a b c 50 min 50 min a b c Textbook Consulting author Dr Ngo Hea Choon Singapore Maths Method Latest Indonesian Syllabus 21st Century Learning Skills
Singapore Maths Method Latest Indonesian Syllabus 21st Century Learning Skills Textbook First Published 2022 6001 Beach Road, #14-01 Golden Mile Tower, Singapore 199589. E-mail: enquiries@praxispublishing.sg ISBN 978-981-17099-0-6 Consulting author Dr Ngo Hea Choon Distributed by PT. Penerbitan Pelangi Indonesia Ruko the Prominence, Block 38G No. 36, Jl. Jalur Sutera, Alam Sutera, Tangerang, 15143, Indonesia. Tel: [021]29779388 Fax: [021]30030507 Email: pelindopublish@pelangibooks.com Printed in Malaysia by The Commercial Press Sdn. Bhd. Lot 8, Jalan P10/10, Kawasan Perusahaan Bangi, Bandar Baru Bangi, 43650 Bangi, Selangor Darul Ehsan, Malaysia. 2022 All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, photocopying, mechanical, recording or otherwise, without the prior permission of
ii Preface MINDS-ON MATHS is an exciting new series that has been developed to match the latest Indonesian Mathematics syllabuses for Primary 1 to Primary 6. This series covers comprehensively all the basic competencies (Kompetensi Dasar) as prescribed by the Indonesian Ministry of Education. MINDS-ON MATHS is a complete mathematics programme that comprises the Textbook, Workbook, Teacher’s Guide and online resources. This series builds a strong foundation of the subject through the use of the well-researched and sound pedagogical principles. Adopting the Singapore Maths method, a world-class maths teaching approach, this series integrates the Indonesian curriculum and 21st century learning skills with the most effective methods of teaching. MINDS-ON MATHS is designed to meet the learning needs of primary-level pupils to understand and strengthen their mathematical concepts and problem-solving skills, as well as assisting teachers in preparing and conducting their Mathematics lessons. CPA approach Concepts and key skills within each chapter are developed in a structured and step-by-step manner following the popular Concrete Pictorial Abstract approach to help pupils gain a firm foundation in mathematics. The method uses a three-step learning model, which consistently introduces concepts in a systematic progression. It moves from the concrete to the visual representation and then to the abstract (questioning and solving written equations). Pupils are taught not only to know how to do something but also why it works. Indonesian Maths Syllabuses Singapore Maths Method 21st Century Learning Skills
iii The contents in this series are clearly structured and move up the levels to ensure a gradual build-up of skills as pupils progress from one stage to the next. At the same time, emphasis is placed on developing pupils’ 21st century skills, such as problem-solving and critical thinking skills. 21st Century Learning Skills Throughout the series, pupils are often challenged with problem-based questions in a fun and collaborative environment. This not only creates opportunities for pupils to think critically and reason logically, but also provides a platform for pupils to communicate effectively, work individually as well as in groups, and to use ICT tools in learning mathematics. 21st Century Learning Skills 5 3 2 3 + 2 = 5 Concrete Pictorial Abstract Critical Thinking Creativity Collaboration Communication MINDS-ON MATHS is designed to meet the individual needs of all learners. Pupils will find this textbook easy to use and understand. It will guide the pupils at a manageable pace to develop their love for maths and thus to inject confidence in them.
iv Contents Special features........................................................... VII Chapter 1 Whole numbers ..................................................... 1 A Numbers greater than 100 000................................. 2 B Place and value ........................................................ 6 C Comparing and ordering numbers within 10 million.. 9 D Rounding off to the nearest thousand and estimation 16 E Multiplying by tens, hundreds or thousands ............. 21 F Dividing by tens, hundreds or thousands.................. 25 Chapter 2a Fractions (1) ........................................................... 28 A Adding unlike fractions.............................................. 29 B Subtracting unlike fractions....................................... 34 C Word problems (1).................................................... 40 D Fractions and divisions ............................................. 43 E Adding mixed numbers ............................................ 47 F Subtracting mixed numbers ..................................... 49 G Word problems (2).................................................... 51 Chapter 3s Fractions (2) ........................................................... 53 A Product of proper fractions ....................................... 54 B Word problems (1) ................................................... 56 C Product of an improper fraction and proper or improper fraction ..................................................... 61 D Product of a mixed number and a whole number .... 63 E Word problems (2) ................................................... 65 F Dividing a fraction by a whole number...................... 68 G Word problems (3) ................................................... 71 Kompetensi dasar 3.1 Menjelaskan dan melakukan penjumlahan dan pengurangan dua pecahan dengan penyebut berbeda 4.1 Menyelesaikan masalah yang berkaitan dengan penjumlahan dan pengurangan dua pecahan dengan penyebut berbeda Kompetensi dasar 3.2 Menjelaskan dan melakukan perkalian dan pembahagian pecahan dan desimal 4.2 Menyelesaikan masalah yang berkaitan dengan perkalian dan pebagian pecahan dan desimal
v Chapter 4 Four operations with decimals ...................... 76 A Addition of decimals.................................................. 77 B Subtraction of decimals ............................................ 80 C Word problems (1) ................................................... 83 D Decimals and fractions ............................................ 86 E Multiplication of decimals ......................................... 90 F Division of decimals by whole numbers.................... 95 G Word problems (2).................................................... 101 Chapter 5 Percentage ............................................................. 104 A Converting more fractions to percentage ................. 105 B Percentage of a quantity........................................... 111 C Word problems ....................................................... 117 Chapter 6 Ratio............................................................................ 122 A Simple ratios ............................................................ 123 B Equivalent ratios ....................................................... 128 C Word problems ......................................................... 133 D Ratio of three quantities............................................ 138 E Scale......................................................................... 140 Chapter 7a Speed ........................................................................ 145 A Distance and speed.................................................. 146 B Average speed.......................................................... 152 C Word problems ......................................................... 158 Chapter 8s Volume of cubes and cuboids ........................ 165 A Drawing cubes and cuboids...................................... 166 B Measuring volume .................................................... 169 Kompetensi dasar 3.4 Menjelaskan skala melalui denah 4.4 Menyelesaikan masalah yang berkaitan dengan skala pada denah Kompetensi dasar 3.3 Menyelesaikan masalah yang berkaitan dengan perbandingan dua besaran yang berbeda (kecepatan, debit) 4.3 Menyelesaikan masalah yang berkaitan dengan perbandingan dua besaran yang berbeda (kecepatan, debit) Kompetensi dasar 3.5 Menjelaskan, dan menentukan volume bangun ruang dengan menggunakan satuan volume (seperti kubus satuan) serta hubungan pangkat tiga dengan akar pangkat tiga
vi C Finding cubes and cube roots .................................. 173 D Volume of a cuboid and of liquid .............................. 178 E More volume of solids .............................................. 183 F More volume of liquids ............................................. 188 G Solving word problems involving volume and capacity .................................................................... 194 H Flow rate................................................................... 197 Chapter 9 Introduction to statistics .................................. 200 A Collecting and organising data ................................ 201 B Tables ..................................................................... 203 C Line graphs .............................................................. 206 D Pie charts.................................................................. 211 3.3 Menjelaskan perbandingan dua besaran yang berbeda (kecepatan sebagai perbandingan jarak dengan waktu, debit sebagai perbandingan volume dan waktu) 3.6 Menjelaskan dan menemukan jaring-jaring bangun ruang serdahana (kubus dan balok) 4.5 Menyelesaikan masalah yang berkaitan dengan volume bangun ruang dengan menggunakan satuan volume (seperti kubus satuan) melibatkan pangkat tiga dan akar pangkat tiga 4.3 Menyelesaikan masalah yang berkaitan dengan perbandingan dua besaran yang berbeda (kecepatan, debit) 4.6 Membuat jaring-jaring bangun ruang serdahana (kubus dan balok) Kompetensi dasar 3.7 Menjelaskan data yang berkaitan dengan diri peserta didik atau lingkungan sekitar serta cara pengumpulannya 3.8 Menjelaskan penyajian data yang berkaitan dengan diri peserta didik dan membandingkan dengan data dari lingkungan sekitar dalam bentuk daftar, tabel, diagram bergambar (piktogram), diagram batang, atau diagram garis 4.7 Menganalisis data yang berkaitan dengan diri peserta didik atau lingkungan sekitar serta cara pengumpulannya 4.8 Mengorganisasikan dan menyajikan data yang berkaitan dengan diri peserta didik dan membandingkan dengan data dari lingkungan sekitar dalam bentuk daftar, tabel, diagram gambar (piktogram), diagram batang, atau diagram garis
vii Special features Chapter Opener Introduces concepts through thought-provoking questions to encourage critical thinking and develop analytical skill. Let’s Think ! Challenges pupils with non-routine questions that promote critical thinking and logical reasoning skills. Provides a list of suitable websites related to the chapter to aid pupils in revision and self-assessment. Maths Online States the learning objectives of the upcoming chapter. Learning Outcomes Directs pupils to the carefully selected videos online for further reinforcement and mastery of concepts. watch me Practice Provides exercises to reinforce pupils’ grasp of mathematical concepts. Contains different types of online activities and games that promote peer interaction and collaborative learning. maths battle Presents informative passages and points out important tips for pupils to take note. MATHS TIPS
viii Special features Activity Provides an activity that engages in the application of knowledge of scientists, mathematicians and engineers. *Available in MINDS-ON MATHS Digital Handbook. Interesting and investigative real-life problems to challenge pupils in realistic and meaningful context. Mathematical Olympiad* quick quiz Provides numerous collections of printable online maths quizzes for pupils to boost their maths knowledge and improve speed with accuracy of maths skills. Helps pupils practise answering questions that promote higher order thinking skills (HOTS). Activity CORNER Provides practical activities to enhance pupils’ interest, knowledge and experience in learning Mathematics.
Indonesia Chapter 1 Whole numbers The area of Indonesia is about 1 904 569 square kilometres. Can you read this number? Learning Outcomes You should be able to • count, read and write numbers greater than 100 000 • compare and order numbers greater than 100 000 • describe and continue number patterns https://qr.pelangibooks.com/?u=MOMG5C1mo1 https://qr.pelangibooks.com/?u=MOMG5C1mo2 https://qr.pelangibooks.com/?u=MOMG5C1mo3 Maths Online Maths Online Maths Online Maths Online 2 3
2 Mathematics Grade 5 A Numbers greater than 100 000 10 ten thousands 10 hundred thousands 10 millions 1 hundred thousand 1 million 1 ten million 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 100 000 100 000 100 000 100 000 100 000 100 000 100 000 100 000 100 000 100 000 100 000 1 000 000 10 000 000 1 000 000 1 000 000 1 000 000 1 000 000 1 000 000 1 000 000 1 000 000 1 000 000 1 000 000 1 000 000 watch me
3 CHAPTER 1 Whole numbers 1 1 1 10 10 100 100 100 100 100 1000 1000 1000 1000 1000 1000 1000 1000 10 000 10 000 10 000 10 000 10 000 100 000 10 000 100 000 100 000 100 000 100 000 Hundred thousands Ten thousands Thousands Hundreds Tens Ones 5 6 8 5 2 3 In numerals : 568 523 In words : Five hundred and sixty-eight thousand five hundred and twenty-three 1 1 1 1 1 1 1 1 10 10 10 10 1000 100 100 1000 1000 1000 1000 10 000 10 10 000 10 000 000 100 000 100 000 100 000 10 1 1 1 1 1 1 1 1 10 10 10 10 1000 100 100 1000 1000 1000 1000 10 000 10 10 000 10 000 000 100 000 100 000 100 000 10 1 1 1 1 1 1 1 1 10 10 10 10 1000 100 100 1000 1000 1000 1000 10 000 10 10 000 10 000 000 100 000 100 000 100 000 10 1 1 1 1 1 1 1 1 10 10 10 10 1000 100 100 1000 1000 1000 1000 10 000 10 10 000 10 000 000 100 000 100 000 100 000 10 1 1 1 1 1 1 1 1 10 10 10 10 1000 100 100 1000 1000 1000 1000 10 000 10 10 000 10 000 000 100 000 100 000 100 000 10 1 1 1 1 1 1 1 1 10 10 10 10 1000 100 100 1000 1000 1000 1000 10 000 10 10 000 10 000 000 100 000 100 000 100 000 10 Hundred thousands Ten thousands Thousands Hundreds Tens Ones 3 4 5 2 5 8 In numerals : 345 258 In words : Three hundred and forty-five thousand two hundred and fifty eight Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones 5 1 2 5 3 0 0 In numerals : 5 125 300 In words : Five million one hundred and twenty-five thousand and three hundred In order to read and write numbers in words, we must know the place values of its digits. 1 1 1 10 10 100 100 100 100 100 1000 1000 1000 1000 1000 1000 1000 1000 10 000 10 000 10 000 10 000 10 000 100 000 10 000 100 000 100 000 100 000 100 000 100 100 1000 100 1000 1000 1000 1000 1 000 000 100 000 10000 10000 1 000 000 1 000 000 1 000 000 1 000 000
4 Mathematics Grade 5 100 100 100 100 100 100 100 100 100 000 100 000 100 000 100 000 100 000 100 000 1 1 1 1 1 1 1 1 000 000 10 1 000 000 1 000 000 1 000 000 1 000 000 1 000 000 1 000 000 Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones 7 6 0 0 8 1 7 In numerals : In words : MATH TIPS When writing a number that has more than four digits, we leave a space before every three digits counting from the rightmost digit to enable easy reading. Examples: (a) 15 247 (b) 380 201 (c) 1 046 352 (d) 3 657 999
5 CHAPTER 1 Whole numbers Practice 1. Write the following in numerals. (a) Two hundred and fifty-two thousand eight hundred and seventy-four (b) Four million one hundred and thirty-nine thousand two hundred and fifty (c) Six million five hundred and forty-seven thousand three hundred and two 2. Write the following numbers in words. (a) 235 450 : (b) 745 105 : (c) 8 402 153 : 3. Fill in the missing numbers. (a) 1 330 482 = + 330 000 + (b) 3 076 950 = 3 000 000 + + 950 (c) 5 000 000 + + 228 = 5 163 228 (d) 7 000 000 + + 13 = 7 546 013
6 Mathematics Grade 5 Since they are in different places, the two digits have different values. B Place and value Do you know the area of Indonesia in square kilometres? Indonesia is the world’s largest island country. The area of Indonesia is about 1 904 569 square kilometres. Look at the place value chart below. In 1 904 569: the digit 9 in the hundred thousands place stands for 900 000, the value of the digit 9 is 900 000. The digit 9 in the ones place stands for 9, the value of the digit 9 is 9. Place value and digit value 1000 1000 1000 1000 100 100 100 100 100 1 000 000 + 900 000 + 0 + 4000 + 500 + 60 + 9 10000 000 100 000 100 000 100 000 100 000 100 000 100 000 100 000 100 000 100 000 Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones 1 9 0 4 5 6 9 10 10 10 10 10 10 1 1 1 1 1 1 1 1 1 1 000 000 watch me
7 CHAPTER 1 Whole numbers Zero as a placeholder Zero has no digit value. However, it is used as a placeholder so that we can write a numeral properly. Look at the number 3405. 3405 Thousands Hundreds Tens Ones 3 4 0 5 This number is three thousand four hundred and five. We use zeros keep the digits in the correct column. If we missed out the zero, 3405 could be mistaken for 345 (three hundred and forty-five). Therefore, “0” is used as a placeholder in a number so that the non-zero digits in the number can be positioned in the correct places. Practice 1. State the place value and digit value of each underlined digit. Number Place value Digit value 49 000 879 368 1 028 174 5 236 997 2 789 300 479 655
8 Mathematics Grade 5 2. State the place value of 0 in each number. (a) 40 147 (b) 399 071 (c) 502 789 (d) 1 087 993 3. Write in expanded form. (a) 250 369 = (b) 364 037 = (c) 765 158 = (d) 2 866 497 = (e) 4 005 310 = (f) 8 247 189 =
CHAPTER 1 Whole numbers 9 C Comparing and ordering numbers within 10 million Yesterday I read a book about Asia. I found out that India has an area of 3 287 263 square kilometres. Does that mean India is bigger than Indonesia? Indonesia has an area of 1 904 569 square kilometres. How do we compare the two numbers? Steps: 1. First, compare the numbers of digits. The number with more digits is the greater number. 2. If the numbers of digits are equal, compare the digits of both numbers starting from the leftmost place. If they are the same, continue to compare until the values of digits are not the same. 3. Use a place value table to compare the digits of both numbers. This means that India has a greater area than Indonesia. Area Country Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones India 3 2 8 7 2 6 3 Indonesia 1 9 0 4 5 6 9 Both numbers have the same number of digits. In the millions place : 3 in the number 3 287 263 has a digit value of 3 000 000. 1 in the number 1 904 569 has a digit value of 1 000 000. 3 000 000 > 1 000 000 Therefore, 3 287 263 is greater than 1 904 569. watch me
10 Mathematics Grade 5 Compare 5 367 890 with 687 324. Which number is greater? Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones 5 3 6 7 8 9 0 6 8 7 3 2 4 5 367 890 has 7 digits. 687 324 has 6 digits. Therefore, 5 367 890 is greater than 687 324. 5 367 890 > 687 324 Which number is greater, 3 209 765 or 3 208 413? Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones 3 2 0 9 7 6 5 3 2 0 8 4 1 3 Both numbers have the same digits. 144444424444443 9 is greater than 8. Both numbers have the same number of digits. Both numbers have the same digits in the millions, hundred thousands and ten thousands places. Compare the thousands : 9000 > 8000. Therefore, 3 209 765 is greater than 3 208 413. 3 209 765 > 3 208 413
11 CHAPTER 1 Whole numbers Arrange the following numbers in ascending order. Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones 2 3 6 2 5 8 2 3 8 4 2 0 8 9 5 4 0 1 2 5 7 6 0 0 Compare the number of digits in each number. 89 540 has only five digits. The other numbers have more than five digits. Therefore, 89 540 is the smallest. 1 257 600 has seven digits. 236 258 and 238 420 have six digits. Therefore, 1 257 600 is the greatest among these numbers. Compare the hundred thousands and ten thousands of 236 258 and 238 420. They are the same. Compare the thousands of 236 258 and 238 420. 6 thousands is smaller than 8 thousands. Therefore, 236 258 is smaller than 238 420. In ascending order: 89 540, 236 258, 238 420, 1 257 600 smallest greatest Arrange the following numbers in descending order. Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones 2 5 8 6 5 0 1 2 5 8 3 6 0 8 3 6 9 1 2 4 8 5 6 9 1 4 0
12 Mathematics Grade 5 Practice 1. Fill in the blanks with “>” or “<”. (a) 363 300 36 000 (b) 378 021 254 699 (c) 321 520 1 125 001 (d) 357 125 357 025 (e) 6 236 789 6 237 209 (f) 8 125 120 8 215 120 2. Arrange these numbers in ascending and descending orders. (a) 2 204 236, 6 204 398, 6 024 398, 3 204 236 Ascending order : Descending order : Compare the number of digits in each number. 258 650 has six digits. The other numbers have seven digits. Therefore, 258 650 is the smallest. Compare the millions of 1 258 360, 8 369 124 and 8 569 140. 1 million is the smallest. Therefore, 1 258 360 is the smallest among the three numbers. Compare the millions of 8 369 124 and 8 569 140. They are the same. Compare the hundred thousands of 8 369 124 and 8 569 140. 5 hundred thousands is greater than 3 hundred thousands. Therefore, 8 569 140 is greater than 8 369 124. In descending order: 8 569 140, 8 369 124, 1 258 360, 258 650 greatest smallest
13 CHAPTER 1 Whole numbers Number patterns 500 +100 600 700 800 900 +100 +100 +100 The sequence of the above numbers follows a certain pattern. Each number increases by 100 to produce the next number. 1240 1205 1170 1135 1100 –35 –35 –35 –35 The sequence of the above numbers follows another pattern. Each number decreases by 35 to produce the next number. What is the next number in the following pattern? 3250 3500 3750 4000 ? 3500 is 250 more than 3250. 3750 is 250 more than 3500. 4000 is 250 more than 3750. 250 more than 4000 is 4250. Therefore, the next number in the sequence is 4000 + 250 = 4250. (b) 1 234 005, 1 236 877, 7 269 507, 7 268 507 Ascending order : Descending order :
14 Mathematics Grade 5 What is the next number in the following pattern? 8805 8605 8405 8205 ? 8605 is 200 less than 8805. 8405 is 200 less than 8605. 8205 is 200 less than 8405. 200 less than 8205 is 8005. Therefore, the next number in the sequence is 8205 – 200 = 8005. What is the next number in the following pattern? 23 590 24 590 25 590 26 590 ? 24 590 is 1000 more than 23 590. 25 590 is 1000 more than 24 590. 26 590 is 1000 more than 25 590. 1000 more than 26 590 is 27 590. Therefore, the next number in the sequence is 27 590. What is the next number in the following pattern? 855 683 805 683 755 683 705 683 ? 805 683 is 50 000 less than 855 683. 755 683 is 50 000 less than 805 683. 705 683 is 50 000 less than 755 683. 50 000 less than 705 683 is 655 683. Therefore, the next number in the sequence is 655 683.
15 CHAPTER 1 Whole numbers What is the next number in the number pattern below? 4, 8, 16, 32, 4 8 16 32 ? 4 × 2 8 × 2 16 × 2 32 × 2 Each number is the double of the number before. This number pattern is increasing by multiplying the previous number by 2. Therefore, the next number is 64. What is the next number in the number pattern below? 120, 130, 150, 180, 120 130 150 180 ? +10 +20 +30 +40 The differences of every two consecutive numbers are 10, 20, 30… The next difference is 40. Therefore, the next number is 220. What is the next number in the number pattern below? 100 000, 9900, 9700, 9400, 100 000 9900 9700 9400 ? –100 –200 –300 – 400 The differences of every two consecutive numbers are 100, 200, 300... The next difference is 400. Therefore, the next number is 9000.
16 Mathematics Grade 5 D Rounding off to the nearest thousand and estimation Rounding off to the nearest thousand Round off 6750 to the nearest thousand. 6000 6100 6200 6300 6400 6500 6600 6700 6800 6750 6900 7000 6750 is between 6000 and 7000. 6750 is closer to 7000 than to 6000. When 6750 is rounded off to the nearest thousand, it becomes 7000. Therefore, 6750 ≈ 7000. Round off 9492 to the nearest thousand. 9000 9100 9200 9300 9400 9500 9600 9700 9800 9900 10 000 9492 9492 is between 9000 and 10 000. 9492 is closer to 9000 than to 10 000. When 9492 is rounded off to the nearest thousand, it becomes 9000. Therefore, 9492 ≈ 9000. Round off 7500 to the nearest thousand. 7000 7100 7200 7300 7400 7500 7600 7700 7800 7900 8000 7500 is halfway between 7000 and 8000. In such a situation, 7500 is rounded up to 8000 as the nearest thousand. Therefore, 7500 ≈ 8000. watch me
17 CHAPTER 1 Whole numbers What is 7728 rounded off to the nearest thousand? 7000 7100 7200 7300 7400 7500 7600 7700 7800 7728 7900 8000 7728 is between and . 7728 is nearer to than . 7728 is when rounded off to the nearest thousand. Therefore, 7728 ≈ . What is 4263 rounded off to the nearest thousand?. 4000 4100 4200 4300 9400 4500 4600 4700 4800 4900 5000 4263 4263 is between and . 4263 is nearer to than . 4263 is when rounded off to the nearest thousand. Therefore, 4263 ≈ . Round off 9650 to the nearest thousand. 9000 9100 9200 9300 9400 9500 9600 9700 9800 9900 10 000 9650 9650 is between and . 9650 is nearer to than . 9650 is when rounded off to the nearest thousand. Therefore, 9650 ≈ .
18 Mathematics Grade 5 Practice Round off these numbers to the nearest ten, hundred and thousand. Number Nearest ten Nearest hundred Nearest thousand 2547 6050 12 388 28 147 32 774 45 902 67 285 Estimation 6348 adults and 3720 children visited the science centre last week. Estimate the total number of people that visited the science centre last week. 6348 ≈ 6000 3720 ≈ 3800 6348 + 3720 ≈ 6000 + 3800 = 9800 The total number of people that visited the science centre last week was about 9800. Let’s round off the numbers to the nearest thousand. Then, let’s estimate the value of 6348 + 3720.
19 CHAPTER 1 Whole numbers Round off the numbers to the nearest thousand. Then, estimate the value of (a) 5432 + 1987 (b) 5432 – 1987 5432 ≈ 1987 ≈ (a) + ≈ + = (b) – ≈ – = Estimate the value of 5347 × 4. First, round off 5347 to the nearest thousand. 5347 ≈ 5000 5347 × 4 ≈ 5000 × 4 = 20 000 Estimate the value of 8966 × 3. 8966 × 3 ≈ × 3 = Round off the 4-digit number to the nearest thousand first.
20 Mathematics Grade 5 Estimate the value of 2346 ÷ 4. 2000 2300 2500 3000 2400 2346 To estimate 2346 ÷ 4, we can choose a number that is close to 2346 and can be divided exactly by 4. 2346 is closer to 2400 than 2000. Then, let’s divide. 2346 ÷ 4 ≈ 2400 ÷ 4 = 600 Therefore, the value of 2346 ÷ 4 is about 600. Estimate 7859 ÷ 9. 7000 7200 7500 7700 7800 8000 8100 7859 7859 is closer to than . 7859 ÷ 9 ≈ ÷ 9 = Therefore, the value of 7859 ÷ 9 is about . 2000 and 2400 do not leave a remainder when divided by 4. 2000 ÷ 4 2346 ÷ 4 2400 ÷ 4
CHAPTER 1 Whole numbers 21 10 10 100 1 10 E Multiplying by tens, hundreds or thousands Multiplying by tens What is 4 × 20? 4 × 20 = 4 × 2 tens = 4 × 2 × 10 = 8 × 10 = 80 Find the value of 18 × 30. 18 × 30 = 18 × 3 tens = 18 × 3 × 10 = 54 × 10 = 540 What is 26 × 30? 26 × 30 = 26 × tens = 26 × × 10 = × 10 = Practice Find the values of the following. 1. 32 × 50 = 2. 168 × 20 = 3. 225 × 40 = 4. 2468 × 60 = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 × 3 × 3 × 2 × 10 × 10 × 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 10 10 100 100 100 100 100 100 100 100 100 100 10 100 watch me
22 Mathematics Grade 5 Multiplying by hundreds or thousands What is 6 × 200? 6 × 200 = 6 × 2 hundreds = 6 × 2 × 100 = 12 × 100 = 1200 Find the value of 24 × 300. 24 × 300 = 24 × 3 hundreds = 24 × 3 × 100 = 72 × 100 = 7200 What is 73 × 400? 73 × 400 = 73 × hundreds = 73 × × = × = Practice Find the values of the following. 1. 92 × 500 = 2. 818 × 600 = 3. 2025 × 700 = 4. 4217 × 800 = 1 1 × 2 1 × 100 100 100 1 1 1 1 1 10 24 × 3 = 72 24 × 300 = 7200 73 × 4 = 73 × 400 = 1000
23 CHAPTER 1 Whole numbers 1000 What is 3 × 4000? 3 × 4000 = 3 × 4 thousands = 3 × 4 × 1000 = 12 × 1000 = 12 000 Find the value of 11 × 6000. 11 × 6000 = 11 × 6 thousands = 11 × 6 × 1000 = 66 × 1000 = 66 000 What is 14 × 3000? 14 × 3000 = 14 × thousands = 14 × × = × = Practice Find the values of the following. 1. 56 × 5000 = 2. 789 × 6000 = 3. 223 × 3000 = 4. 904 × 8000 = 1 × 4 1 × 1000 1 1 1 10 10 000 11 × 6 = 66 11 × 6000 = 66 000 14 × 3 = 14 × 3000 = 1000
24 Mathematics Grade 5 Estimate the value of 438 × 19. 438 × 19 ≈ 400 × 20 = 400 × 2 × 10 = 800 × 10 = 8000 The value of 438 ×19 is about 8000. Let’s check the answer. 438 × 19 = 8322 Estimate the value of 277 × 42. 277 × 42 ≈ × = × × = × = Practice Estimate the values of following. 1. 590 × 23 2. 34 × 672 Steps: 1. Round off 438 to the nearest hundred. 438 ≈ 400 2. Round off 19 to the nearest ten. 19 ≈ 20 3. Multiply. 800 is close to 8322. Therefore, 8000 is a reasonable answer. Steps: 1. Round off 277 to the nearest hundred. 277 ≈ 2. Round off 42 to the nearest ten. 42 ≈ 3. Multiply.
CHAPTER 1 Whole numbers 25 F Dividing by tens, hundreds or thousands Dividing by tens Find the value of 60 ÷ 20. 60 ÷ 20 = 60 ÷ 10 ÷ 2 = 6 ÷ 2 = 3 What is 720 ÷ 80? 720 ÷ 80 = 720 ÷ 10 ÷ 8 = ÷ 8 = Find the value of 5600 ÷ 70. 5600 ÷ 70 = 5600 ÷ ÷ = ÷ 7 = Practice Find the values of the following. 1. 180 ÷ 30 = 2. 650 ÷ 50 = 3. 2700 × 90 = 4. 6400 ÷ 80 = 5600 ÷ 7 = 5600 ÷ 70 = 720 ÷ 8 = 90 720 ÷ 80= ÷ 10 ÷ 2 10 10 10 10 10 10 1 1 1 1 1 1 1 1 1 watch me
26 Mathematics Grade 5 Dividing by hundreds or thousands What is 600 ÷ 200? 600 ÷ 200 = 600 ÷ 100 ÷ 2 = 6 ÷ 2 = 3 Find the value of 6000 ÷ 2000. 6000 ÷ 2000 = 6000 ÷ 1000÷ 2 = 6 ÷ 2 = 3 What is 4800 ÷ 600? 4800 ÷ 600 = 4800 ÷ 100 ÷ 6 = ÷ 6 = Find the value of 54 000 ÷ 9000. 54 000 ÷ 9000 = 54 000 ÷ 1000 ÷ 9 = ÷ 9 = Practice Find the values of the following. 1. 900 ÷ 300 = 2. 2800 ÷ 400 = 3. 6300 ÷ 700 = 4. 25 000 ÷ 500 = 5. 72 000 ÷ 8000 = 6. 108 000 ÷ 9000 = 54 000 ÷ 9 = 54 000 ÷ 9000 = 4800 ÷ 6 = 4800 ÷ 600= 6000 ÷ 2 = 3000 6000 ÷ 2000 = 3 600 ÷ 2 = 300 600 ÷ 200 = 3
27 CHAPTER 1 Whole numbers Estimate the value of 1954 ÷ 57. To estimate 1954 ÷ 57, we round off the divisor 57 to 60. Then, choose a number close to 1954 that does not leave a remainder when divided by 60. 1800 1954 2400 1954 is closer to 1800 than 2400. 1954 ÷ 57 ≈ 1800 ÷ 60 = 1800 ÷ 10 ÷ 6 = 180 ÷ 6 = 30 Therefore, the value of 1954 ÷ 57 is about 30. Estimate the value of 3467 ÷ 856. 856 ≈ 3467 ÷ 856 ≈ ÷ = ÷ ÷ = ÷ = Practice Estimate the values of the following. 1. 772 ÷ 18 2. 5389 ÷ 86 3. 8531 ÷ 97 4. 6640 ÷ 382 2700 3467 3600
Maths Online Maths Online Maths Online Maths Online Chapter 2 Fractions (1) Learning Outcomes You should be able to • identify like fractions with same denominators • identify unlike fractions with different denominators • add and subtract fractions with different denominators • express division as a fraction and vice versa • add and subtract mixed numbers • solve word problems involving fractions Mother eats 1 6 of the pizza. You can have 1 3 of the remaining pizza. How much of the pizza do you get? https://qr.pelangibooks.com/?u=MOMG5C2mo1 hhttps://qr.pelangibooks.com/?u=MOMG5C2mo2 https://qr.pelangibooks.com/?u=MOMG5C2mo3 4 https://qr.pelangibooks.com/?u=MOMG5C2mo4 Maths Online 2 3 4
CHAPTER 2 Fractions (1) 29 A Adding unlike fractions To add fractions with different denominators, equalise the denominators first. Sam ate 1 3 of a pie. His brother ate 1 6 of the same pie. What fraction of the pie did they eat altogether? + = 1 3 1 6 1 6 1 6 1 6 1 3 + 1 6 = 1 3 + 1 6 = 2 6 + 2 6 = 3 6 = 1 2 Always write your answer in its simplest form. 3 6 = 1 2 1 2 Simplest form 1 3 = 2 6 × 2 × 2 watch me
30 Mathematics Grade 5 Add 1 3 and 5 9 . 1 3 = 1 3 + 5 9 = + = Practice (a) 1 2 + 1 4 = + 1 4 (b) 1 5 + 7 10 = + 7 10 = = (c) 1 3 + 5 12 = (d) 1 8 + 1 4 + 3 8 = 1. Add. What is 1 2 + 3 8 ? 1 2 = 1 2 + 3 8 = + 3 8 = × 4 × 4 × × = ? 1 3 5 9 1 2 = ? 3 8
CHAPTER 2 Fractions (1) 31 3 4 + 5 12 = 9 12 + 5 12 = 14 12 = 12 12 + 2 12 = 1 2 12 = 1 1 6 They ate 1 1 6 chocolate bars altogether. Find the sum of 1 2 , 4 5 and 3 10. 1 2 + 4 5 + 3 10 = 5 10 + 8 10 + 3 10 = 16 10 = 8 5 = 5 5 + 3 5 = 1 3 5 Simplest form Simplest form 1 2 = 5 10 4 5 = 8 10 Joe and Farah had a chocolate bar each. Joe ate 3 4 of his chocolate bar. Farah ate 5 12 of her chocolate bar. What fraction of chocolate bars did they eat altogether? Joe Farah 3 4 5 12 3 4 = 9 12 × 3 × 3 1 6 8 5
32 Mathematics Grade 5 List the multiples of the denominators, 3 and 4. Multiples of 3 : 3, 6, 9, 12 , 15, ... Multiples of 4 : 4, 8, 12 , 16, 20, ... 12 is the first common multiple of 3 and 4. 1 3 = 4 12 × 4 × 4 1 4 = 3 12 × 3 × 3 ? = 4 12 1 3 = 3 12 1 4 1 3 + 1 4 = 4 12 + 3 12 = 7 12 They ate 7 12 of the cake altogether. Anna and Karim shared a cake. Anna ate 1 3 of the cake. Karim ate 1 4 of it. What fraction of the cake did they eat altogether? 1 3 + 1 4 = Let’s add 1 3 and 1 4. To add, we have to convert them to like fractions.
CHAPTER 2 Fractions (1) 33 Find the first common multiple of 2 and 5. 2 : 2, 4, 6, 8, 10 , 12, ... 5 : 5, 10 , 15, 20, ... Find the sum of 1 2 and 2 5 . 1 2 + 2 5 = 1 2 = 10 × × 2 5 = 10 × × 1 2 + 2 5 = 10 + 10 = What is the value of 1 2 and 3 7 ? 1 2 + 3 7 = 1 2 = 3 7 = 1 2 + 3 7 = + = Practice 1. Add. (a) 1 6 + 1 4 = (b) 1 3 + 2 5 = Find the first common multiple of 2 and 7. 2 : 2, 4, 6, 8, 10, 12 14 , 16, ... 7 : 7, 14 , 21, ...
Mathematics 34 Grade 5 B Subtracting unlike fractions Melissa has 5 6 piece of ribbon. Nora has 2 3 piece of ribbon. Who has a longer piece of ribbon? How much longer? Melissa Nora 2 3 5 6 5 6 – 2 3 = 5 6 – 4 6 = 1 6 Melissa has a longer piece of ribbon. It is 1 6 longer. To subtract fractions with different denominators, equalise the denominators first. Find the difference between 5 8 and 1 2 . 1 2 = 8 × 4 × 4 5 8 – 1 2 = 5 8 – 8 = 2 3 = 4 6 × 2 × 2 1 ? 2 5 8 watch me
CHAPTER 2 Fractions (1) 35 What is 4 7 – 5 14 ? 4 7 = × × 4 7 – 5 14 = – = Subtract 5 9 from 2 3 . 2 3 = × × 2 3 – 5 9 = – = Practice 1. Subtract. (a) 1 3 – 1 6 = – (b) 1 – 5 8 = – = = (c) 2 5 – 3 10 = (d) 1 – 3 12 – 2 3 = 5 ? 9 2 3 5 ? 14 4 7
36 Mathematics Grade 5 Ben ordered 2 pizzas. He ate 3 8 of a pizza. What fraction of the pizzas were left? 3 8 2 – 3 8 = 1 8 8 – 3 8 = 1 5 8 or 2 – 3 8 = 16 8 – 3 8 = 13 8 = 8 8 + 5 8 = 1 5 8 1 5 8 of the pizza were left. What is the value of 3 – 7 9 ? 3 – 7 9 = 2 9 9 – 7 9 = 2 2 9 or 2 = 1 + 1 = 1 + 8 8 = 1 8 8 We can also convert the whole number into a mixed number first. 2 = 8 8 + 8 8 = 16 8 or 2 = 2 1 = 16 8 × 8 × 8 3 = 2 + 1 = 2 + 9 9 = 1 8 1 3 8 5 )
CHAPTER 2 Fractions (1) 37 3 – 7 9 = 27 9 – 7 9 = 20 9 = 2 2 9 Find the difference between 4 and 2 5 . 4 – 2 5 = 3 – 2 5 4 – 2 5 = 5 – 2 5 = 3 = 5 = Practice 1. Subtract. (a) 2 – 6 15 = (b) 3 – 7 12 = (c) 5 – 5 6 = (d) 8 – 3 11 = To convert the whole number into mixed number. 3 = 9 9 + 9 9 + 9 9 = 27 9 or 3 = 3 1 = 27 9 × 9 × 9 or 2 9 2 0 1 8 2 )
38 Mathematics Grade 5 Julie had 5 6 m of rope at first. She used 4 9 m of the rope for an art project. How many metres of rope did she have left? 5 6 – 4 9 = List the multiples of the denominators, 6 and 9. Multiples of 6 : 6, 12, 18 , 24, ... Multiples of 9 : 9, 18 , 27, ... 18 is the first common multiple of 6 and 9. 5 6 = 15 18 × 3 × 3 4 9 = 8 18 × 2 × 2 ? 15 18 5 6 =fifi 8 18 4 9 =fifi 5 6 m – 4 9 m = 15 18 m – 8 18 m = 17 18 m She had 7 18 metres of rope left. Let’s subtract 4 9 from 5 6 . To subtract, we have to convert them to like fractions.
CHAPTER 2 Fractions (1) 39 Find the difference between of 5 6 and 3 4 . 5 6 – 3 4 = 5 6 = 12 × × 3 4 = 12 × × 5 6 – 3 4 = 12 – 12 = Subtract 2 5 from 2 3 . 2 3 – 2 5 = 2 3 = 2 5 = 2 3 – 2 5 = – = Practice Subtract. 1. 2 3 – 3 12 = 2. 5 6 – 5 9 = Find the first common multiple of 6 and 4. 4 : 4, 8, 12 , 16, ... 6 : 6, 12 , 18, ... Find the first common multiple of 3 and 5. 3 : 3, 6, 9, 12, 15 , 18, ... 5 : 5, 10, 15 , 20, ...
Mathematics 40 Grade 5 C Word problems (1) Murni is mixing a drink with orange juice and mango juice. She pours 3 4 l of orange juice and 5 8 l of mango juice into a container. How much juice is in the container? 3 4 l + 5 8 l = 6 8 l + 5 8 l = 11 8 l = 1 3 8 l 1 3 8 l litres of juice is in the container. Lily ate 3 5 of a cake. Later, John ate 1 3 of the same cake and Maria ate 4 15 of it. What fraction of the cake did they eat altogether? 3 5 + 1 3 + 4 15 = 15 + 15 + 15 = 15 = + = = They ate cake altogether. × 2 × 2 watch me
CHAPTER 2 Fractions (1) 41 Lisa had 7 m of wire. She used 1 6 m to make some key chains. She used another 7 12 m to make some frames. How many metres of wire did she have left? 7 m – 1 6 m – 7 12 m = 6 12 12 m – 1 6 m – 7 12 m 1 6 m + 7 12 m = 2 12 m + 7 12 m = 6 12 12 m – 2 12 m – 7 12 m 7 m – 9 12 m = 6 12 12 m – 9 12 m = 6 3 12 m or = 6 3 12 m = 6 1 4 m = 6 1 4 m She had 6 1 4 metres of wire left. Siti was given 12 hours to complete her school project. She works for 1 3 h and another 5 9 h. How much time does she have left ? 12h – 1 3 h – 5 9 h = 11 9 9 h – 1 3 h – 5 9 h + = + = 11 9 9 h – 3 9 h – 5 9 h or = = 11 1 9 h – = – = She has hours left. 4 1 4 1
