1 © Penerbitan Pelangi Sdn. Bhd. 1. Whole number is said and written in numerals or words starting from the left to the right. Example: 675 090 Left Right 2. A number pattern is a series of numbers formed according to a pattern or a certain order. Number patterns can be formed by (a) adding, subtracting, multiplying or dividing the previous number with a certain fixed number. Example: 15 200, 16 200, 17 200, 18 200 (Increasing order by one thousands) (b) adding, subtracting, multiplying or dividing the previous number according to a certain number pattern. Example: 500, 600, 800, 1 100, 1 500 + 100 + 200 + 300 + 400 3. A 7-digits whole number can also be stated in fraction or decimal followed by the word million. Example: Decimal ➞ 4.693 million is said and written as four point six nine three million. Fraction ➞ 2 3 5 million is said and written as two and three-fifth of a million. 4. Fraction of a million (a) Convert the fraction of a million to a whole number. Example: 1 1 2 million = 3 2 × 1 000 000 = 3 000 000 2 = 1 500 000 Multiply the fraction with one million. Simplify. Write the digits in whole number. (b) Convert a whole number to the fraction of a million. Example: 1 300 000 = 1 300 000 1 000 000 = 13 10 million = 1 3 10 million Divide the whole number with one million. Simplify. Write the digits in fraction followed by the word million. 5. Decimal of a million (a) Convert the decimal of a million to a whole number. Example: 1.39 million = 1.39 × 1 000 000 = 1 390 000 Multiply the decimal number with one million. Move the decimal point 6 places to the right. Write the digits in whole number. (b) Convert a whole number to the decimal of a million. Example: 19 000 = 19 000 ÷ 1 000 000 = 0.019 million Divide the whole number with one million. Move the decimal point 6 places to the left. Write the digits in decimal followed by the word million. Name:........................................................................... Class:.............................. Date:....................... Whole Numbers and Operations 1 Unit Theme 1 Numbers and Operations Let’s Learn! 01 Unit 1.indd 1 21/08/2023 4:35 PM
Mathematics Year 6 Unit 1 Whole Numbers and Operations 2 © Penerbitan Pelangi Sdn. Bhd. 6. Basic operation (a) Whole number (i) For addition, subtraction and multiplication, whole numbers are arranged in vertical form according to its place value and solved starting from the right to the left. (ii) For division, after writing in vertical form, the operation is solved starting from the left to the right. (b) Fraction (i) For addition and subtraction operations involving fractions: Equate the denominator. Solve. State the answer in the simplest form. (ii) For multiplication operation involving fractions: Multiply the numerators and then the denominators. For mixed numbers, convert into an improper fraction before multiplying. Solve. State the answer in the simplest form. (iii) For division operation: The divisor needs to be inverted. The division operation is changed to multiplication before it is solved. Example: 1 3 million ÷ 1 2 = 1 3 million × 2 1 = 2 3 million For mixed numbers, change into an improper fraction 1 3 4 million ÷ 2 = 7 4 million × 1 2 = 7 8 million (c) Decimal (i) For addition, subtraction and multiplication, the decimal numbers are arranged in vertical form with the decimal points arranged in a straight line and is solved from the right to the left. (ii) For division, after writing in vertical form, the operation is solved from the left to the right. 7. Mixed operations (a) A mixed operation is a process that involves more than one operation. (b) Solving process: Mixed operations Solution steps Addition and subtraction Calculation is done from the left to the right Multiplication and division Addition and multiplication Solve multiplication followed by addition Subtraction and multiplication Solve multiplication followed by subtraction Addition and division Solve division followed by addition Subtraction and division Solve division followed by subtraction (c) For a mixed operation that involves brackets, solve the operation that is in the brackets first, followed by the other operations. 8. Prime numbers and composite numbers (a) Prime numbers are whole numbers divisible (without any balance) by 1 or the number itself. (b) Composite numbers are numbers that can be divided with 1, itself and other numbers. (c) 0 and 1 are not prime or composite numbers. Example: Number Divisible by Prime Number Composite 1 and Number itself Other numbers 5 3 7 3 7 8 3 3 7 3 16 3 3 7 3 23 3 7 3 7 01 Unit 1.indd 2 21/08/2023 4:35 PM
Mathematics Year 6 Unit 1 Whole Numbers and Operations 3 © Penerbitan Pelangi Sdn. Bhd. 1 Instruction: Answer all questions. 1.1 Whole number up to 10 000 000 Textbook / page 1 - 14 1. ‘Eight million seven hundred five thousand and thirty-four’ written in numerals is PL 1 [1 mark] 2. Write the number represented on the abacus below in words. PL 1 Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones [1 mark] 3. Arrange the numbers below in ascending order. PL 2 3 259 142 3 276 842 3 219 902 3 272 094 [2 marks] 4. The diagram below shows a number sequence. 4 697 182, 4 707 182, 4 717 182, 4 727 182 Tick (✓) the correct statement regarding the number sequence. PL 3 Ascending order by ten thousands Ascending order by one hundred thousands [1 mark] 5. State seven and five-eighths of a million in numerals. PL 1 [1 mark] 6. State 3.407 million in words. PL 1 [1 mark] 7. 5 250 000 in fraction of a million is PL 2 [1 mark] 8. Convert 0.075 million to a whole number. PL 2 [1 mark] 01 Unit 1.indd 3 21/08/2023 4:35 PM
Mathematics Year 6 Unit 1 Whole Numbers and Operations 4 © Penerbitan Pelangi Sdn. Bhd. 1.2 Basic and mixed operations Textbook / page 15 - 40 9. 2 1 2 million + 240 500 + 3.5 million = Give the answer in a whole number. PL 3 [2 marks] 10. – 7.04 million = 40 thousand Find the value in the empty box above. Give the answer in a whole number. PL 3 [2 marks] 11. 3 2 5 million ÷ 8 = PL 2 [2 marks] 12. The diagram below shows a mathematical sentence. (5 000 + 735 000) × 7 = Solve the mathematical sentence above and state the answer in the decimal of a million. PL 2 [2 marks] 13. The diagram below shows a number line. 0.58 million P Q 0.62 million Find the value of P + Q. PL 3 HOTS Applying State the answer in a whole number. [2 marks] 14. 25 000 × 20 = State the answer in fraction of a million. PL 2 [2 marks] 15. 6 2 5 million – 3 050 000 ÷ 5 = PL 3 [2 marks] 1.3 Prime numbers and composite numbers Textbook / page 42 - 43 16. The diagram shows some number cards. PL 3 1 2 17 21 31 (a) List all prime numbers. (b) Calculate the sum of all prime numbers. [2 marks] 17. The diagram shows some numbers on a whiteboard. PL 3 49 11 29 97 87 Circle all the composite numbers. [2 marks] 01 Unit 1.indd 4 21/08/2023 4:35 PM
Mathematics Year 6 Unit 1 Whole Numbers and Operations 5 © Penerbitan Pelangi Sdn. Bhd. 1.4 Problem solving Textbook / page 45 - 57 18. A food factory produces 2 1 5 million tins of biscuits. All of them are distributed equally to 400 supermarkets all over the country. How many tins of biscuits does each supermarket receive? PL 4 HOTS Applying [3 marks] 19. The table below shows the number of Mathematics activity books printed by a printing company. PL 4 Year Number of books 2019 0.64 million 2020 452 500 2021 Total 3 1 4 million Calculate the number of books printed in the year 2021. [3 marks] 20. A total of 2 1 4 million people visited the National Planetarium last year. This year, the number of visitors is expected to increase by 0.5 million people. Calculate the estimated number of visitors for this year. PL 4 [3 marks] 21. A factory produced 1 2 5 million bottles of cooking oil. 75 thousand bottles of cooking oil were kept in the warehouse and the remaining bottles were distributed equally to 10 wholesalers. How many bottles of cooking oil did each wholesaler receive? PL 5 HOTS Applying [3 marks] 22. A factory distributes 1 1 8 million of school bags to 250 supermarkets equally. Calculate the number of school bags received by 10 supermarkets. PL 5 [3 marks] 23. The product of two numbers is 4.24 million. If the first number is 20 thousand, what is the second number? PL 5 HOTS Analysing [2 marks] 01 Unit 1.indd 5 21/08/2023 4:35 PM
Mathematics Year 6 Unit 1 Whole Numbers and Operations 6 © Penerbitan Pelangi Sdn. Bhd. (c) The diagram shows the population distribution by gender in Bandar Perdana. The male population is not shown. 2.822 million If the total population is 5.796 million, calculate the male population in Bandar Perdana. Give the answer in a whole number. PL 4 [3 marks] (d) The table shows the population distribution by age in Bandar Perdana in the year 2023. Age Population 0 – 14 years 1 3 10 million 15 – 64 years 3.76 million 65 years and above 736 000 Calculate the population below 65 years old in Bandar Perdana. PL 4 [3 marks] 1. (a) The total population in Bandar Perdana in the year 2021 is 5.54 million. (i) Write the total population in words. PL 1 (ii) Convert 5.54 million to a whole number. PL 2 [3 marks] (b) The table shows the population of Bandar Perdana in the year 2022 and 2023. Year Population 2022 5 694 900 2023 5.796 million Calculate the difference in population between the two years. PL 3 [3 marks] 2 Instruction: Answer all questions. 01 Unit 1.indd 6 21/08/2023 4:35 PM
Mathematics Year 6 Unit 1 Whole Numbers and Operations 7 © Penerbitan Pelangi Sdn. Bhd. 2. (a) The table shows the number of pens produced by Colour Plus Company over the three months. Month Number of pens January 872 400 February 1.08 million March 1 1 5 million What is the total number of pens produced in the three months? PL 4 [3 marks] (b) The diagram shows the number of pens of different colours produced by Colour Plus Company in April. The number of black pens is not shown. Blue pen million Red pen 469 327 Black Pen 1 2 Calculate the number of black pens produced if the total number of pens produced in April is 1 2 5 million. PL 5 [3 marks] (c) Colour Plus Company produced 350 000 pencils every month. Calculate the number of pencils produced in one year. Give the answer in decimal of a million. PL 5 [3 marks] (d) The diagram shows the number of pencils that can be filled in a box. PL 5 24 pencils How many boxes are needed to pack 9 3 5 million pencils? [3 marks] 01 Unit 1.indd 7 21/08/2023 4:35 PM
Mathematics Year 6 Unit 1 Whole Numbers and Operations 8 © Penerbitan Pelangi Sdn. Bhd. Section A 1. ‘Five million four hundred seven thousand and eighty-nine’ in numerals is [1 mark] 2. Complete. 4 750 000 = 4 million [1 mark] 3. Convert 4 925 000 to a decimal of a million. [1 mark] 4. 2 1 2 million + 934 095 + 4.05 million = [2 marks] 5. 1 3 4 million ÷ 25 = [2 marks] 6. The table below shows the total number of magazines sold in a year. Magazine Total sales Entertainment 2 5 million Comic 0.92 million more than entertainment magazines Calculate the total number of magazines sold in that year. [2 marks] 7. The table below shows the number of gloves produced by a factory from April till June. Month Number of gloves (pairs) April 1 3 8 million May 1 650 000 June 1.05 million The factory has to achieve a production target of 4 500 000 pairs of gloves in the three months. How many more pairs of gloves need to be produced to achieve the production target for the three months? [3 marks] Instruction: Answer all questions. Summative Practice 1 01 Unit 1.indd 8 21/08/2023 4:35 PM
Mathematics Year 6 Unit 1 Whole Numbers and Operations 9 © Penerbitan Pelangi Sdn. Bhd. Section B 1. (a) The table shows the number of buttons produced by Shiny Button Manufacturer in October and November. The number of buttons produced in September is not shown. September October 357 200 November 400 000 (i) State the button production in November in fraction of a million. (ii) The number of buttons produced in October was 1 8 million less than the previous month. Calculate the number of buttons produced in September. [3 marks] (b) The diagram shows the number of buttons produced in a box. 1 000 buttons Shiny Button Manufacturer produces 30 boxes of buttons in a day. Calculate the number of buttons produced in December if the manufacturer operates every day. State the answer in decimal of a million. [2 marks] (c) The diagram shows a shirt produced by Molek Clothing Company. The company produces 22 5 million shirts of the same type. Calculate the number of buttons used by the company. [3 marks] (d) The table shows the number of white and black buttons in a box. White button Black button 1 4 million 55 000 (i) State the number of white buttons in a whole number. (ii) Molek Clothing Company needs 0.4 million black buttons to sew on the shirts it produces. The company buys 7 similar boxes of buttons. Is the number of black buttons enough for all the shirts required? [4 marks] Gamified HOTS Practice 1 Quiz 1 01 Unit 1.indd 9 21/08/2023 4:35 PM
A1 © Penerbitan Pelangi Sdn. Bhd. Answers 1 Unit Whole Numbers and Operations 1 1. 8 705 034 2. Two million fifty thousand three hundred and forty-nine 3. 3 219 902, 3 259 142, 3 272 094, 3 276 842 4. Ascending order by ten thousands 5. 7 5 8 million 6. Three point four zero seven million 7. 5 1 4 million 8. 75 000 9. 6 240 500 10. 7 080 000 11. 425 000 12. 5.18 million 13. 1 200 000 14. 1 2 million 15. 5 790 000 16. (a) 2, 17, 31 (b) 50 17. 49, 87 18. 5 500 19. 2 157 500 20. 2 750 000 21. 132 500 22. 45 000 23. 212 2 1. (a) (i) Five point five four million (ii) 5 540 000 (b) 101 100 (c) 2 974 000 (d) 5 060 000 / 5.06 million 2. (a) 3 152 400 (b) 430 673 (c) 4.2 million (d) 400 000 / 0.4 million Summative Practice 1 Section A 1. 5 407 089 2. 4 3 4 million 3. 4.925 million 4. 7 484 095 5. 70 000 6. 1 720 000 7. 425 000 Section B 1. (a) (i) 2 5 million (ii) 482 200 (b) 0.93 million (c) 7 200 000 / 7.2 million / 7 1 5 million (d) (i) 250 000 (ii) Number of black buttons needed = 400 000 Number of black buttons bought = 385 000 Therefore, the number of black buttons is not enough. 2 Unit Fractions, Decimals and Percentages 1 1. 1 20 2. 18 3. 1 1 3 4. 13 5. 3 8 6. 3 7. 13 3 5 8. 4.875 9. 32.798 10. 23.67 11. 4.21 12. 27.684 10 Answers.indd 1 21/08/2023 4:44 PM