M A T H S · 2020. 6. 10. · 1. Brief concise explanation. 2. Rule or formula or set of steps in larger print. 3. Fully worked ... least 2 exercises in each chapter. All students

iUnderstanding Year 5 Maths Advanced Edition

Warwick Marlin © Five Senses Education

ADVANCED ED IT ION

UNDERSTANDING

Y E A R 5

Warwick Marlin B.Sc. Dip.Ed.

M A T H

Author

CLEAR AND CONCISE

GRADED EXERCISES

SOLUTIONS AT BACK

ALL ABILITY GROUPS

VERY USER FRIENDLY

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Understanding Year 5 Maths Advanced EditionWarwick Marlin © Five Senses Educationvv

Page

CONTENTS

INTRODUCTION vi

NUMBER AND ALGEBRA

NUMBER AND PLACE VALUE 1

FRACTIONS AND DECIMALS 41

MONEY AND FINANCIAL MATHEMATICS 77

PATTERNS AND ALGEBRA 103

MEASUREMENT & GEOMETRY

USING UNITS OF MEASUREMENT 129

SHAPE 165

LOCATION AND TRANSFORMATION 181

GEOMETRIC REASONING 201

STATISTICS & PROBABILITY

CHANCE 227

DATA REPRESENTATION AND INTERPRETATION 243

SOLUTIONS TO GRADED EXERCISES 263

NOTE: The New Australian National Curriculum has been split into 3 major strands:

A Number & Algebra B Measurement & Geometry C Statistics & Probability

In the Year 5 content descriptions, these 3 major strands have been further subdivided into the 10 chapters shown above.

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ixUnderstanding Year 5 Maths Advanced Edition


HOW CAN THIS BOOK HELP?

1) Firstly, the book has been split up into the 10 MAJOR IMPORTANT TOPICS.

2) Each of these major topics has been broken down into a number of simpler ideas and rules, thus saving educators and students valuable TIME in research.

3) Each page covers only one idea or rule, thus giving students CLARITY.

4) Each concept is thoroughly, but simply, explained for UNDERSTANDING.

5) Each formula, rule or set of steps is highlighted in larger print for ease of MEMORISING.

6) Each formula and page contains at least one fully worked example. This is not only reinforces understanding, but also shows the student how to APPLY each formula to typical questions.

7) At the end of each chapter, there are usually 7 or more comprehensive graded exercises for PRACTICE, which cover all the ideas in the topic. If a student is not sure how to do a particular problem, all they need to do is turn back to the page number shown in order to find a very similar example. (Please, read more about these exercises in the next section.)

8) In addition, the text presentation is well spaced out, in order to make the subject matter more APPEALING and USER FRIENDLY to this age group.

As you can see this book should prove to be an invaluable teaching aid for teachers, coaches and tutorial centers, because it thoroughly summarizes the 10 major topics which are the basis of the Australian Curriculum.

It will be very beneficial to parents, because it will provide them with a structured and clear idea of the core syllabus, and what their children should know by the end of Year 5. If their child has a particular problem (say on adding fractions) it is very easy to find the page and explanations relating to that idea – and hence help their child.

Most important of all, it will prove to be an excellent reference for students of all abilitygroups. The user friendly format and layout makes it very much faster for a pupil to thoroughlymaster one major topic in a relatively short period of time, because it is so easy to see how each idea is linked to the previous one. It has all the rules and corresponding examples clearlyset out topic by topic, page by page. In addition it teaches the pupils to read explanations, as well as to look back and research similar problems. And of course the graded exercises at the end of each topic chapter will help students of all abilities to practise and apply their knowledge.It is so easy for students to work through the book by themselves with the minimum of supervision and help.

1. Brief concise explanation.

2. Rule or formula or set of steps in larger print.

3. Fully worked examples.

Each page explains only ONE simple important

idea or formula as shown on the left.

SAMPLE

xUnderstanding Year 5 Maths Advanced EditionWarwick Marlin © Five Senses Education

HOW TO USE THIS BOOK EFFECTIVELY?

As stated in the previous section, each chapter has been carefully split up into all the important ideas relating to that particular major topic. After carefully reading through and understanding a chapter, the next stage is for the student to work through some of the revision exercises given at the end. These have been carefully graded into different levels of difficulty, and most Grade 5 students should try to complete the first 3 levels. Remember that completing a level involves careful marking of your answers from the solutions given at the back of the book. If you got any questions wrong, then it is very important to find out why you got them wrong, before you move onto the next level.

Note: Most chapters have six graded exercises at the end, but longer chapters may have 7 or 8 graded exercises. The reference pages work in the following way. For example: 117, 178 in the margin means turn back to page 177 and page 178. However 173-176 means turn back to pages 173, 174, 175 and 176.

EASIER QUESTIONS

These questions given in level 1 (sometimes also in level 2) are intended to build up confidence. Most of the questions are almost identical to the examples given throughout the chapter – except with the numbers changed. If the student does have difficulty, then he/she can easily refer back to a similar example on the page number shown in the margin.

AVERAGE QUESTIONS

The questions in Level 2 and Level 3 are of average difficulty level, and will give all students (weak, average & gifted) a good opportunity to practice and consolidate the ideas and rules given throughout most of the chapter. Once again, if a student does have difficulty with a particular problem, then he/she can quickly refer back to a similar example on the page number shown. All students should try to complete and understand the questions in the first 3 levels.

HARDER QUESTIONS

The questions in this level are more difficult than the ones in level 2 and 3. The numbers involved are larger, and some of the more difficult ideas in the topic are tested. Reference page numbers have NOT been included in the margin, in order to make students who reach this level more skilful in researching through the chapter for their own information. Level 4 should be done by more capable students, or those students who have found earlier levels straightforward.

PROBLEM SOLVING

This more difficult level has been included to challenge those students who are more gifted at Maths. Usually the questions are more sentence and problem oriented, and therefore they involve more reading and comprehension skills. It is unlikely that any of the questions in this level can be done mentally, because several different ideas, rules or steps are usually required. Because ‘problem solving’ is becoming very important in examinations, I have tried to include at least 2 exercises in each chapter.

All students should try to complete at least the first

3 levels. The last 2 levels are aimed at keener and more

gifted students.

SAMPLE

2Understanding Year 5 Maths Advanced EditionWarwick Marlin © Five Senses Education

ANCIENT NUMBER SYSTEMS

Many thousands of years ago, when people first started living in communities and tribes, it became increasingly necessary and important to have a counting system. For example, shepherds had to know how many sheep, goats or cattle they were looking after. The early traders had to be able to count beads, precious stones, silks, money and other items. Different civilisations (Mayas, Greeks, Chinese, Egyptians, Babylonians, Hindus, Arabs, etc.) developed their own counting systems over the centuries. Many of these counting systems were eventually discarded in favour of more advanced systems.

For example, the early EGYPTIAN system is shown below:

1 2 3 4 5 6 7 8 9 10 20 100

| || ||| |||| ||| ||| |||| |||| ||| ∩ ∩∩

|| ||| ||| |||| |||

|||

One of the most ancient systems was developed many thousands of years ago by the MAYA civilisation who lived in central America. It was quite a clever system based on 3 symbols:a dot , a straight line — and an oval with a v inside it v .

1 2 3 4 5 6 7 8 9 10 11 12 20 etc.

v

Our number system which is in use today (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, etc.) is called HINDU-ARABIC numerals. Archaeologists and historians believe it was first developed about 2300 years ago. (300 B.C.) in India. This counting system was then taken by traders and scholars to Arabia. The Arabs invaded Spain in the eighth century, and the Hindu-Arabic system was widely used throughout Europe by 1100 A.D.

One old system which is still widely used in this day and age is the ROMAN number system. Many clocks (particularly antiques and grandfather clocks) still have Roman numerals on their faces. Also you may have seen old buildings (such as churches, town halls and courthouses) which have the year they were built written on them in large Roman numerals.SAMPLE

3Understanding Year 5 Maths Advanced Edition


ROMAN NUMERALS

When the Roman empire became powerful, its number system spread to many other countries. The system used a subtraction and addition idea. When a smaller unit appears before a larger one, it is subtracted from the larger one. When a smaller unit appears after the larger unit, it is added to the larger unit. Therefore the position of the symbols is important.

IV means 5 – 1 = 4 whereas VI means 5 + 1 = 6 XL means 50 – 10 = 40 whereas LX means 50 + 10 = 60

1 2 3 4 5 6 7 8 9I II III IV V VI VII VIII IX

10 20 30 40 50 60 70 80 90X XX XXX XL L LX LXX LXXX XC

100 200 300 400 500 600 700 800 900C CC CCC CD D DC DCC DCCC CM

1 000 = M

Example 1: Change the Roman numerals into our own numerals: (a) XI (b) XXIV (c) LXXIII (d) DCLXIV

Solutions: (a) X + I (b) X + X + IV (c) L + X +X + III (d) D + C + L + X + IV = 10 + 1 = 10 + 10 + 4 = 50 + 10 + 10 + 3 = 500 +100 + 50 + 10 + 4 = 11 = 24 = 73 = 664

Example 2: Change these Hindu-Arabic numerals into Roman numerals: (a) 8 (b) 46 (c) 214 (d) 594

Solutions: (a) 5 + 3 (b) 40 + 6 (c) 200 + 10 + 4 (d) 500 + 90 + 4 = V + III = XL + VI = CC + X + IV = D + XC + IV = VIII = XLVI = CCXIV = DXCIV

You will often get questions in tests which ask you to change from Roman to Hindu-Arabic, and vice versa.

SAMPLE


THE HINDU-ARABIC NUMBER SYSTEM

The number system that we use today is called the Hindu-Arabic number system because it was first developed in India and Arabia over 1 000 years ago. This system uses the 10 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and it is based on multiples of 10 with zero as a ‘place holder’.

Example: Find the place value of 8 in each of the following:

a) 3 718 b) 3 781 c) 3 871 d) 8 371

Solutions: a) The place value of 8 is 8 × 1 = 8 b) The place value of 8 is 8 × 10 = 80 c) The place value of 8 is 8 × 100 = 800 d) The place value of 8 is 8 × 1 000 = 8 000

Important note:

Example: Write fifty-seven thousand, six hundred and eighty-two

a) using a comma b) using a space

Solutions: a) 57,682 b) 57 682

The Hindu-Arabic number system uses a place value system.Each place value is 10 times greater than the place value directly to its right.The value of any digit in a number depends on which position (or place) it sits in that number.

The value of 8 depends on its place in the

number.

Some teachers and some Maths text books will place a ‘comma’ to separate every 3 digits in a larger whole number.Other teachers and texts will use a ‘space’ to separate every 3 digits in a larger whole number.Both methods are correct and you should use the method explained to you by your teacher.

In this book we will be using a ‘SPACE’ as a

separator.

SAMPLE



PLACE VALUE

Since this chapter deals with WHOLE NUMBERS, the first important idea is to understand the value of each of the different columns. Our number system today is based on the Hindu-Arabic system where the VALUE of a number is determined by its PLACE in a particular column.For example, what does 3 520 697 really mean?

The place value of 9 is 90 or ninety. The place value of 2 is 20 000 or twenty thousand. The place value of 6 is 600 or six hundred.

There are 3 ways or notations of describing a whole number:1. AS AN ORDINARY NUMERAL: 3 520 697

2. IN WORDS: Three million, five hundred and twenty thousand, six hundred and ninety-seven.

3. IN EXPANDED NOTATION: (3 × 1 000 000) + (5 × 100 000) + (2 × 10 000) + (0 × 1 000) + ( 6 × 100) + (9 × 10) + (7 × 1)

Example:

a) b) c)

For each abacus above, write the numeral. Also write the numeral in words and in expanded notation.

Solutions: a) Numeral = 3 524 In words: Three thousand, five hundred and twenty-four In expanded notation: (3 × 1 000) + (5 × 100) + (2 × 10) + (4 × 1) b) Numeral = 5 143 In words: Five thousand one hundred and forty-three In expanded notation: (5 × 1 000) + (1 × 100) + (4 × 10) + (3 × 1)

c) Numeral = 4 072 In words: Four thousand and seventy-two In expanded notation: (4 × 1 000) + (0 × 100) + (7 × 10) + (2 × 1)

You must be able to change from one notation to another.

It can be seen that each column has a different

PLACE VALUE.

100

000

10 0

001

000

100

10 1milli

ons

hund

red th

ousan

ds

ten th

ousan

ds

thousa

nds

hund

reds

tens

ones

or un

its

1 00

0 00

0

3 5 2 0 6 9 7

Th H T U Th H T U Th H T USAMPLE

LEVEL 1 — NUMBER AND PLACE VALUE

Q1. Write the following using Hindu-Arabic numerals (our present number system): 3 a) XVII b) XXIV c) LXIII d) CCXXX

Q2. Write the following using Roman numerals: 3 a) 9 b) 27 c) 74 d) 93

Q3. Write the following numbers in words: 5, 6 a) 379 b) 4 065 c) 4 605 d) 15 032

Q4. Write the following as ordinary numerals: 4-6 a) Four hundred and seventy-nine b) Three thousand and twelve

Q5. Write the following as ordinary numerals: 4-6 a) (6 × 1 000) + (8 × 100) + (5 × 1) b) (4 × 1 000) + (7 × 10) + (3 × 1)

Q6. Write the following in expanded notation: 4-6 a) 561 b) 7 348 c) 9 067 d) 15 406

Q7. For each abacus below, write: 5 (i) the numeral (ii) the numeral in words a) b) c)

Q8. What is the place value of 3 in the following numbers: 4, 5 a) 432 b) 7 307 c) 31 408 d) 83 625

Q9. Write the following numbers in descending order: 5, 6 a) 9 514, 9 415, 9 145, 9 451, 9 154 b) 7 603, 7 306, 7 630, 7 360, 7 036

Q10. List all the factors of the following: 7 a) 10 b) 12 c) 30 d) 13

Q11. Some of the listing you did in Q10. should help you to find the highest common 10 factor (HCF) of the following pairs of numbers: a) 10 and 12 b) 12 and 30 c) 10 and 30 d) 12 and 18

Q12. Find the six multiples of the following numbers: 9 a) 4 b) 6 c) 8 d) 20

Q13. Some of the listing you did in Q12. should help you to find the lowest common 11 multiple (LCM) of the following pairs of numbers: a) 4 and 6 b) 6 and 8 c) 8 and 20 d) 6 and 20

Q14. List the prime numbers between 20 and 40. 8

H T U H T UTh H T U

This parachute is descending

PageNote: Only turn back to page number shown if you have difficulty.



EASIER QUESTIONS

SAMPLE

Tth Th H T U Tth Th H T U Tth Th H T U

PageNote: Only turn back to page number shown if you have difficulty.



LEVEL 3 — NUMBER AND PLACE VALUE

Q1. Write the following using Hindu-Arabic numerals ( our present number system): 3 a) LIX b) LXXXII c) DCCXIV d) MDCCCXLIII

Q2. Write the following using Roman numerals: 3 a) 34 b) 327 c) 736 d) 1 548

Q3. For each abacus below, write the numeral, and also the numeral in words: 5 a) b) c)

Q4. Write the following as ordinary numerals: 5, 6 a) Six hundred and twenty-five thousand, four hundred and eighty-two b) Four million and thirty-eight thousand, six hundred and seven

Q5. Write the following in words: 5, 6 a) 37 504 b) 602 891 c) 5 048 329 d) 46 308 076

Q6. Write the following in numbers in ascending order: 5 a) 853 629, 863 529, 835 629, 856 329, 836 529, 865 329 b) 1 792 436, 1 297 436, 1 972 436, 1 729 436, 1 927 436, 1 279 436

Q7. Find the value for each underlined digit below: 4, 5 a) 17 682 b) 29 407 c) 651 348 d) 972 462

Q8. a) Write down all the factors of 30. b) Write down all the factors of 45. 7, 10 c) What is the highest common factor (HCF) to both numbers?

Q9. a) List the first 6 multiples of 12. b) List the first 6 multiples of 15. 9, 11 c) What is the lowest common multiple (LCM) to both numbers?

Q10. Round off the following numbers to the nearest 1 000: 12 a) 8 431 b) 7 501 c) 63 490 d) 4 500

Q11. Firstly round off the following numbers to the nearest hundred, and then estimate 12, 13 the final answers: a) 971 + 843 b) 719 – 482 c) 7 380 – 2 069 d) 6 951 – 3 749

Q12. Firstly round off the following numbers to the nearest ten, and then estimate 12, 13 the final answers: a) 497 ÷ 13 b) 603 × 18 c) 304 ÷ 23 d) 486 × 23

Q13. Find the average of the following sets of numbers: 23 a) 17, 31 b) 18, 23, 49 c) 16, 18, 23, 47 d) 17, 22, 4, 60, 67

Q14. After 6 cricket matches Rakesh has a batting average of 21 runs per match. 23 He wants to end the season with a batting average of 25 runs per match. How many runs will he have to score in the final 7th match to achieve his goal?

AVERAGE QUESTIONS

SAMPLE



LEVEL 5 — NUMBER AND PLACE VALUE HARDER QUESTIONS

Q1. Write in words: a) 2 473 907 b) 97 003 002 c) 817 653 d) 4 703 046

Q2. Round off the following numbers to the nearest thousand: a) 72 506 b) 676 403 c) 3 408 500 d) 6 547 498

Q3. Find the value of the underlined digit in the numbers below: a) 74 389 b) 6 582 391 c) 67 109 d) 5 487 392

Q4. Find the HCF of the following pairs of number: a) 45 and 60 b) 28 and 42 c) 144 and 240 d) 102 and 136

Q5. Find the LCM of the following pairs of numbers: a) 6 and 15 b) 25 and 40 c) 24 and 30 d) 12 and 18

Q6. In the school library, there were 7 326 books in Room A, 4 561 books in Room B and 6 497 books in Room C.

a) Round off each of the above quantities to the nearest thousand, and then ESTIMATE the total number of books altogether. b) Now find the exact total of the books in the 3 rooms. c) What is the average number of books in each room? d) The school has a goal to reach a total of 25 000 books in the library. How many more books do they still need?

Q7. Find the product of the following numbers: a) 327 × 51 b) 857 × 62 c) 1 593 × 34 d) 11 927 × 43

Q8. Find the following quotients: a) 1 527 ÷ 15 b) 1 234 ÷ 13 c) 3 631 ÷ 17 d) 7 421 ÷ 9

Q9. a) What is the difference between 125 and the product of 12 and 9? b) Increase the quotient of 30 and 6 by the difference between 19 and 12. c) Decrease the product of 12 and 3 by the square of 5. d) Decrease the sum of 12 and 92 by 43.

Q10. My cricket batting average is 24 runs for 5 matches. If I score 126 runs in my 6th match, what is my new batting average?

Q11. Find a) 24 ‒ 3 ÷ 3 + 2 b) 24 ‒ 12 ÷ 3 ‒ 2 c) 12 ÷ 4 + 9 ÷ 3 d) (24 ‒ 12) ÷ 3 – 2 e) 5 + 4 ÷ 2 × 3 ‒ 2

Q12. Zhang Wei has 3 shirts, 2 belts and 4 ties. How many different groupings of a shirt, a belt and a tie can he wear?

Q13. 27 small cubes have been glued together to make one larger cube as shown on the left. This large cube is then painted blue all over. How many of the small cubes will have:

a) 3 sides painted b) 2 sides painted c) 1 side painted d) no sides painted.SAMPLE


LEVEL 6 — NUMBER AND PLACE VALUE PROBLEM SOLVING

Q1. Seo-jun used her cell phone 5 287 times last year. Each call costs 8 cents. By rounding off 5 287 to the nearest 1 000, and rounding off 8 cents to the nearest 10, ESTIMATE how much Seo-jun spent on calls last year.

Q2. Mount Everest, the highest mountain in the world, has a height of 8 850 m. The climbing team managed to climb 2 739 m on the first day, and 1 946 m on the second day. How much further did they have to climb?

Q3. Mr. & Mrs. Drapel took their 4 children to the movies. They spent a total of $70.00 for the 6 tickets. If the children were charged at one third of the adult price, what was the cost of each adult ticket?

Q4. Jinhi bought 3 hamburgers and 4 cokes for $17.50. The following day her friend Trinh bought 4 hamburgers and 2 cokes for $19.50. How much is the cost of each item?

Q5. Josh and Jess took part in a multiple choice mathematics competition. Altogether there were 50 questions in the test. Each correct answer would be given 7 marks, but for each incorrect answer a 4 mark penalty would be deducted. The total score for both together was 348. If Jess made 4 extra mistakes compared to Josh, how many did Jess get correct?

Q6. A one-way train ticket costs $18.00. A return ticket costs $32.50. The total cash collected from the sale of 50 tickets was $1 219. How many return tickets were sold?

Q7. By using quick method, find the sum of the first fifty even numbers. 2 + 4 + 6 + 8 + 10 + .......... + 96 + 98 + 100

Q8. Write the 7th smallest number using all the digits 5, 6, 7 and 8. No number may be repeated.

Q9. I think of a certain number larger than 20, and when I divide it by 7 I get a remainder of 6. And when I divide the number by 8 I get a remainder of 7. What is the number?

Q10. I think of a number and multiply it by 8, and then subtract 15 to give me a total of 89. What is the number I first thought of?

Q11. James is 4 years older than his younger sister Jenny. Four times James’s age plus three times Jenny’s age is equal to 107. What are the ages of James and Jenny?

Q12. A group of bush walkers went on a 14 day hike up into the mountains. On a good sunny day they could walk 22 km in one day, but on a rainy day they could only manage 17 km. If they walked 283 km during the 2 weeks, how many days were fine and sunny.

Q13. Rebecca had a pair of rabbits which had 6 baby rabbits, 4 female and 2 male. By the following summer, every female rabbit had given birth to 3 new baby rabbits. Providing that no rabbits died, how many rabbits does Rebecca have in total?

Q14. I am a five digit number less than 30 000 and all my digits are different odd numbers. The digit in the ten thousand column is 4 less than the digit in the thousands column. If the digit in the units column is one third of the digit in the hundreds column, what number am I?

SAMPLE


LEVEL 1 – Number and Place Value

Q1. a) 17 b) 24 c) 63 d) 230 Q2. a) IX b) XXVII c) LXXIV d) LXLIII Q3. a) Three hundred and ninety-seven b) Four thousand and sixty-five c) Four thousand, six hundred and five d) Fifteen thousand and thirty-two Q4. a) 479 b) 3 012 Q5. a) 6 805 b) 4 073 Q6. a) (5 × 100) + (6 × 10) + (5 × 1) b) (7 × 1 000) + (3 × 100) + (4 × 10) + (8 × 1) c) (9 × 1 000) + (6 × 10) + (7 × 1) d) (1 × 10 000) + (5 × 1 000) + (4 × 100) + (6 × 1) Note: If there is a zero in the place, then the number doesn’t have to be written. (9 × 1 000) + (0 × 100) + (6 × 10) + (7 × 1) OR (9 × 1 000) + (6 × 10) + (7 × 1) are both correct. Q7. a) 537 b) 6 302 c) 705 Q8. a) 30 b) 300 c) 30 000 d) 3 000 Q9. a) 9 514, 9 451, 9 415, 9 154, 9 145 b) 7 630, 7603, 7 360, 7 306, 7 036 Q10. a) {1, 2, 5, 10} b) {1, 2, 3, 4, 6, 12} c) {1, 2, 3, 5, 6, 10, 15, 30} d) {1, 13} Q11. a) HCF = 2 b) HCF = 6 c) HCF = 10 d) HCF = 6 Q12. a) {4, 8, 12, 16, 20, 24} b) {6, 12, 18, 24, 30, 36} c) {8, 16, 24, 32, 40, 48} d) {20, 40, 60, 80, 100, 120} Q13. a) LCM = 12 b) LCM = 24 c) LCM = 40 d) LCM = 60 Q14. {23, 29, 31, 37}


Q1. a) 90 b) 50 c) 300 d) 350 Q2. a) 700 + 900 = 1 600 b) 4 800 – 3 300 = 1 500 c) 80 × 10 = 800 d) 90 ÷ 10 = 9 Q3. a) 681 b) 818 c) 5 832 d) 8 060 Q4. a) 514 b) 449 c) 1 935 d) 2 906 Q5. a) 388 b) 445 c) 2 178 d) 3 983 Q6. a) 980 b) 4 900 Q7. a) 13 b) 19 c) 15 rem 1 d) 4 rem 4 Q8. a) 22 b) 20 c) 14 d) 4 Q9. a) 63 b) 18 c) 6 d) 49 e) 21 f) 6 Q10. a) 6 145, 6 154, 6 415, 6 451, 6 514, 6 541 b) 8 357, 8 375, 8 537, 8 573, 8 735, 8 753 Q11. a) 9 000 b) 600 c) 30 d) 20 000 Q12. a) 9 = 8 b) 17 < 6 + 9 c) 27 > 8 × 3 d) \x = 7 e) 10 ÷ 5 < 2 f) \72 = 49


Q1. a) 59 b) 82 c) 714 d) 1 843 Q2. a) XXXIV b) CCCXXVII c) DCCXXXVI d) MDXLVIII Q3. a) 24 371 Twenty-four thousand, three hundred and seventy-one b) 28 053 Twenty-eight thousand and fifty-three c) 72 530 Seventy-two thousand, five hundred and thirty Q4. a) 625 482 b) 4 038 607 Q5. a) Thirty seven thousand, five hundred and four b) Six hundred and two thousand, eight hundred and ninety-one c) Five million, forty-eight thousand, three hundred and twenty-nine d) Forty-six million, three hundred and eight thousand and seventy-six Q6. a) 835 629, 836 529, 853 629, 856 329, 863 529, 865 329 b) 1 279 436, 1 297 436, 1 729 436, 1 792 436, 1 927 436, 1 972 436 Q7. a) 7 000 b) 20 000 c) 300 d) 900 000

SAMPLE

Documents

M A T H S · 2020. 6. 10. · 1. Brief concise explanation. 2. Rule or formula or set of steps in larger print. 3. Fully worked ... least 2 exercises in each chapter. All students