of 92.158 – 5.62. 92.158 – 5.62 = 86.538 81 1 1 92.158 Write 5.62 as 5.620. – 5.620 86.538 The estimated value found in c) is 86. My answer here is close to the estimate. So, it is reasonable. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 21
Practices10 1. Estimate and then add or subtract. Estimate Add or subtract 35.290 a) 35.29 + 16.871 ≈ + + 16.871 = 35.290 b) 35.29 – 16.871 ≈ – – 16.871 = Add or subtract SCHOLASTIC2. Estimate and then add or subtract. Estimate a) 40.73 + 8.095 ≈ + = b) 7.902 + 56.48 ≈ + = c) 65.952 – 3.41 ≈ – = d) 50.18 – 26.709 ≈ – = 22 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Solving word problems Learn a) A truck traveled 16.054 kilometers from Town A to Town B. It then traveled another 15.26 kilometers from Town B to Town C. What is the distance between Town A and Town C? 16.054 km 15.26 km A B C 16.054 + 15.26 = 31.314 The distance between Town A and Town C is 31.314 kilometers. SCHOLASTIC16.054 + 15.26 ≈ 16 + 15 = 31 My answer is close to the estimate. So, it is reasonable. b) There were 50.33 liters of water in a tank. Mr. Martin used 3.062 liters of water from the tank. How many liters of water were left in the tank? 50.33 L ? 3.062 L 50.33 L – 3.062 L = 47.268 L There were 47.268 liters of water left in the tank. 50.33 – 3.062 ≈ 50 – 3 = 47 My answer is close to the estimate. So, it is reasonable. © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 23
Practices11 Solve the word problems. Show your work clearly. 1. A plant was 0.287 meter tall in Week 1. In Week 3, the plant was 0.474 meter tall. By how much did the plant grow? 0.287 m ? Week 1 Week 3 0.474 m SCHOLASTIC 2. Chef Luis used 1.065 kilograms of sugar to bake some cakes. He used 0.845 kilogram more flour than sugar to bake the cakes. How much flour did Chef Luis use? 3. Roy’s living room has an area of 5.035 square meters. His living room is 2.45 square meters bigger than his kitchen. What is the area of Roy’s kitchen? 24 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Lesson 4 Multiplication by Tens, Hundreds or Thousands Learning Outcomes: • Multiply decimals by 10, 100 or 1000 • Multiply decimals by tens, hundreds or thousands Multiplying tenths, hundredths or thousandths by 10 Learn a) Multiply 0.6 by 10. 0.1 0.1 SCHOLASTIC 11 0.1 × 10 = 1 0.1 0.1 11 × 10 0.1 0.1 11 0.6 × 10 = 6 b) Multiply 0.06 by 10. 0.01 0.01 0.1 0.1 0.01 × 10 = 0.1 0.01 0.01 0.1 0.1 × 10 0.01 0.01 0.1 0.1 0.06 × 10 = 0.6 c) Multiply 0.006 by 10. 0.001 0.001 0.01 0.01 0.001 × 10 = 0.01 0.001 0.001 0.01 0.01 × 10 0.001 0.001 0.01 0.01 0.006 × 10 = 0.06 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 25
Multiplying decimals by 10 Learn a) Multiply 0.023 by 10. 0.01 0.01 × 10 0.1 0.1 0.001 0.001 0.001 0.01 0.01 0.01 Ones Tenths Hundredths Thousandths . × 10 2 × 10 3 SCHOLASTIC .2 3 0.023 × 10 = 0.23 0.0 2 3 c c b) Multiply 1.23 by 10. 1 × 10 10 0.1 0.1 11 0.1 0.1 0.1 0.01 0.01 0.01 Tens Ones Tenths Hundredths 1 × 10 1. 23 × 10 × 10 2. 3 1.23 × 10 = 12.3 1.2 3 When we multiply a decimal by 10, we move the decimal point 1 place to the right. 26 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Multiplying decimals by tens Learn Multiply 5.78 by 60. 5.78 × 60 = 5.78 × 6 × 10 44 = 34.68 × 10 5.7 8 = 346.8 ×6 3 4.6 8 Practices12 Multiply. 1. a) 0.5 × 10 = c) 0.08 × 10 = SCHOLASTIC b) 0.05 × 10 = d) 0.008 × 10 = b) 0.93 × 10 = 2. a) 0.046 × 10 = d) 4.35 × 10 = c) 3.7 × 10 = f) 5.002 × 10 = e) 9.032 × 10 = b) 0.93 × 30 b) 4.35 × 50 3. a) 0.046 × 20 = 0.046 × 2 × 10 = × 10 = 4. a) 3.7 × 40 d) 5.002 × 70 c) 9.032 × 60 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 27
Multiplying decimals by 100 Learn Multiply 3.21 by 100. 111 × 100 100 100 100 0.1 0.1 10 10 0.01 1 Hundreds Tens Ones Tenths Hundredths 1 3 .2 × 100 × 100 1 . × 100SCHOLASTIC 32 3.21 × 100 = 321 3.2 1 c c When we multiply a decimal by 100, we move the decimal point 2 places to the right. Multiplying decimals by 1000 Learn Multiply 0.102 by 1000. Hundreds Tens Ones Tenths Hundredths Thousandths × 1000 . 1 × 1000 2 1 2. 0.102 × 1000 = 102 0.1 0 2 When we multiply a decimal by 1000, we move the decimal point 3 places to the right. 28 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Practices13 1. Multiply. c c 0.5 0 0.5 00 a) 0.5 × 100 = b) 0.5 × 1000 = d) 0.08 × 1000 = c) 0.08 × 100 = f) 6.052 × 1000 = e) 6.052 × 100 = 2. Complete the table.SCHOLASTIC × 10 × 100 × 1000 Decimal a) 0.003 b) 1.548 c) 5.006 d) 7.25 e) 28.04 f) 30.2 3. Fill in the blanks. = 79 b) × 0.5 = 5 a) 0.79 × = 304.5 d) × 0.09 = 90 c) 3.045 × = 692.3 f) × 2.86 = 2860 e) 69.23 × = 8302 h) × 0.715 = 715 g) 8.302 × j) × 0.409 = 409 i) 1.3 × = 130 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 29
Multiplying decimals by hundreds or thousands Learn 12 3.0 2 5 a) Multiply 3.025 by 400. ×4 3.025 × 400 = 3.025 × 4 × 100 = 12.1 × 100 1 2.1 0 0 = 1210 b) Multiply 3.025 by 4000. 3.025 × 4000 = 3.025 × 4 × 1000 = 12.1 × 1000 = 12 100 Practices14SCHOLASTIC Multiply. 1. a) 0.64 × 300 = 0.64 × 3 × 100 0 .6 4 ×3 = × 100 = b) 0.64 × 3000 = 0.64 × 3 × 1000 = × 1000 = 2. a) 2.43 × 500 = 2.43 × 5 × b) 2.43 × 5000 c) 47.92 × 600 d) 5.004 × 7000 30 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Lesson 5 Division by Tens, Hundreds or Thousands Learning Outcomes: • Divide whole numbers or decimals by 10 or tens • Divide whole numbers or decimals by 100 or hundreds • Divide whole numbers by 1000 or thousands Dividing ones, tenths or hundredths by 10 Learn a) Divide 6 by 10. SCHOLASTIC 11 0.1 0.1 1 ÷ 10 = 0.1 11 ÷ 10 0.1 0.1 11 0.1 0.1 6 ÷ 10 = 0.6 b) Divide 0.6 by 10. 0.1 0.1 0.01 0.01 0.1 ÷ 10 = 0.01 0.1 0.1 0.01 0.01 ÷ 10 0.1 0.1 0.01 0.01 0.6 ÷ 10 = 0.06 c) Divide 0.06 by 10. 0.01 0.01 0.001 0.001 0.01 ÷ 10 = 0.001 0.01 0.01 0.001 0.001 ÷ 10 0.001 0.001 0.01 0.01 0.06 ÷ 10 = 0.006 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 31
Dividing whole numbers or decimals by 10 Learn a) Divide 23 by 10. 10 10 ÷ 10 1 1 111 0.1 0.1 0.1 Tens Ones Tenths Hundredths 2 ÷ 10 3 ÷ 10 . 3 2. c SCHOLAS cTIC 23 ÷ 10 = 2.3 2 3.0 b) Divide 4.2 by 10. 111 1 ÷ 10 0.1 0.1 0.1 0.1 0.1 0.1 0.01 0.01 Ones Tenths Hundredths Thousandths 4 ÷ 10 . 2 ÷ 10 . 42 4.2 ÷ 10 = 0.42 4.2 When we divide a whole number or a decimal by 10, we move the decimal point 1 place to the left. 32 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Dividing whole numbers or decimals by tens Learn 0.5 a) Divide 2 by 40. 4 2.0 0 2 ÷ 40 = 2 ÷ 4 ÷ 10 20 = 0.5 ÷ 10 20 = 0.05 0 b) Divide 0.56 by 80. 0.56 ÷ 80 = 0.56 ÷ 8 ÷ 10 0.56 ÷ 8 = 0.07 = 0.07 ÷ 10 b) 4 ÷ 10 = d) 0.04 ÷ 10 = SCHOLASTIC= 0.007 Practices 15 Divide. 1. a) 40 ÷ 10 = c) 0.4 ÷ 10 = 2. a) 65 ÷ 10 = b) 3.9 ÷ 10 = c) 7.2 ÷ 10 = d) 1.45 ÷ 10 = e) 20.28 ÷ 10 = f) 80.08 ÷ 10 = 3. a) 65 ÷ 20 = 65 ÷ 2 ÷ 10 b) 3.9 ÷ 30 b) 1.45 ÷ 50 = ÷ 10 = 4. a) 7.2 ÷ 40 c) 20.28 ÷ 60 d) 80.08 ÷ 70 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 33
Dividing whole numbers or decimals by 100 Learn a) Divide 21 by 100. 10 10 ÷ 100 0.1 0.1 1 0.01 Tens Ones Tenths Hundredths 2 ÷ 100 1 . ÷ 100 1 .2 cSCHOLAS cTIC 21 ÷ 100 = 0.21 2 1.0 b) Divide 35.2 by 100. Tenths Hundredths Thousandths Tens Ones 3 ÷ 100 5 . ÷ 2 ÷ 100 100 5 .3 2 35.2 ÷ 100 = 0.352 3 5.2 When we divide a whole number or a decimal by 100, we move the decimal point 2 places to the left. 34 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Dividing whole numbers by 1000 Learn Divide 2 by 1000. Ones Tenths Hundredths Thousandths 2 . ÷ 1000 . 2 2 ÷ 1000 = 0.002SCHOLASTIC c0 0 2.0 When we divide a whole number by 1000, we move the decimal point 3 places to the left. Practices 16 1. Divide. c c 04.0 004.0 a) 4 ÷ 100 = b) 4 ÷ 1000 = c) 52 ÷ 100 = d) 52 ÷ 1000 = e) 601 ÷ 100 = f) 601 ÷ 1000 = 2. Complete the table. ÷ 10 ÷ 100 ÷ 1000 Number a) 3 b) 16 c) 248 d) 3003 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 35
3. Divide. b) 49.7 ÷ 100 = a) 17.4 ÷ 100 = d) 5.6 ÷ 100 = c) 9.2 ÷ 100 = 4. Divide. b) 82.5 ÷ 100 = a) 15.4 ÷ 100 = d) 0.3 ÷ 100 = c) 7.9 ÷ 100 = 5. Fill in the blanks. a) 9.7 ÷ = 0.97 b) 50 ÷ = 0.5 d) 45.7 ÷ = 0.457 c) 3045 ÷SCHOLASTIC = 30.45 f) 2.05 ÷ = 0.205 h) 200 ÷ = 0.2 e) 38 ÷ = 0.038 j) ÷ 1000 = 4.09 g) 630 ÷ = 6.3 i) ÷ 100 = 1.3 Dividing whole numbers or decimals by hundreds or thousands Learn a) Divide 20.5 by 500. 20.5 ÷ 500 = 20.5 ÷ 5 ÷ 100 4.1 = 4.1 ÷ 100 5 2 0.5 20 = 0.041 5 5 0 b) Divide 364 by 7000. 364 ÷ 7000 = 364 ÷ 7 ÷ 1000 52 = 52 ÷ 1000 7 364 35 = 0.052 14 14 0 36 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Practices 17 Divide. 1. a) 15.6 ÷ 600 = 15.6 ÷ 6 ÷ 100 = ÷ 100 6 15.6 = b) 500 ÷ 4000 = 500 ÷ 4 ÷ 1000 = ÷ 1000 = 2. a) 23.2 ÷ 800SCHOLASTIC b) 4 ÷ 500 c) 702 ÷ 9000 d) 504 ÷ 3000 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 37
Lesson 6 Multiplication by 2-digit Whole Numbers Learning Outcomes: • Estimate products • Multiply decimals by 2-digit whole numbers • Solve word problems Multiplying decimals by 2-digit whole numbers Learn Estimate and then find the value of 0.42 × 79. 0.42 × 79 ≈ 0.4 × 80 = 0.4 × 10 × 8 =4×8 = 32 The product should be about 32. SCHOLASTIC 1 31 2 2 1 3 2 1 0.4 2 31 31 × 79 0.4 2 0.4 2 × 79 3 78 × 79 3 7 8 ← 0.42 × 9 2 9 4 0 ← 0.42 × 70 3 78 3 3 . 1 8 ← 0.42 × 79 29 40 Multiply 0.42 × 79 = 33.18 0.67 33.18 is about 32. The answer is reasonable. × 87 Practices318 1. Estimate and then multiply. Estimate a) 0.67 × 87 ≈ × = 38 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Estimate Multiply 3.92 b) 3.92 × 51 ≈ × × 51 = Multiply 2. Estimate and then multiply. 0.28 Estimate × 92 a) 0.28 × 92 ≈ × = 47.03 SCHOLASTIC × 68 b) 47.03 × 68 ≈ × = b) 6.72 × 47 3. Multiply. a) 5.7 × 32 c) 2.08 × 54 d) 35.67 × 83 e) 41.78 × 62 f) 60.39 × 75 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 39
Solving word problems Learn There are 28 erasers, each with a mass of 5.85 grams. What is the total mass of the erasers? 5.85 × 28 = 163.8 11 64 The total mass is 163.8 grams. 5.85 5.85 × 28 ≈ 6 × 30 × 28 = 180 My answer is close to 180. 46 80 It is reasonable. 117 00 163.80 SCHOLASTICPractices319 Solve the word problems. Show your work clearly. 1. A can of soup has a mass of 0.35 kilogram. What is the total mass of 43 such cans of soup? 0.35 × 43 = 0.35 × 43 40 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
2. Celine made some buntings for her school carnival. The length of each bunting was 2.75 meters. What was the total length of 32 similar buntings? 3. Roger spends P27.50 a day on transport. How much money does he spend on transport in 25 days? 4. In a factory, a machine dispenses 34.02 liters of ketchup in a minute. How much ketchup can the machine dispense in 56 minutes? SCHOLASTIC © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4 41
Lesson 7 Multiplication of Decimals Learning Outcomes: • Multiply decimals • Estimate products • Solve word problems Multiplying tenths by tenths or hundredths Learn a) Multiply 0.3 by 0.5. 0.3 × 0.5 = SCHOLASTIC3 ×5 First, express the decimals as fractions. 10 10 Then, multiply the fractions. Lastly, express the fraction as a decimal. = 15 100 = 0.15 b) Multiply 0.4 by 0.06. 0.4 × 0.06 = 4 × 6 10 100 = 24 1000 = 0.024 Multiplying decimals Learn a) Multiply 145 by 35. 1 Multiply 145 by 5. 2 Multiply 145 by 30. 3 Add. 22 11 11 145 22 22 × 35 145 145 725 × 35 × 35 7 2 5 ← 145 × 5 4 3 5 0 ← 145 × 30 725 4350 5 0 7 5 ← 145 × 35 42 © 2017 Scholastic Education International (S) Pte Ltd ISBN 978-981-47-6946-4
Search
