6 Student Handbook
CONTOH PENGGUNAAN LOGO DI PERINGKAT KEMENTERIAN (BI) MINISTRY OF EDUCATION MALAYSIA © English Language Teaching Centre, Ministry of Education Malaysia Kompleks Pendidikan Nilai Bandar Enstek, Lebuh Enstek, Bandar Enstek, 71760 Negeri Sembilan Tel: 06-797 9000 Website: http://www.eltc.edu.my All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronics, mechanical, photocopying, recording or otherwise, without the prior permission of English Language Teaching Centre, Ministry of Education Malaysia. e ISBN 978-629-97581-6-7
CONTENTS Contents Introduction Functions of Icons in the Book UNIT 1: WHOLE NUMBERS AND OPERATIONS Number Value Read and say numbers Let’s Practise 1A Number patterns Let’s Practise 1B Recognise fraction of a million and decimal of a million Let’s Practise 1C Convert numbers Let’s Practise 1D Whole number to decimal of a million and fraction of a million Let’s Practise 1E Basic operations Addition Let’s Practise 1F Subtraction Let’s Practise 1G Multiplication Let’s Practise 1H Division Let’s Practise 1I Mixed operations Addition and subtraction Let’s Practise 1J Multiplication and Division Let’s Practise 1K Addition and multiplication, subtraction and multiplication Let’s Practise 1L Addition and division, subtraction and division Let’s Practise 1M Basic Operations and mixed operations involving unknown prime numbers Let’s Practise 1N Know your prime numbers Let’s Practise 1O Solve the problems Let’s Practise 1P UNIT 2: FRACTIONS, DECIMALS, AND PERCENTAGES Fractions Division of fractions Dividing proper fractions with whole numbers Dividing mixed numbers with whole numbers Dividing proper fractions with proper fractions
Dividing mixed numbers with proper fractions Let’s Practise 2A Decimals Multiplication of decimals Division of decimals Let’s Practise 2B Percentages Convert decimals to percentage Let’s Practise 2C Addition and subtraction of percentages Let’s Practise 2D The value of quantity and the value of percentages Let’s Practise 2E Mixed operations Addition and subtraction Multiplication and division Addition and multiplication Subtraction and multiplication Addition and division Subtraction and division Let’s Practise 2F Problem solving Let’s Practise 2G UNIT 3: MONEY Recognise cost price, selling price, profit and loss Let’s Practise 3A Recognise discount, rebate and voucher Let’s Practise 3B Recognise invoice, bill, receipt and service tax Let’s Practise 3C Recognise interest and dividend Let’s Practise 3D Asset and liability Let’s Practise 3E Insurance and takaful Let’s Practise 3F Let’s Practise 3G Let’s Practise 3H Let’s Practise 3 I Solve the problems UNIT 4: TIME Time Zone Recognise time zone Let’s Practise 4A Determine time difference between two cities located in different time zones Let’s Practise 4B Solve daily problems involving time zone Let’s Practise 4C
UNIT 5: MEASUREMENT Length and volume of liquid Mass and volume of liquid Length and mass Let’s Practise 5A UNIT 6: SPACE Angles Draw regular polygons up to eight sides and measure the interior angles formed Let’s Practise 6A Form angles based on given degrees Let’s Practise 6B Circles Recognise centre, diameter and radius of a circle. Practise 6C Draw a circle based on given radius then label centre, radius and diameter Let’s Practise 6D Problem solving involving space Let’s Practise 6E UNIT 7: COORDINATES, RATIO, AND PROPORTION Coordinates Distance between two coordinates Let’s Practise 7A Ratio Ratio between two quantities Let’s Practise 7B Proportion Determine the proportionate quantity Let’s Practise 7C Let’s Practise 7D Solve the problems UNIT 8: DATA HANDLING AND LIKELIHOOD Pie Charts Complete pie chart and interpret data Let’s Practise 8A Likelihood Likely and unlikely Let’s Practise 8B Problem solving Let’s Practise 8C
INTRODUCTION Learning Mathematics can be quite challenging for some pupils. However, with the appropriate approach and techniques, they will find Mathematics an enjoyable subject. Dual Language Programme — Mathematics Made Easy for Year 6 KSSR is specially written to help pupils understand Mathematical concepts using stepby-step methods and explanations with clear guided samples. This book comprises eight topics that conform fully to the syllabus and requirements of the Dokumen Standard Kurikulum dan Pentaksiran (DSKP) Mathematics Year 5 KSSR. Each topic begins with Content and Learning Standards as outlined in the DSKP-KSSR. Many interesting features such as Let’s Learn, Helpful Tips, Remember and Do You Know? can be found throughout this book. They are meant to reinforce pupils’ understanding and recall key concepts. Furthermore, pupils can apply the mathematical knowledge learned to solve problem statements confidently under the Let’s Practise and Problem Solving features. There are also Dictionary Skills to explain the meaning of difficult words and Say It Right that acts as a pronunciation guide to help with difficult words. Dual Language Programme — Mathematics Made Easy for Year 6 KSSR has been carefully developed to support pupils in building a solid foundation of basic mathematical concepts and skills. Daily experiences have been incorporated in every topic to help pupils relate to matters in their daily life. Hence, this is an excellent resource to develop a comprehensive understanding for Mathematics.
FUNCTIONS OF ICONS IN THE BOOK Content Standard Based on the Content Standard outlined in the DSKP-KSSR Mathematics Year 6. Learning Standard Based on the Learning Standard outlined in the DSKP-KSSR Mathematics Year 6. Let’s Learn Briefly explains Mathematical concepts in simple English and illustrated with examples. Helpful Tips Additional knowledge for easy recall. Remember To reinforce understanding of key concepts. Do You Know? Additional information for pupils. Let’s Practise Pupils work independently. Problem Solving Problem statements for pupils to analyse and solve confidently. Dictionary Skills Explain meaning of difficult words.
1 1 Read and say numbers 7 326 519 millions hundred thousands ten thousands thousands hundreds tens ones 7 3 2 6 5 1 9 Say the number 7 326 519 as: Seven million three hundred twenty-six thousand five hundred and nineteen 2 437 109 Write the number 2 437 109 in words. 2 437 109 Two million four hundred thirty-seven thousand one hundred and nine 1 2 Learning Standard 1.1.1 Number Value Let’s Learn WHOLE NUMBERS AND BASIC OPERATIONS
2 Let’s Prac�se 1A Let’s Learn 1 Say the numbers aloud. Then, write the numbers in words. (a) 3 610 290 (b) 3 610 209 (c) 3 601 029 2 Write the numbers in numerals. (a) three hundred fi�y thousand two hundred and sixty-four (b) one million three hundred seventy thousand five hundred and nineteen (c) four million eight hundred and sixteen Number pa�erns Here is a number pa�ern. 265 260 255 250 -5 -5 The number pa�ern “decreases by 5” or “is minus 5”. What are the missing numbers? Here is an incomplete number pa�ern. +100 +100 8 245 8 345 8 445 8 645 The number pa�ern increases by 100. What are the missing numbers? Look at this sequence of numbers. Do you see any pa�ern? +100 +200 +300 +400 +500 +600 The number pa�ern is in ascending order. What is the next number? 600 700 900 1200 1600 2100 ? 2 ? 3 1 Learning Standard 1.1.2 ? A B Dic�onary Sequence follow one a�er another -5
3 Let’s Prac�se 1B Iden�fy and state the following number pa�erns. a) ______________________________________________________________________________ b) ______________________________________________________________________________ c) ______________________________________________________________________________ d) ______________________________________________________________________________ Recognise frac�on of a million and decimal of a million Read, say and write frac�on of a million. (a) Read the given frac�on of a million given in words. Example: Five and three-fourths of a million. (b) Say the frac�on of a million given in numeral form. Example: Five and three-fourths of a million Let’s Learn 1 Learning Standard 1.1.3, 1.1.4 1 231 453 1 231 463 1 231 473 1 231 483 1 231 493 1 000 5 000 25 000 125 000 625 000 1 000 000 500 000 250 000 125 000 62 500 8 275 142 7 275 142 6 275 142 5 275 142 4 275 142 1 5 can also read as five, three over four.
4 Read, say and write decimal of a million. (a) Read the decimal of a million given in words. Example: three point eight seven million (b) Say aloud the given decimal of a million in number. Example: 3.87 million So, 3.87 million is read as three point eight seven million. 1 Say the numbers aloud. Then, write the numbers in words. (a) million (b) 0.56 million (c) 8.34 million (d) 2 million (e) 2.075 million 2 Write the following numbers in numerals. (a) Three-fi�hs of a million (b) five and five-eighths of a million (c) zero point three million (d) six point zero one two million Convert Numbers Convert 4.69 million to a whole number. 4.69 million = ______________________ Let’s Prac�se 1C Learning Standard 1.1.5 1 4.69 million = 4 million + 0.6 million + 0.09 million = 4 millions + 6 hundred thousands + 9 ten thousands 2. The decimal point a�er the whole number is read as ‘point’. 3. The digits a�er the decimal point should be read separately or individually. 4. The word ‘million’ is read a�er the last digit. 1. Whole number is men�oned by its value. 2
5 Method 1 Place value millions hundred thousands ten thousands thousands hundreds tens ones Digit value 4 6 9 0 0 0 0 Method 2 4.69 million = 4.69 × 1 million = 4 . 6 9 0 0 0 0 × 1 000 000 = 4 690 000 4.69 million = 4 690 000 5 million = 5 million + million = 5 000 000 + 750 000 = 5 750 000 million = 250 000 million = 750 000 Method 1: 6 million = 6 × 1 million = 6 × 1 million = 6 × 1 million = 6 . 4000 0 0 × 1 000 000 = 6 400 000 Method 2: 6 million = 6 × 1 million = 6 × 1 miliion = 6 × 1 miliion = × 1 000 000 = 6 400 000 1 million = 1 000 000 million million million million 250 000 250 000 250 000 250 000 2 3
6 Let’s Prac�se 1D 1 Convert decimal of a million to whole numbers. (a) 0.7 million = (b) 0.19 million = (c) 1.8 million = (d) 3.05 million = (e) 0.043 million = (f) 8.021 million = 2 Convert frac�on of a million to whole numbers. (a) million = (b) million = (c) million = (d) 5 million = (e) 7 million = (f) 9 million = Whole numbers to decimal of a million and frac�on of a million State 250 000 in decimal of a million. 250 000 = ________________ million Place value millions hundred thousands ten thousands thousands hundreds tens ones Digit value 0 2 5 0 0 0 0 250 000 = 0.25 million 1 2 The digit value in the millions place value is 0. Place the decimal point between the millions place value and hundred thousands place value. Ignore the digit 0 a�er 5. Write the word million. The answer is 0.25 million. Let’s Learn Learning Standard 1.1.5
7 Let’s Prac�se 1E Convert 3 520 000 to a decimal of a million. 3 520 000 = __________________ million 3 520 000 = ( 3. 5 2 0 0 0 0 ÷ 1 000 000) million = 3.52 million State 900 000 in frac�on of a million. 900 000 = ___________ million 900 000 = ( ) million = million Convert 7 500 000 to a frac�on of a million. 7 500 000 = 7 million + ( ) million = 7 million + million = 7 million + million = million 1 Convert whole numbers to decimal of a million. (a) 125 000 = (b) 600 000 = (c) 875 000 = (d) 1 300 000 = (e) 5 700 000 = (f) 8 400 000 = 2 Convert whole numbers to frac�on of a million. (a) 300 000 = (b) 400 000 = (c) 750 000 = (d) 2 500 000 = (e) 7 600 000 = (f) 8 800 000 = 2 3 4
8 Addi�on During the vote for the best singer, a total number of million people voted on the first day and 250 000 on the second day. How many people voted on both days? million + 250 000 = 500 000 + 250 000 = 750 000 (answer in whole number) million + 250 000 = million + million = million + million = million + million = million (answer in frac�on) 162 000 + 1.688 million = 162 000 + (1.688 × 1 000 000) = 162 000 + 1 688 000 = 1 850 000 (answer in whole number) 162 000 + 1.688 million = (162 000 ÷ 1 000 000) million + 1.688 million = 0.162 million + 1.688 million = 1.85 million (answer in decimal) 2.095 million + 2 million + 3 905 000 = (2.095 × 1 000 000) + (2.5 × 1 000 000) + 3 905 000 = 2 095 000 + 2 500 000 + 3 905 000 = 8 500 000 (answer in whole number) Basic Opera�ons Let’s Learn 1 2 3 Learning Standard 1.2.1
9 Let’s Prac�se 1G Let’s Prac�se 1F 1. Find the sum. (a) million + 750 000 = (b) 0.4 million + 1 500 000 = (c) 340 000 + 1 million + 2.36 million = (d) 1.93 million + 45 000 + 5 million = 2. (a) Find the total of 2 471 500, 0.182 million and 2 million. (b) Add up 328 000 , million and 0.472 million. Subtrac�on million – 320 000 = (0.8 1 000 000) – 320 000 = 800 000 – 320 000 = 480 000 RM9.65 million – RM4.897 million = RM4.753 million 1. Find the difference. (a) 890 000 – million = (b) 4 million – 1 700 000 = (c) 0.95 million – 235 000 = (d) 3.98 million – 1 million = (e) 5 330 000 – 0.7 million – 2 million = 1 2 Let’s Learn Learning Standard 1.2.1
10 1 Mul�plica�on 42 × 25 000 = State the answer in decimal of a million. Method 1: Ver�cal form 2 5 0 0 0 × 4 2 5 0 0 0 0 1 0 0 0 0 0 0 1 0 5 0 0 0 0 42 × 25 000 = (1 050 000 ÷ 1 000 000) million = 1.05 million Method 2: La�ce Mul�plica�on 2 5 0 0 0 × 1 (0+1) 0 8 2 0 0 0 0 0 0 0 4 0 (8+2) 0 4 1 0 0 0 0 0 0 0 2 (4+1) 5 0 0 0 0 42 × 25 000 = (1 050 000 ÷ 1 000 000) million = 1.05 million 1 Let’s Learn Learning Standard 1.2.1
11 7 × 0.25 million= State the answer in decimal of a million or frac�on of a million. Method 1 1 3 0.2 5 million × 7______ 1.7 5 million Method 2 7 × 0.25 million = 7 × million = million = 1 million 7 × 0.25 million = 1.75 million or 1 million Calculate the product of 5 and 1.3 million. State the answer in frac�on of a million. Method 1 5 × 1.3 million = 1 1 .3 million × 5______ 6. 5 million 6. 5 million = 6 million = 6 million = 6 million Method 2 5 × 1.3 million = 5 × 1.3 million = 5 × 1 million 1 = 5 × million 2 = million = 6 million 2 0.25 million = million = million = million 3
12 Let’s Prac�se 1H 1. Find the product. (a) 4 × 275 000 = (b) 4 × 1 million = (c) 5 × 1.8 million = 2. Calculate. Give the answer in whole numbers. (a) 7 × 0.46 million = (b) 24 × 0.063 million = (c) 9 × million = (d) 3 × 1 million = Division A total of 240 000 packets of rice have been distributed to 1 000 old folks’ homes throughout the country. How many packets of rice will each old folks’ home will receive? 240 000 ÷ 1 000 = 240 ÷ 1 = 240 Calculate. Give the answer in decimal of a million and whole numbers. 6.48 million ÷ 3 = million = 2.16 million 6.48 million ÷ 3 = (6.48 × 1 000 000) ÷ 3 = 6 480 000 ÷ 3 = 2 160 000 4 million ÷ 20 = 4.7 million ÷ 20 = 0.235 million 4 million ÷ 20 = 4 700 000 ÷ 20 = 235 000 1 2 3 3 Let’s Learn Learning Standard 1.2.1
13 Let’s Prac�se 1J Let’s Prac�se 1 1. Find the product. (a) 7 080 000 ÷ 3 = (b) 7.8 million ÷ 10 = 2. Calculate. Give the answer in whole numbers. (a) 9.06 million ÷ 3 = (b) 2 million ÷ 5 = (c) 4.23 million ÷ 18 = Addi�on and Subtrac�on 0.6 million +2 500 000 – million = 600 000 + 2 500 000 – 800 000 = 2 300 000 6 575 000 – (2.509 million + 1 million) = 6 575 000 – (2 509 000 + 1 500 000) = 6 575 000 – 4 009 000 = 2 566 000 1. Solve and the answer in whole numbers. (a) 900 000 – million + 4.25 million = (b) 6 million – (2.95 million + 625 000) = (c) 7 500 000 – (2.78 million + 2 million) = 1 2 Mixed Opera�ons Let’s Learn Learning Standard 1.2.1
14 Let’s Prac�se 1K Mul�plica�on and Division 4 million ÷ 10 × 9 = 4 700 000 ÷ 10 × 9 = 470 000 × 9 = 4 230 000 9.75 million ÷ (15 × 2) = 9 750 000 ÷ 30 = 325 000 0.875 million × (5 000 ÷ 1 000) = 0.875 million × 5 = 4.375 million 0.875 million × (5 000 ÷ 1 000) = 875 000 × 5 = 4 375 000 1. Calculate and answer in whole numbers. (a) million × 3 ÷ 5= (b) 15 × 0.128 million ÷ 4 = (c) 8 × 1.686 million ÷ 12 = (d) 2 million ÷ (5 × 4) = Addi�on And Mul�plica�on, Subtrac�on And Mul�plica�on 250 000 + 0.43 million × 9 = 250 000 + 3 870 000 = 4 120 000 ( million + 50 000) × 12 = (700 000 + 50 000) × 12 = 750 000 × 12 = 9 000 000 4.34 million – 10 000 × 40 = 4 340 000 – 400 000 = 3 940 000 (4 million – 4.25 million) × 35 = (4.4 million – 4.25 million) × 35 = 0.15 million × 35 = 5.25 million 1 2 3 1 0.43 million × 9 = 3.87 million = 3 870 000 2 3 4 Let’s Learn Let’s Learn Learning Standard 1.2.1 Learning Standard 1.2.1
15 Let’s Prac�se 1L Let’s Prac�se 1M 1. Calculate. Give the answer in whole number or in decimal of a million. (a) 300 000 + 0.48 million × 6 = (b) 0.46 million + 1 200 × 15 = (c) 23 × (0.01 million + million) = (d) 1.12 million × 8 – 5 million = (e) (5 million – 4.84 million) × 10 = (f) 8 million – 0.84 million × 9 = Addi�on And Division, Subtrac�on And Division (6.9 million + 2 million) ÷ 5 = (6.9 million + 2.8 million) ÷ 5 = 9.7 million ÷ 5 = 1.94 million 2 million + 6.3 million ÷ 7 = 2.75 million + 0.9 million = 3.65 million (680 000 – million) ÷ 20 = (680 000 – 400 000) ÷ 20 = 280 000 ÷ 20 = 14 000 4 350 000 – 7.2 million ÷ 4 = 4.35 million – 1.8 million = 2.55 million 1. (a) 2 150 000 + 0.63 million ÷ 7 = (b) 0.72 million ÷ 24 + 1 million = (c) 6 600 000 ÷ 5 – 0.87 million = (d) 1.02 million – 8 million ÷ 25 = 1 2 3 4 Let’s Learn Learning Standard 1.2.1
16 Basic Opera�ons And Mixed Opera�ons Involving Unknown 0.9 million + y = 2.5 million y = 2.5 million – 0.9 million = 1.6 million y – million = million y = million + million = million + million = million y – million = million y – 0.2 million = 0.1 million y = 0.1 million + 0.2 million y = 0.3 million 5 × y = 1 500 000 y = 1 500 000 ÷ 5 y = 300 000 y ÷ 6 = 0.42 million y = 0.42 million × 6 y = 2.52 million y – 0.2 million + 0.38 million = 500 000 y = 500 000 + 0.2 million – 0.38 million y = 0.5 million + 0.2 million – 0.38 million y = 0.32 million y ÷ 3 × 4 = 400 000 y = 400 000 ÷ 4 × 3 y = 100 000 × 3 y = 300 000 1 TIPS 2 + y = 6 y = 6 – 2 = 4 2 TIPS y – 2 = 6 y = 6 + 2 = 8 3 TIPS 4 × y = 8 y = 8 ÷ 4 y = 2 4 TIPS y ÷ 2 = 3 y = 3 × 2 y = 6 5 TIPS y – 2 + 3 = 4 y = 4 + 2 – 3 y = 3 6 TIPS y ÷ 2 × 3 = 12 y = 12 ÷ 3 × 2 y = 8 Let’s Learn Learning Standard 1.2.1
17 y + 4 × 0.1 million = 1 200 000 y + 0.4 million = 1.2 million y = 1.2 million – 0.4 million y = 0.8 million y – 1 million × 2 = 0.5 million y – 1.5 million × 2 = 0.5 million y – 3 million = 0.5 million y = 0.5 million + 3 million y = 3.5 million y – 1.92 million ÷ 6 = 0.38 million y – 0.32 million = 0.38 million y = 0.38 million + 0.32 million y = 0.7 million 6.89 million + y ÷ 3 = 8.52 million y ÷ 3 = 8.52 million – 6.89 million y ÷ 3 = 1.63 million y = 1.63 million × 3 y = 4.89 million (y + 0.02 million) × 10 = 450 000 (y + 0.02 million) = 450 000 ÷ 10 y + 0.02 million = 45 000 y + 20 000 = 45 000 y = 45 000 – 20 000 y = 25 000 (2 .9 million – y ) ÷ 100 = 2 000 2 900 000 – y = 2 000 × 100 2 900 000 – y = 200 000 y = 2 900 000 – 200 000 y = 2 700 000 7 TIPS y + 2 × 4 = 9 y + 8 = 9 y = 9 – 8 y = 1 8 TIPS y − 2 × 4 = 5 y − 8 = 5 y = 5 + 8 y = 13 9 TIPS y – 10 ÷ 5 = 4 y − 2 = 4 y = 4 + 2 y = 6 10 TIPS 6 + y ÷ 2 = 8 y ÷ 2 = 8 – 6 y ÷ 2 = 2 y = 2 × 2 y = 4 11 12
18 Let’s Prac�se 1N M 1. Find the values of K. (a) K + 0.27 million = 1.1 million (b) K – 5 million = 1 million (c) 8 × K = 8.064 million (d) K ÷ 5 = 0.35 million (e) K – million + 0.08 million = 125 000 (f) K ÷ 9 × 5 = 0.085 million (g) K + 4 × 0.25 million = 1.625 million (h) K – million × 6 = 1.07 million (i) K + 600 000 ÷ 15 = 0.375 million (j) (2 million – p) ÷ 10 = 0.079 million Know your prime numbers Prime numbers are whole numbers greater than 1 and can only be divided by itself and 1. Composite numbers are numbers that can be divided by 1, itself and other numbers without any remainder. 0 and 1 are neither prime nor composite numbers. Look at these numbers. 7 7 ÷ 1 = 7 7 ÷ 7 = 1 7 can only be divided by 1 and itself. 8 8 ÷ 1 = 8 8 ÷ 2 = 4 8 ÷ 4 = 2 8 ÷ 8 = 1 8 can be divided by 1, 2, 4 and itself. 9 9 ÷ 1 = 9 9 ÷ 3 = 3 9 ÷ 9 = 1 9 can be divided by 1, 3 and itself. 10 10 ÷ 1 = 10 10 ÷ 2 = 5 10 ÷ 5 = 2 10 ÷ 10 = 1 10 can be divided by 1, 2, 5 and itself. 11 11 ÷ 1 = 11 11 ÷ 11 = 1 11 can only be divided by 1 and itself. The numbers 7 and 11 are prime numbers because they can be divided by 1 and themselves. The numbers 8, 9 and 10 are composite numbers. They can be divided by numbers other than 1 and themselves. 3 2 1 Prime Number Let’s Learn Learning Standard 1.2.1
19 2 3 5 7 11 13 17 19 Let’s Prac�se 10 4 6 8 10 12 14 15 16 18 20 Here are all the composite numbers between 1 and 20. 1. Iden�fy and classify prime numbers and composite numbers. i) Prime numbers : ___________________________________________ ii) Composite numbers : _______________________________________ 2. List all the composite numbers up to 100, which has digit 7 at the ones place value. ______________________________________________________________ 3. The following is an incomplete number sentence. + = 20 What are the prime numbers that can be filled in the boxes? 4. (a) List the prime numbers that are more than 40 and less than 60. ___________________________________________________________________ (b) How many prime numbers are there between 40 to 60? ____________________________________________________________________ Helpful Tips I am not a prime number. 1 is not a prime number. A prime number must be greater than 1. 42 46 47 41 43 44 45 48 49 50 Here are all the prime numbers between 1 and 20.
20 A ba�ery factory produces 4.082 million ba�eries of AA size. The factory produces size C ba�eries which are 1 million less than the number of AA size, and 860 000 ba�eries of size D. What is the total number of size C and D ba�eries produced? A library has 1 million books. Damaged books are kept in 3 boxes. Each box has 0.003 million books. How many books are in good condi�on? Step 1: Total number of damaged books: 3 x 0.003 million = 0.009 million Step 2: Total number of books in good condi�on: 1 million – 0.009 million = 1.250 million – 0.009 million = 1.241 million Answer: The number of books in good condi�on is 1.241 million Step 1: Number of size C ba�eries: 4.082 million - 1 million = 4.082 million – 1.800 million = 2.282 million Step 2: Total number of size C and D ba�eries produced: 2.282 million + 860 000 = 2.282 million + 0.86 million = 3.142 million Answer: The number of size C and D ba�eries produced is 3.142 million. 1 2 Solve The Problems Let’s Learn
21 5 prin�ng machines are used to print 3 million pamphlets. Each machine can print equal numbers of pamphlets. How many pamphlets can be printed by 7 prin�ng machines of the same type? A factory produced million table tennis balls. 0.04 million balls are separated for orders while the remaining balls are distributed equally to 100 sports stores. Is the number of table tennis balls distributed to the stores less than 4 000 balls? Prove it. Step 1 : Number of pamphlets can be printed by one prin�ng machine: 3 million ÷ 5 = 3.875 million ÷ 5 = 0.775 million Step 2: Total number of pamphlets can be printed by 7 prin�ng machines: 0.775 million x 7 = 5.425 million Answer: The number of pamphlets that can be printed by 7 prin�ng machines is 5.425 million. Step 1: The number of table tennis balls remaining for distribu�on to sports stores: million – 0.04 million = 0.40 million – 0.04 million = 0.36 million Step 2: The number of table tennis balls in each sports store: 0.36 million ÷ 100 = 360 000 ÷ 100 = 3 600 Answer: Yes. The number of table tennis balls distributed to the stores is less than 4 000 balls. 3 4
22 Let’s Prac�se 1P In conjunc�on with the fes�ve season, Si� Cake Shop received orders for peanut and dahlia biscuits. The table shows the number of orders received by a supermarket. Biscuits Peanut Dahlia Number of jars 0.06 million million What is the total number of jars of peanut biscuits and dahlia biscuits ordered by 15 supermarkets. 1.Solve the following problems. (a) A company produces 1 million branded sport shoes every month. 0.87 million of the total number of the sport shoes are exported and the remaining are sold in the local market. Calculate the number of branded sport shoes sold in the local market in 3 months. (b) A factory produced 1.35 million boxes of various flavoured milk in January. The produc�on of milk in February increased by 0.012 million compared to January. i. State the number of boxes of milk produced by the factory in January in whole number. ii. Calculate the total number of boxes of milk produced by the factory in the two months. (c) i. List all composite numbers in between 20 to 35. ii. Calculate the number of prime numbers in between 30 to 50. (d) A factory produced million T-shirts. 0.09 million T-shirt are separated for orders while the remaining T-shirt are distributed equally to 100 shops. Is the number of T-shirts distributed to the shop less than 5000 ? Prove.it Step 1: The total number of jars of peanut biscuits and dahlia biscuits ordered by a supermarket = 0.060 million + million = 0.060 million + 0.125 million = 0.185 million Step 2: The total number of jars of peanut biscuits and dahlia biscuits ordered by 15 supermarkets = 0.185 million x 15 = 2.775 million Answer: The total number of jars of peanut biscuits and dahlia biscuits ordered by 15 supermarkets is 2.775 million. 5
23 Let’s Learn FRACTIONS, DECIMALS AND PERCENTAGES Frac�ons Division of frac�ons Dividing proper frac�ons with whole numbers 1) What is the frac�on of one part a�er cakes are cut into six equal parts? Method 1 : Draw diagram 2 Learning Standard 2.1.1 is cut into 6 equal parts. There is 1 part of The frac�on of one part will be
24 Method 2: Inverse opera�on and divisor Mul�ply both the numerators Mul�ply both the denominators Dividing mixed numbers with whole numbers 1 Dividing proper frac�ons with proper frac�ons How many are there in ? Simplify the frac�on to its simplest form Convert mixed numbers to improper frac�on Perform division with cancella�on 3 1 1 part 1 part 1 part 1 part 4 equal parts Inverse opera�on and divisor TIPS For the final answer an improper frac�on should be converted to a mixed number. 2 5
25 Therefore, Dividing mixed numbers with proper frac�ons How many are there in 12 Convert the mixed number to improper frac�on and invert the opera�on and divisor. 1 4 Perform division with cancella�on Mul�ply both the numerators Mul�ply both the denominators Do you remember how to convert an improper frac�on to a mixed number? 2 5 1 4 – 1 0 4 Denominator Whole number Numerator
26 Decimals Mul�plica�onof decimals Learning Standard 2.2.1 Let’s Learn 1 Calculate. (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) 2 Solve these number sentence. (a) (b) (c) (d) The mass of a bo�le of mineral water is 0.5 kg. The mass of a small book is 0.2 �mes the mass of a mineral water. Calculate the mass, in kg, of the book. Method 1 : Shading parts of 100 boxes to represent the decimal Shade 0.5 Shade 0.2 There are 10 overlapping squares. remember? Every digit in a decimal has a place value and a digit value: 1 Let’s Prac�se 2A
27 Method 2 : Convert decimals to frac�ons Method 3 : Standard wri�en method = = 0.10 = 0.1 = 0.1 0.8 × 15.25 = 15.25 × 0.8 = = 12.2 = 9 = 3.15 0 . 5 × 0 . 2 0 .1 0 1 5. 2 5 × 0. 8 1 2. 2 0 0 2 2 1 1 decimal place 1 decimal place 2 decimal places 2 decimal places 1 decimal place 3 decimal places Tips to divide decimal number by a decimal number: a) Convert the divisor to a whole number by moving the decimal point to the right. b) Convert the number dividend by the number of decimal points in (a) Standard wri�en method : Division of decimals Learning Standard 2.2.2 Tips • Mul�ply the numbers like whole numbers. Ignore the decimal point. • Then, mark the decimal point in the answer. The number of decimal places is equal to the number of decimal places in the ques�on. Standard wri�en method : 9 27 0
28 Let’s Learn Percentages 1 Find the product of decimals. (a) (b) (c) (d) (e) 2 Divide. (a) (b) (c) (d) (e) Convert decimals to percentage Convert 4.1 to percentage. Method 1: Mul�ply by 100% 4.1 = (4.1 × 100)% = (4.1 × 100)% = 410 % Method 2: Convert to frac�ons and mul�ply by 100% 4.1 = (4.1 × 100)% = = = (41 × 10)% = 410 % 1 Learning Standard 2.3.1 Itis easy to mul�ply a decimal by 10,100 or 1 000. Just move the decimal point by 1, 2 or 3 places to the right. Remember Let’s Prac�se 2B
29 Let’s Learn State 245% in decimal. Method 1: 245% = a frac�on with a denominator of 100 is equal to the numerator divided by 100. = = in division, the point will be move to the le�) = 2.45 Method 2: 245% = 100% +100% + 45% = 1.0 + 1.0 + 0.45 = 2.45 1 Convert the decimals to percentages. (a) 0.06 = (b) 0.7 = (c) 0.19 = (d) 1.08 = (e) 8.3 = (f) 4.56 = 2 Convert the percentages to decimals. (a) 5% = (b) 20% = (c) 13% = (d) 205% = (e) 620% = (f) 995% = Addi�on and subtrac�on of percentages 91% + 6% + 101% = 215% - 48% - 25% = Step 1 : Step 2 : 2 1 5 % 1 6 7 % - 4 8 % - 2 5 % 1 6 7 % 1 4 2 % 1 . 0 1 . 0 + 0 . 4 5 2 . 4 5 2 Let’s Prac�se 2C 1 2 Learning Standard 2.3.2 Remember : 1 = 1.0 = 100%
30 Let’s Prac�se 2D 1 Find the total. (a) 2% + 5% = (b) 16% + 5% = (c) 33% + 27% = (d) 12% + 15% = (e) 29% + 7% = (f) 53% + 39% = 2 Calculate the differences. (a) 15% - 2% = (b) 18% - 7% = (c) 23% - 15% = (d) 47% - 12% = (e) 70% - 29% = (f) 91% - 57% = The value of quan�ty and the value of percentages 70% of 2.4 kg What is the percentage of 2.55 compared to 0.5? = 2.4kg = = = 1.68 = = = ( = (5.1 100)% = 510% Standard wri�en method : 5.1 - 25 5 - 5 0 1 Calculate the value of quan��es. (a) 10% of 12.6 kg = (b) 40% of 70.5 = (c) 110% of 8.25 = (d) 120% of 69.8 cm = (e) 250% of 3.25 km = (f) 330% of RM9.50 = (g) 110% × 0.9 = (h) 230% × 6.4 = (i) 500% × 21.5 = 2 Calculate the percentages. (a) 100% = (b) × 100% = (c) × 100% = (d) 100% = (e) × 100% = (f) × 100% = (g) 1.2 compared to 0.4 (h) 0.9 compared to 1.5 (i) 6.75 compared to 4.5 Learning Standard 2.3.2 1 2 Let’s Prac�se 2E Let’s Learn
31 Mixed Opera�on Let’s Learn Addi�on and subtrac�on 3 Mul�plica�on and division Addi�on and mul�plica�on 3 . 5 5 . 3 0 + 1 . 8 - 2 . 4 7 5 . 3 2 . 8 3 3 4 . 5 0 . 7 3. 1 5 Step 2: 0. 6 9 6 + 8. 2 5 0 8. 9 4 6 Step1: 1 0 . 1 2 5 . 8 0 9 6 + 6 0 0 . 6 9 6 1 Learning Standard 2.4.1 Convert frac�ons to decimals. = 3.5 Convert frac�ons to decimals. = 4.5 1.575 0 -2 1 1 - 1 0 1 5 -1 4 1 0 1 0 3 Tips In mixed opera�ons involving addi�on and mul�plica�on, carry out mul�plica�on first. Notes : Add zero at the empty place. 2
32 Subtrac�on and mul�plica�on Addi�on and division Subtrac�on and division Solve these. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) Let’s Prac�se 2F 4 5 6
Problem Solving 0.18 0.18 0.18 1.68 1.68 3.23
34 Step 1 : Calculate the mass of wheat flour a�er kg was taken out. kg = = 35 kg Step 2 : Find the mass for each plas�c which has been put equally into 8 plas�cs. Solve the problems. (1) The table shows the percentages of pupils according to their gender in a school. Calculate the percentage of boys. Pupils Boys Girls Percentage 44% (2) Rusdi has 5m of rope. He uses 85% of the rope to �e a few boxes. What is the length of rope used by Rusdi to �e all the boxes? (3) The mass of rack M is �mes the mass of rack N. The mass of rack N is . Calculate the mass, in kg, of rack M. State your answer in frac�ons. (4) The table below shows the length of two ribbons. Ribbon Red Yellow Length 0.75 m 1.8 �mes the length of red ribbon. (i) Calculate the length, in m, of yellow ribbon. (ii) What is the total length in m, of two ribbons. (5) Encik Badrul buys 30 kg of rice. He divides all the rice equally into a several containers. Every container is filled with kg of rice. How many containers would Encik Badrul need then? Let’s Prac�se 2G 4.375 -32 30 - 24 60 - 56 40 -40
35 (6) A jug contains of orange juice. Munira pours all the orange juice equally into 20 glasses. Calculate the volume of orange juice in each glass. State your answer in frac�ons. (7) The total mass of plates in a box is 27.6 kg. Each plate in the box weighs 0.6 kg. Calculate the number of plates in the box. (8) The diagram shows the length and width of a paper. Calculate the area of the paper. Give your answer in decimals. (9) The table shows the mass of old newspapers collected by two pupils. Pupil Mass of old newspaper Maisara 90.5 kg Juwita 120% of the mass of Maisara’s newspapers (i) Calculate the mass of old newspapers collected by Juwita. Give your answer in decimals. (ii) Calculate the differences between the mass of old newspaper collected by them. (10) Lina wants to make a rose crochet using red yarn. She has of yarn. Each crochet needs of yarn. (i) How many similar crochets can be made by her? (ii) If Lina wants to make 30 crochets, how many more red yarn, in m, she has to add? 8.5 cm cm
36 Let’s Learn 3 MONEY Financial Management Recognise cost price,selling price, profit and loss 3 a) Learning Standard 3.1.1 Selling price = Cost price + profit Cost price = Selling price – profit Profit = Selling price – cost price Loss = Cost price – selling price What is the cost price of the bag? Cost price = Selling price – Profit = RM150.50 – RM60 = RM90.50 Selling price : RM150.50 Profit : RM60 Cost Price The original price of goods before being sold to another person. Selling Price The price of goods which a buyer needs to pay. Dic�onary
37
38 Rebate Voucher
39 1. Calculate the value of discount. 2. Calculate the price a�er discount. 3. Calculate the price a�er rebate. 4. Calculate the total price a�er rebate. 5. Danish spent RM58.30 and he used this voucher. Calculate the price he had to pay. 6. When you buy 1 piece of cupcake with this voucher, you will get _____________________________________ Let’s Prac�se 3B Original price RM280 Special price RM239 Selling price RM460 Discount 5% RAYA PROMOTION Rebate RM760 Original price RM2 689
40 Recognise invoice, bill, receipt and service tax 3 Learning Standard 3.1.1 Let’s Learn List of goods or services with the price sent by the supplier to the customer. A bill is a detailed statement on the price of goods or services received. The receipt is an official statement that shows payment has been received. The tax that must be paid for the services rendered by certain businesses such as restaurants and hotels. Invoice Bill Receipt and Tax
41 Fill in the blanks based on the given informa�on. 1. 2. 3. Let’s Prac�se 3C MUMMY’S SEDAP FOOD Table No: 2 Receipt No: AB27 5/7/2023 3 Nasi Lemak RM15 2 Burgers RM10 4 Ice tea RM12 ------------------------------------------------- Total Service tax 5% ------------------------------------------------- Total payment COSY COFFEE HOUSE Table No: 6 Receipt No: D012 12/8/2023 3 Americano RM36 4 Espresso RM60 4 Cappucino RM44 ------------------------------------------------- ------------------------------------------------- Total Service tax 4% ------------------------------------------------- Total payment INDIGO SUPER HOTEL Room No: 1120 Receipt No: IS008 7/12/2023 2 day 1 Night RM580 Deluxe Suit Room Service RM100 ------------------------------------------------- Total Service tax 6% ------------------------------------------------- Total payment Total payment -------------------------------------------------
42 Recognise interest and dividend 3 1. Savings: RM30 000 Interest rate: 1% per annum Interest value = × RM30 000 = RM300 2. Savings: RM75 000 Interest rate: 3% per annum Interest value = × RM75 000 = RM2 250 3. Investment: RM8 000 Dividend rate: 5% per annum Dividend value = × RM8 000 = RM400 4. Investment: RM15 000 Dividend rate: 8% per annum Dividend value = × RM15 000 = RM1 200 Learning Standard 3.1.1 Dividend Shared profits for the money invested in business or shares Dictionary Interest Interest is an amount of money received when an individual saves money in a bank for a certain period of �me Dic�onary Interest value = interest rate × savings Dividend value = dividend rate × investment RM 750 x 3 RM2 250 RM 150 × 8 RM1 200 RM 80 x 5 RM400 Let’s Learn
43 Calculate the interest value or dividend below. 1. VISTA BANK Savings: RM7000 Interest rate: 2% per annum Interest value = 2. GAGAH FINANCE INSTITUTE Fixed deposit: RM25 000 Interest rate: 3.5% per annum Interest value = 3. CAHAYA BANK OF COMMERCE Savings: RM42 000 Interest rate: 6.8% per annum Interest value = 4. ONE UNIT TRUST Investment: RM18 000 Dividend rate: 7% per annum Dividend value = 5. SETIA UNIT SHARES Investment: RM35 000 Dividend rate: 8.2% per annum Dividend value = 6. ONE UNIT TRUST Investment: RM89 000 Dividend rate: 9.5% per annum Dividend value = Let’s Prac�se 3D