math grade 5 teaching guide

CountdownLEVEL FIVE MATHS

Teachers Guide and Answer Key

L.W. DownesAsima Ali

1

New Edition

1Great Clarendon Street, Oxford OX2 6DP

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This New Edition published in 2003

ISBN-13: 978-0-19-579978-1ISBN-10: 0-19-579978-X

Second Impression 2006

Printed in Pakistan atIbn-e-Hasan Offset Printing Press, Karachi.

Published byAmeena Saiyid, Oxford University Press

No. 38, Sector 15, Korangi Industrial Area,P.O. Box 8214, Karachi-74900, Pakistan.

SOME IMPORTANT GENERAL NOTESTO TEACHERS OF BOOK 5

1. Much of the work in Book 5 uses the same basic mathematicalconcepts as in earlier books. But these concepts are extendedto greater numbers and more involved calculations. It is, therefore,vital that teachers look carefully at the earlier books (3 and 4,perhaps borrowed from the colleagues) to see how the varioustopics and ideas progress from stage to stage.

2. Getting Ready and the various Reviews in the Book willdemonstrate the truth of what is said in 1 above. Careful analysisof errors occurring and some basic reteaching at this stage willprevent many error occuring and some basic reteaching at thisstage will prevent many errors occuring later.

3. It is imperative that, before asking children to do any work on aparticular page or topic, the teacher himself (or herself) mustwork through all the examples and word problems. In this way hecan anticipate difficulties and satisfy himself (or herself) that allthe material is understandable by the children. That is goodteaching!

4. If the teacher himself (or herself) finds difficulty in understanding,he should consult again these teachers notes for a particularpage (and also the authors notes at the beginning of the childrensbooks). It is also useful to discuss difficulties with mathematicalcolleagues.

5. Book 5 is not a workbook. Most of the work will be done in exercisebooks. These should not be scrap books. The exercise shouldbe carefully set out so that the processes can easily be seen(and marked!). Such careful setting out leads to betterunderstanding.

6. At certain stages (see later in these notes) there will be a needfor squared paper and graph paper. If these are loose theyshould be pinned or pasted into the exercise books for laterreference.

1

7. Much greater use of the blackboard by the teacher will benecessary to demonstrate new ideas and to give childrenconfidence that they are getting their work right and makingprogress.

Pages 1 to 3. Getting Ready. These pages cover all the conceptsmet in Books 3 and 4. But remember that much of this will, for thetime being, have been forgotten. The children will need to bereminded of what they have previously worked on. The topicscovered in these pages include: place value, addition, subtraction,long multiplication, long division, H.C.F., L.C.M., fractions,decimals, divisibility, angles, perimeter, shapes, time, area, money,and length.

A careful analysis will be required to see what reteaching is necessary.You may find that it will take a considerable part of the first few weeksof the first term.

If there are any items on pages 1 to 3 where a majority of the childrenare failing, it would be wise to take examples from the pages andwork them out on the blackboard for the whole class, for example,they might need to be reminded of lacs; of quick division by 10 and100; of the rules of divisibility, etc. They will also need protractorsand set-squares.

Pages 4 to 6. Help the children to distinguish between block graphsand line graphs. Block graphs (sometimes called column graphs orbar graphs) provide information which is quickly and easily understoodby immediate observation, for example, the attendance in the classeach separate day of the school week; the heights of a group ofindividual children measured separately on the same day; favouritefoods of a class. The information is always separate and discrete.

Line graphs, on the other hand, give information which is changingfrom time to time or from a quantity of articles to another quantity.Sometimes the line graph will indicate that the amount of growth isdifferent from one day to another (as in the illustration of the growth ofa plant on page 4). Other line graphs show straight growth, for example,if the cost of one article is Rs 3 then 2 artciles will cost Rs 6 and 3articles Rs 9 and so on.

2

Make sure:

(a) That the children have suitable graph paper.

(b) That they label their graphs with a title and that each dimension(horizontal and vertical) is clearly indicated (e.g. time againstdistance travelled). Without these labels the graph has nomeaning.

It is helpful if the children themselves can make up long-termgraphs which they can consult and discuss from time to time, forexample, the growth of a plant in the classroom; the temperatureover a period of a day or a week. They should also realize that ona line graph they are able to interpolate information which is notnecessarily on the graph itself. For example, if the temperature at9 oclock is 20 and at 10 oclock is 28, it can be assumed that at9.30 it was probably 24.

Pages 7 to 15. Revise the idea of place-value which the childrenhave dealt with over several years. Look at local and nationalnewspapers which use the lac to indicate numbers higher than tenthousand (i.e., 100,000). Discuss the relationship between thePakistani system and that used in the international situation (Forexample the need to use millions, etc., in industry and bankingand exports when dealing with the outside world which may notunderstand lacs). The important thing for them to remember isthat 10 lac = 1 million. The same thinking and discussion shouldapply when introducing the crore which is equivalent to 10 million.Give time for the slower children to work out the numbers. It isalmost impossible to visualize a lac, a crore, or a million. Perhapsthey may have seen a crowd on television numbering manythousands but beyond that the number becomes very difficult tocomprehend. You can get near to it by building up a diagram withthe class. Use mm graph paper and a very large sheet of paper onwhich to stick the strips which the children have made. (Use thefloor to display the whole million of cm squares).

3

10,000 10,000 10,000 10,000 10,000 10,000 10,000 10,000 10,000

A stripof

100,000squares

< 100 cm >< 1

00 cm

>

One millioncm squares

This may be the only time they will ever see a million of anything andit will be memorable.

Pages 16 to 18. Addition and subtraction by big numbers. Somechildren (and teachers) may enquire why it is necessary to calculatesuch big numbers. This will particularly occur with those who haveseen or used the digital electronic calculators and computers whichare now very common. Discuss this with the class and emphasizethat these inventions depend on place-value. Furthermore, an abilityto calculate in the usual way prevents them making silly mistakeswhich might occur if they press the wrong button, e.g. if they seethey are adding two numbers both of which are in millions, the totalshould also be in millions. In other words they are getting sensibleanswers.

It should also be pointed out that such calculations, if carried outaccurately and carefully and without boredom, will provide the childrenwith a mental discipline which will be valuable in their future learning.

4

The work in addition and subtraction becomes easier if the columnsof figures are accurately set out. To avoid errors, provide the childrenwith squared paper.

Pages 19 to 22. Rounding off. This is a technique which all of usshould have, i.e. the ability to make an intelligent guess (i.e anapproximate answer) when we do not need exact measurement. Thisapplies to numbers, time and all the measures.

To introduce the idea, draw on the blackboard a series of straightlines, e.g. of an approximate length, about 50 cm, 92 cm, 28 cm,45 cm. Ask the children to make an intelligent guess at the lengths.Then bring out children to make a more accurate measurement. Thecorrect measurements were:

1. 51.3 cm. This is rounded down to 51 cm.2. 92.8 cm. This is rounded up to 93 cm.3. 28.6 cm. This is rounded up to 29 cm.4. 45.4 cm. This is rounded down to 45 cm.5. 27.5 cm. This is half-way between 27 cm and 28 cm. It is usual

to round this up to 28 cm.

Let the children do the same with a series of lines on paper withoutmeasurement. They then write an estimate for each. Then theymeasure carefully and write a measurement which is rounded downor rounded up. They do the same by estimating books, desks, etc.,and writing rounded measurements for each to the nearestcentimetre. For example, Countdown Book 5 has an approximatemeasurement of 18 cm by 24 cm.

Discuss the many examples on pages 19 to 22 and gradually bringthe class to understand the rounding off of bigger numbers. Put onthe blackboard the number 28764 which is taken from a newspaperto indicate the attendance at a football match:

28760 to the nearest ten

28800 to the nearest hundred28764

29000 to the nearest thousand

30000 to the nearest ten-thousand

5

Pages 23 to 26. Quickly, on the blackboard, go through the variousstages in multiplication to remind them of the method. Follow theexample on page 23 of the pupils book.

It is always helpful to put the place-value headings on each columnand to use squared paper to emphasize accuracy.

Do the same to remind them of the techniques in division using place-value headings, for example,

Th H T U9 3 5

9 8 4 2 18 1

3 22 7

5 14 5

6

)8421 9 = 935 rem. 6

Follow the stages of division outlined on page 24. Make sure thatguesses are sensible. Each guess must be tried out on a squaredpiece of paper. The difficulties increase when the first guess is wrongas is shown in the example on page 25. Here the try-out may bedone two or three times. Give help with the reading and understandingof the word problems on page 26.

Page 27. When this page is completed make an analysis of errorsso that reteaching can be done on particular topics.

Pages 28 to 33. The first two pages show what to do when + x come together and if there are no brackets. The children learn therule D.M.A.S. Do several examples on the blackboard so that theylearn the rule.

The next pages deal with brackets which help to simplify the example.Go through the various types of brackets so that the children knowin which order to take them.

6

Pages 34 to 37. Most of the work on these pages is self-explanatory. Provide plenty of cm. squared paper and wherenecessary let them cut up composite shapes so as to understandtheir area. Get the children also into the habit of making roughdrawings and labelling them with their measurements. This willprevent silly mistakes. Note also that the triangles on these pagesare right-angled triangles.

Pages 38 and 39. Read the Teachers Notes on the second page ofthe Introduction to Book 5 about areas of parallelograms. Check thatall the children understand what is meant by the height. They shouldalways draw a line (or dotted line) to show this. They should not multiplythe slant height by the length (the formula should really be l x h notl x b). This idea can then be used to find the area of any triangle bysplitting it into 2 right-angled triangles.

Pages 40 to 45. Emphasize that volume of an object is not onlyconcerned with cuboids but is the amount of space occupied by anobject or the amount of space contained by an object (e.g. arefrigerator, an empty box, etc.). When dealing with cuboids givepractical experience, showing how it is built first in strips of cubes,then layers. This then leads to the formula V = (l x b) x h.

On page 43 go carefully on the blackboard, through the method offinding the measurements of a cuboid, once the volume and one ofthe lengths or heights is known. Check the results of Exercise C tosee whether the idea and method is understood.

In front of the class demonstrate the making of a 1000 cm cubewith cardboard and tape. (Grease the edges). Pour in a litre of waterand learn that 1000 cubic cm = 1 litre = 1000 millilitres.

As an extra, it is interesting that by using the idea of capacityand the notion of displacement they can find the volume of anirregular object (For example, a stone). Put a known quantityof water in a measuring vessel and notice the level. Then put inthe stone and notice that the level is higher. The differencebetween the 2 levels gives the volume of water displaced, whichis also the volume of the stone.

7

30 ml 20 ml = 10 ml. Volume of stone is 10 cm3

20 ml

30 ml

Page 46. As before, when the page is completed make an analysisof errors so that reteaching on various topics can be given.

Pages 47 to 57. Before the class starts on this work, give a quickblackboard review of multiples, factors, H.C.F., L.C.M., prime numbersand prime factors (and co-prime numbers). Since this is not aworkbook, the children should be given copies of (or they shoulddraw) the crossword on page 47.

Though much of the work on these pages may be regarded as magic,it is useful for the children (particularly the bright ones) to see thelogic and sense behind the methods. Use notebooks for all theexercises on Review Page 58.

Pages 59 to 61. The work here is a review of the work done onfractions in Book 3 and 4. Check from the blackboard that they knowwhat is meant by numerator, denominator, common denominator,lowest terms, mixed numbers and improper fractions. Equivalentfractions can be found by multiplying or dividing both the numeratorand the denominator by the same number:

8

e.g. = = =

Give many examples on the blackboard and question the childrenon them.

Page 61. Multiplying a fraction by a whole number. Some childrenmay be puzzled by the reversals in Exercise A where the wholenumber comes first. Point out that this is exactly the same when3 x 4 = 4 x 3 which they know well. Language used is important.Encourage them to say and think, for example, 3 lots of

2 fifths 3 x 25

!"

#$

.

Pages 62 to 64. It is important for the children to have notebooksready so that they can draw diagrams and be able to visualizethe fractions involved, for example, three-quarters of three-fifths

34

x 35

!"

#$ . This is done before the actual multiplication

3 x 34 x 5

920

=!"

#$ .

Show many examples of drawings on the blackboard.

Pages 65 & 66. Again remind the children that, as for the equivalenceof fractions, they must divide both top and bottom of a fraction by thesame number to reduce it to its lowest terms. They also have toremember when using brackets, that the order of the numbers(fractions) does not alter the answer. Remind them of (2 x 3) x 4 = (3x 2) x 4 = 4 x (3 x 2) etc. This, of course, is only true of addition andmultiplication.

Pages 67 to 70. The idea of cancelling can be misunderstoodand dangerous to getting a correct answer, unless the childrensee that what they are doing is again the same as before withequivalence, i.e. dividing the top and bottom by the same number,for example,

= and later

56

10 212 2

40 448 4

4 x 57 x 5

2035

(22 2) x (15 5)(5 5) x (4 2)

22 x 155 x 5

11 3

1 1

22 x (15 5)(5 5) x 4

9

They have effectively divided the numerator and the denominatorby 5 and then by 2 (altogether division by 10). Cancelling is aconvenient way of showing this. If this is understood it will preventridiculous errors in later mathematics, for example,

Pages 71 to 81. The stages set out in the text of Book 5 are verycarefully arranged. Follow the argument and directions at each stagewith the accompanying exercises. Use the proper words as shown,e.g. How many thirds in one whole? How many sevenths in 3 wholes,etc. The table at the top of page 72 should be copied into theirnotebooks. When it is completed, the class should be asked, Whatdo you notice?

2 How many ninths in 2 wholes? 2 x 18

3 How many sevenths in 3 wholes? 3 x 21

5 How many eighths in 5 wholes? 5 x 40

191718

917181

etc.Then:

2 How many two-ninths in 2 wholes? 2 x 9

3 How many six-sevenths in 3 wholes? 3 x = 3

10 How many five-eighths in 10 wholes? 10 x 16

1296758

927685

2

2

2

a + b c 1=c x b + a 2

1 1 1

1 1 1

They should notice from the table that the denominator in the divisoris now a numerator and multiplication takes place. They learn therule To divide by a fraction you turn the divisor upside down andmultiply. The danger here is that some children will not understandwhat is happening and later (For example on page 75 will not knowwhich fraction to invert. It must be the divisor.

72

12

10

This leads to the idea and discussion of reciprocals which should bethoroughly understood. A problem of understanding may occur onpage 76 when they are asked How many twos make a quarter?This at first does not make sense, but if put differently it does, forexample, Divide 6 by 12 is the same as saying What is a half of14 . The answer is one eighth.

14

x 12

= 18

. The use of reciprocal

and multiplication solves the division.

The simplification of the more complicated fraction examples on page81 can be dealt with using the D.M.A.S. rule and the various types ofbrackets, as shown earlier.

Pages 82 to 96. Page 82 requires that the class be givensquared paper and the use of their notebooks to show fractionsand their decimal equivalents and to complete the table and thecrossword.

Before going further, it is worthwhile to review once more the idea ofplace-value on the blackboard and give particular attention to thosenumbers which are less then a unit. Put this on the blackboard:

Then bring out various children in turn to the blackboard and askthem to put in various numbers which you call out, e.g., four hundredand twelve and 3 tenths; twenty and 6 hundredths; one thousandand one and one thousandth, etc.

This will reinforce the work on pages 83 and 84. Where necessary,get the children to put in place-value headings. They will also seethe value of using unlike and like decimals, though these termsshould be dropped when their place-value work is efficient.

Th H T U t h th tth

4 1 2 3 etc.

2 0 0 6

11

Pages 85 to 99. These pages link decimal fractions with the ordinaryfractions: tenths, hundredths, thousandths. This is to promote theunderstanding of what decimals are. When multiplying or dividingdecimals by a whole number it is exactly as they have done before.But they must always remember to leave the decimal point in thecorrect place. In the example x 28 the multiplication by 20means that the 2 hundredths become 4 tenths (putting a zero in thetenths place) and the 6 tenths becomes 1 ten and 2 units, etc. Thisprocedure is no different from long multiplication.

When the children have worked through the example on page 88they will see that they have multiplied tenths by tenths givinghundredths (in fractional form). The answer should therefore show 2decimal places.

So that there is no possible misinformation, you must emphasizethat the squares pictured here are not cm squares. They are onlyfor illustration, to make the working clear.

The following pages use the idea of equivalence of fractions. Theywill remember that in a fraction you can multiply or divide the top andbottom by the same number without changing the value of the fraction,

for example, 2 x 43 x 4

812

and 8 412 4

23

=

= . Similarly they can think of

0.12 0.6 as a fraction, for example, 0.120.6

. Multiply both numerator

and denominator by 10 so as to make the denominator into a whole

number. You then get 0.12 x 100.6 x 10

= 1.20

6 = 0.2.

Changing fractions into decimals by division is a necessarypreliminary to the work on later pages. What happens, of course, isthat the dividend is set out in decimal form and division takes placein the usual way. When the divisor is a decimal, it is changed to awhole number (For example, 1.04 0.2 becomes 10.4 2) as at thetop of page.

HTU th174.62

12

Pages 100 to 102. Go through the work on page 100 on theblackboard, asking the class questions at each point. Remind themof the idea of rounding off (see pages 19-22) and estimating (sensibleguessing).

On page 101 emphasize again that the cm rulers are illustrations(they are seen as under a magnifying glass). They are not realcentimetres.

Pages 103 to 110. Since this is not a workbook the children willneed to be given squared paper to deal with page 103 and to giveanswers in their notebooks.

The notion of percentage is very easy to understand when thechildren realize that they are changing their fractions into hundredths(by equivalence). These hundredths have the special name of

percentage. The fraction 23

is saying we have 2 in every 3. The

fraction 7

100 is saying we have 7 in every 100. Another way of

expressing this is we have 7 per cent. To change any fraction to apercentage, we merely multiply the numerator by 100 and divide by

the denominator, e.g. 34

% 3 x 100

4 % 75%. In the case of fraction

where 100 is not a multiple of the denominator (e.g. 3, 7, 9, 11, 13,etc.) then the division must go on to give an answer in decimals whichwill be rounded off to the required number of decimal places, forexample,

So 23 = 66.67%.

25

1

Th H T U2 9 3

x 1 72 0 5 1 = 7 times 2932 9 3 0 = 10 times 2934 9 8 1 = 17 times 293

H T U1 4 7x 68 8 2

4

13

On page 104, in finding a percentage of a quantity, the children willrealize that they have the simple task of treating the percentage as afraction with the denominator as a 100. Thus 70% of 90 is

70100

x 90 = 63 which they have learned to do many times before.

Pages 111 to 113. When thinking about averages, the children mayalready have read in the newspapers, or met on television and radio,the scores of various cricketers in test matches. They will see thatsome have a batting average over several games. Bowlers showaverages in a game indicating and any other sporting events.

Discuss also the fact that sometimes a simple average does notmake much sense. For example, if a factory employs 10 work peoplewho get Rs 1000 each and 2 managers who get Rs 10,000 each, wecould say that the average wage is Rs 2500. (Rs 10,000 + Rs 20,000) 12 = Rs 2500. That would not be of much use in negotiationsabout wages.

Similarly if you were trying to find the average length of 5 lines,and you had lengths of 7 cm, 8 cm, but the last line was 22 cm,then the average is 10 cm, which does not tell us much aboutthe lines.

The children, of course, who go on to study mathematics includingstatistics at a later level, will learn about measures of centraltendency and that there are various kinds of averages (mean,mode, etc.).

Pages 114 to 118. On page 114 discuss the idea of profit and loss,first by not mentioning percentages. Thus if they buy something forRs 10 and sell it for Rs 12, they make a profit of Rs 2. If they sell it forRs 8, they make a loss of Rs 2. Percentage profit or loss becomesimportant when a businessman wants to find out whether oneparticular item is more profitable than another (in which case heperhaps will want to stock more of the more profitable one). Thisdiscussion should lead to the idea of cost price (C.P.) and sellingprice (S.P.).

7 9

10 1

14

On page 117 discuss with the class the idea of lending and borrowing,perhaps playing a borrow-lend game at the front of the class. Oneboy has a sum of imitation money. Another comes to the front andasks to borrow, for example Rs 100. The first boy agrees but asksWhen will you pay me back? It is agreed that the money will be paid1 year later but the amount paid back will be Rs 105 (i.e. Rs 5 morethan was borrowed). Put on the blackboard.

Interest Rs 5 on Rs 100

Rate of Interest 5100

% 5% for one year.

Ask How much should he pay back if he borrows for 2 years? Yes,Rs 5 x 2 = Rs 10. Do this several times with other children and usingdifferent amounts and different rates of interest for different amountsof time.

Now go back to discussion and reading of pages 116 & 117 wherethe children learn the vocabulary of banking and money lending,e.g. bank account, deposit, loan, withdrawal, interest, principal,percentage interest, amount (total after time x interest is added tothe original principal).

Ask Why do you think that the interest a bank charges on a loan isgreater than the interest it gives to someone depositing money inthe bank?

Pages 119 to 121. Provide the children each with a protractor, aruler and a sharp pencil. To measure the size of angles on thesepages it will be necessary to increase the length of the rays of eachangle, so that they can be seen through the protractor.

Pages 135 to 139. The work on these pages is very practical andself-explanatory. Provide the children with the necessary materialsfor the work and check on their accuracy. Make sure too that theycan spell words like radius, radii, diameter, chord, centre of a circle,semi-circle, quadrant, compasses, arc. (Difficulties sometimes arisewhen the pencil is not tightly screwed or is not an even length withthe point of the compass. Make sure that pencil points are sharp).

15

Another useful device for drawing a circle can easily be made by thechildren themselves. They need a strip of card, marked in centimetresand a drawing pin. Small holes are made at cm intervals. A pencil isput in the hole and a circle is drawn.

The pin is the centre of the circle and is fixed at that point on thepaper on which the circle is to be drawn.

Pages 122 to 132. When the children have learned the names ofvarious triangles (and can spell their names) ask them to look aroundthe classroom and other places to find examples of each. Right-angled triangles will be most obvious in the construction of buildings.Ask why triangles are so frequently used in construction. Point outand demonstrate that the triangle is the most rigid and safest shapefor the purpose. (A four-sided figure made of cardboard strips andpinned at the corners will, under pressure, change its shape, but atriangle constructed in the same way is rigid).

Drawing Pin

1 2 3 4 5 6 7 8 9 10

16

A rectangular (quadrilateral) shape can be reinforced and made rigidby turning it into triangles. Other shapes can also be made rigid inthe same way.

The construction of triangles is clearly set out on pages 127 to 129and is made easier if the children have good rulers, compasses,protractors and sharp pencils.

Pages 133 to 134. The word perpendicular means extending in astraight line to the centre of the earth, or at right-angles to a givenline or surface. It is useful to discuss this with the children. If theyattach a weight to a piece of string and hold it out, the string will beperpendicular to the ground. But if they look at Exercises A and Bthey can see which lines are perpendicular to other lines by findingthe right-angles.

They should be encouraged to look for perpendicular lines in whatthey see around them (walls, doors, etc.). What happens if they arenot perpendicular?

Using their knowledge of the perpendicular they can then drawparallel lines. (They are not necessarily horizontal). What wouldhappen if railway lines were not parallel? Look again for parallel linesall around them (the opposite edges of a book or desk or table).

Pages 140 to 143. These Reviews of the Year are not in themselvesan examination. They are intended to provide the children with anopportunity to refresh their understanding of mathematical topics.But above all, the reviews are an opportunity for teachers to find outwhat topics may need reteaching before the end of term (and perhapsbefore examinations take place). To this end teachers should, aseach page is completed, make an analysis of errors and discuss theresults with the children as a class or individually.

17

A

1. 13 ; 5 2. 13 ; 263. 1 ; 6 ; 5 ; 7 4. 30 ; 21 ; 51 ; 35 ; 56 ; 55. 85 ; 197 6. 3 ; 22 ; 25 ; 30 ; 5 ; 407. 5 ; 1 ; 6 ; 6 ; 7 ; 1 ; 14 ; 8 ; 15 ; 14

B

1. 18 2. 32cm

3. (a) 210 (b) 5

100 (c) 8

1000 4. 0.042 m5. 18 hr 15 min 6. Rs 8.107. 9 8. 496,3209. 86 r 59 10. 143 m2

11. 2 312 + 48

12 = 61112 12. 2.21

13. 28 14. 4.4

Page 2 A

1. Four lac, fifty thousand, two hundred and nineteen.2. One lac, sixty thousand, five hundred and twenty four.3. Eight hundred and thirty two thousand, eight hundred and seventy.4. Ninety thousand and four.5. Nine hundred thousand, six hundred and seventy five.6. Eighteen thousand, three hundred and one.

B

1. 26,503 ; 2,650.302. 1587.5 ; 158.753. 30,729.6 ; 3072.964. 839.8 ; 83.985. 42706.7 ; 4270.676. 9435.1 ; 943.51

C

1. 9000 or nine thousands 2. 0000 or zero ten thousands3. 8 or eight units 4. 400,000 or four lacs

18

5. .06 = 6100 or six hundredths

6. .002 = 21000 or 2 thousandths

7. .0 = 010 or zero tenths8. 30 or three tens

D

1. 123,168 2. 127,660 3. 48,4124. 7.224 5. 137.466 6. 167.120

E

1. 16.25 2. 1.32 3. 12.144. 23.02 5. 9.18 6. 20.35

F

1. 3.15, 3.165, 3.51, 3.55 2. 5.249, 5.492, 5.924, 5.9423. 0.001, 0.02, 0.112, 0.121 4. 7.184, 7.481, 7.84, 7.841

G

1. 14 1100 2. 7562

100 3. 8438

1000

4. 10 51000 5. 1881

100

3 A

1. 56.05 2. 2.106 3. 36.3834. 9.5 5. 12.769 6. 65.895

B

1. 2310 2.113

6 3.514

4. 9711 5.11310 6.

775

19

C1. 9 2. 2 3. 54. 8 5. 12 6. 20

D

3,06,054 ; 30.906 ; 118.53

E

1. 5 12201520+( ) = 5 2720 = 6 720

2. 4 7646 ( ) = 4 36 = 4 12

3. 5 210 + 63

10 = 115

10 = 1112

4. 10 324 42024 = 5

724

5. 9 414 11314

= 81814 11314 = 7

514

6. 20 418 + 41118

= 19 2218 41118 = 15

1118

F

1. 8.05 2. 6.023 3. 4.14. 7.5 5. 18.12 6. 9.124

G

1. 321,671 2. 77,441 3. 167,1874. 233,184

20

HPupils to do this.

I

Pupils to do this.

J

Pupils to do this.

Page 4 A

1. 2 cm 2. 6 cm 3. 6 cm4. 3 cm 5. 2nd & 3rd days 6. 5

B

1. Rs 45 2. Rs 75 3. 34. Rs 105 5. Rs 375

Page 5 A

300g ; 400g ; 500g : 600g

B

Pupils to do this.

C

1. Rs 60 2. Yes 3. Rs 60

D

1. 200km 2. 100km 3. 1st & 2nd4. Brown: 150km ; Black: 75km 5. 1st hr.6. It was travelling at a constant speed of 50km per hour and did

not stop on the way.

21

A

1. 9.00 2. 20km 3. 11.00 ; 11.304. 6km 5. 10.006. From 10.00 to 10.30, i.e., 3rd half-hour. 7. 4km8. 10km

B

1. 4000 2. 15,000 3. 90004. 60005. From 9.30 a.m. to 10 a.m., i.e. 2nd half-hour. The match was

about to begin.6. 27,000

Page 7 A

1. fifteen lac 2. sixty lac 3. twelve lac4. forty-eight lac 5. fifty-five lac

B

1. 19,00,000 2. 84,00,000 3. 70,00,0004. 62,00,000 5. 13,00,000

C

1. 31,19,624 Thirty-one lac, nineteen thousand six hundredand twenty-four.

2. 60,30,158 Sixty lac, thirty thousand, one hundred and fiftyeight.

3. 74,68,301 Seventy-four lac, sixty-eight thousand, threehundred and one.

4. 95,00,463 Ninety-five lac, four hundred and sixty three.5. 10,57,600 Ten lac, fifty-seven thousand, six hundred.

D

1. 71,12,042 2. 50,23,905 3. 33,90,5674. 18,04,272 5. 69,72,835

22

A

1. 29,05,384 ; 2,905,384 2. 13,20,059 ; 1,320,0593. 64,70,317 ; 6,470,317 4. 59,08,620 ; 5,908,6205. 11,24,969 ; 1,124,969

B

1. Four million. 2. Nine million.3. Eight million. 4. Three million.5. Six million, five hundred thousand.

C

1. 2,500,000 2. 4,100,000 3. 8,600,0004. 9,900,000 5. 1,850,000

D

1. 6,029,347 2. 2,500,123 3. 8,417,8694. 1,903,001 5. 2,748,625

Page 9 A

1. Two lac or 2,00,000 2. Seventy thousand or 70,0003. Six lac or 6,00,000 4. Six hundred or 6005. Twenty lac or 20,00,000 6. Ninety thousand or 90,0007. Sixty lac or 60,00,000 8. Forty thousand or 40,000

B

1. Seven hundred, two thousand and nineteen.2. Six million, seven hundred fifty thousand and forty-two.3. Sixty lac, three thousand and seven.4. Five million, nine thousand and ninety-six.5. Forty-three lac, forty-six thousand, two hundred and thirteen.

C

1. 28,60,713 2. 5,008,023 3. 35,41,0184. 7,400,600

23

D1. 4,000,000 + 500,000 + 30,000 + 2,000 + 400 + 80 + 12. 20,00,000 + 8,00,000 + 10,000 + 6,000 + 10 + 93. 10,00,000 + 7,00,000 + 50,000 + 3,000 + 200 + 20 + 44. 6,000,000 + 90,000 + 3,000 + 40 + 85. 1,000,000 + 900,000 + 30,000 + 7000 + 600 + 90 + 4

E

1. 18,06,259 ; 18,06,295 ; 18,60,9952. 4,033,965 ; 4,035,812 ; 4,053,612 ; 4,530,2163. 1,694,732 ; 1,964,732 ; 1,965,738 ; 1,966,3274. 24,05,031 ; 24,15,396 ; 24,51,9692 ; 4,51,9965. 9,09,499 ; 9,09,949 ; 9,09,999

F

1. 18,20,199 2. 6,242,999 3. 53,59,9994. 8,014,299 5. 94,15,099

Page 10 A

1. 44,06,310 2. 67,12,504 3. 3,742,0694. 8,503,740 5. 90,46,191

B

1. Eight million, ninety-six thousand, four hundred and thirty-two.2. Eighty-eight lac, sixteen thousand, and forty-seven.3. Sixty-four lac, three thousand, one hundred and fifteen.4. Nine million, one hundred, thirty thousand and thirty-two.5. Ten lac, one thousand, one hundred.6. One million, one hundred thousand and one.7. Two million, eight hundred and forty-three thousand, three

hundred and forty-eight.

C

1. 15,00,962 ; 15,00,629 ; 15,00,269 ; 15,00,2662. 23,41,381 ; 23,41,380 ; 23,14,381 ; 23,14,0383. 5,691,441 ; 5,691,410 ; 5,690,410 ; 5,690,4014. 58,04,075 ; 58,03,275 ; 58,02,375 ; 58,01,7355. 9,401,062 ; 9,400,622 ; 9,400,266 ; 9,400,262

24

D1. 4,084,620 > 4,084,2602. 18,50,119 < 18,51,1193. 23,62,731 > 23,26,7314. 5,116,290 = 51,16,2905. 64,03,495 < 64,04,495

Page 11 A

1. 4 crore 2. 6 crore 3. 2 crore4. 5 crore 5. 9 crore

B

1. 8,00,00,000 2. 1,00,00,000 3. 7,00,00,0004. 2,00,00,000 5. 9,00,00,000

C

2,08,678 ; 2,71,019 ; 2,71,200; 2,94,757 ;2,69,802 ; 1,95,389

Page 12 A

1. Six crore, seventy-three lac, one hundred and fifty-nine.2. Three crore, eight lac, forty-six thousand and two.3. Seven crore, thirty lac, fifty-two thousand, eight hundred and

fourteen.4. one crore, twelve lac, twenty-one thousand, one hundred and

twenty.5. Five crore, eighty-nine lac, sixty-four thousand, three hundred

and seventy-one.

B

1. 3,11,42,300 2. 8,30,19,461 3. 4,86,50,0924. 6,00,49,703 5. 7,00,00,356

C

1. Eight thousand or 8,000 2. 8,00,00,000 or eight crore3. Ninety thousand or 90,000 4. Seventy lac or 70,00,0005. Four lac or 4,00,000 6. Five hundred or 500

25

D1. 6,00,00,000 + 10,00,000 + 8,00,000 + 30,000 + 500 + 90 + 62. 7,00,00,000 + 5,00,000 + 10,000 + 2,000 + 800 + 40 + 73. 1,00,00,000 + 10,00,000 + 90,000 + 5,000 + 700 + 30 + 84. 4,00,00,000 + 60,000 + 7,000 + 100 + 40 + 35. 5,00,00,000 + 90,00,000 + 4,00,000 + 3,000 + 70 + 5

E

1. 3,18,72,500 2. 4,08,24,000 3. 8,72,40,0004. 9,58,00,000 5. 2,30,00,000

Page 13 A

1. Thirty-eight million, one hundred thousand, five hundred andeighty.

2. Fifty-one million, sixty-nine thousand, one hundred andtwenty.

3. Nineteen million, four hundred and five thousand, three hundredand twenty-eight.

4. Seventy-two million, six hundred and seventeen thousand, onehundred and thirty-four

5. Sixty million, one hundred and seventy-four thousand andfive.

B

1. 3,81,06,254 38,106,2592. 1,24,50,031 12,450,0313. 4,19,65,478 41,965,4784. 7,38,12,096 73,812,0965. 2,67,94,502 26,794,502

C

1. 31,510,603 2. 49,103,582 3. 78,400,8124. 20,637,555 5. 88,000,015

26

A

1. Eighty-five million, six hundred and twenty-three thousand andfive.

2. Seven crore, forty-eight lakh, one thousand, six hundred andtwenty-three.

3. Ninety-four million, thirty-eight thousand, one hundred and sixty-eight.

4. Seventy-two million, four hundred and forty-six thousand, andthirty-nine.

5. Eight crore, fifteen lac, sixteen thousand and seventy-five.

B

1. 4,10,15,804 2. 86,027,320 3. 1,94,06,4134. 54,322,548

C

1. 26,399,999 2. 18,349,999 3. 4,24,09,9994. 1,38,12,099 5. 93,049,999

D

1. 50,000,000 + 2,000,000 + 10,000 + 8000 + 600 + 20 + 32. 1,00,00,000 + 20,00,000 + 9,00,000 + 40,000 + 2000 + 603. 4,00,00,000 + 50,00,000 + 3,00,000 + 8000 + 400 + 90 + 24. 60,000,000 + 4,000,000 + 200,000 + 30,000 + 100 + 50 + 95. 3,00,00,000 + 2,00,000 + 40,000 + 9000 + 400 + 60 + 3

Page 15 A

1. 50 million2. 30 million3. Five hundred thousand4. Eleven hundred thousand or one million one hundred thousand5. Two million three hundred thousand6. Eighteen million seven hundred thousand7. Nine million eight hundred thousand8. Sixty-two million five hundred thousand

27

B8 crore 70 lac ; 4 crore 50 lac4 crore 20 lac ; 1 crore 52 lac2 crore 14 lac ; 13 crore 20 lac5 crore 40 lac ; 15 lac1 crore 70 lac ; 10 crore

Page 16 A

1. 3,999,969 2. 39,99,999 3. 4,781,9714. 42,72,771 5. 54,95.330 6. 29,263,5567. 7,333,720 8. 88,680,191 9. 4,53,98,54810. 9,35,71,973

B

1. 6,037,686 2. 94,43,300 3. 9,878,7374. 65,66,609 5. 2,692,219 6. 1,074,5107. 2,453,371 8. 2,49,01,878 9. 5,62,94,72310. 85,91,442

C

1. 1,300,456 2. 14,34,187 3. 20,050,6244. 1,84,80,000 5. 3,491,531

Page 17 A

1. 1,291,610 2. 3,643,111 3. 14,46,2074. 13,53,784 5. 2,561,621 6. 31,109,1877. 84,64,653 8. 22,047,868 9. 1,61,86,60910. 14,542,372

B

1. 99,99,999 2. 99,999,999 3. 1,00,00,000 1,00,000 99,999 9,99,99998,99,999 99,900,000 90,00,001

28

C1. 68,402,276 2. 25,846,285 3. 1,99,61,6154. 2,37,71,134 5. 7,405,428 6. 2,476,5677. 3,43,77,513 8. 3,974,662 9. 30,569,51210. 7,94,86,516

D

1. 49,838,328 2. 8,625,189 3. 11,46,4004. 7,592,700 5. 52,08,864

Page 18 B

1. 7,967,338 2. Sindh 56,321,1073. 21,227,213 4. Balochistan 42,960,0655. 15,393,704

Page 19 A

1. 50 2. 50 3. 204. 20 5. 100 6. 10007. 1250 8. 2470 9. 406010. 2010

B

1. 200 2. 200 3. 4004. 800 5. 500 6. 97007. 4000 8. 6900 9. 220010. 1700

Page 20 A

1. 110 2. 500 3. 3204. 120 5. 21,320 6. 16,0007. 10,990 8. 6990

B

1. 400 2. 200 3. 10004. 1700 5. 8800 6. 11007. 14,000 8. 19,700 9. 24,700

29

C1. Rs 2200 2. Rs 3500 3. Rs 57004. Rs 10,400 5. Rs 8600 6. Rs 4400

D

209,000 ; 112,000 ; 620,000 ;131,000 ; 761,000

Page 21 A

1. 12.15 p.m. 2. 4.35 a.m. 3. 10.15 p.m.4. 6.05 p.m. 5. 11.20 a.m. 6. 1.00 p.m.7. 4.00 a.m. 8. 9.45 p.m. 9. 5.35 a.m.10. 12.20 p.m.

B

1. 11 years 2. 9 years 3. 9 years4. 11 years 5. 8 years

C

1. 5.3 cm 2. 4.5 cm 3. 3.8 cm5 cm 5 cm 4 cm

4. 4.7 cm5 cm

D

8100 ; 7,800 ; 7,700 ; 7,600

EDifference

1. 30 + 40 + 20 = 90 22. 60 + 40 + 40 = 140 53. 30 + 30 + 20 = 80 54. 90 + 50 + 40 = 180 45. 60 + 100 + 50 = 210 1

30

A

1. 270,007 2. 150,000 3. 640,0004. 420,000 5. 750,000 6. 380,000

B

1. 2,600,000 2. 4,200,000 3. 6,300,0004. 3,500,000 5. 9,400,000

C

7,000,000 ; 6,000,000 ; 1,000,0005,000,000 ; 2,000,000

D

1. 4,332,000 2. 47,000,000 3. 2,200,0004. 340,300

Page 23 A

1. 632,448 2. 380,314 3. 412,8304. 664,740 5. 772,005

B

1. 1,658,057 2. 8,229,375 3. 3,823,4464. 2,923,708 5. 4,511,728 6. 2,476,8997. 2,278,892 8. 3,591,675 9. 4,378,75210. 4,400,344

C

1. 843,600 2. 2372500 m3. Rs 7,51,275 23725 Km

Page 24 A

1. 1120 r 17 2. 780 r 6 3. 1600 r 84. 1484 r 32 5. 1563 r 23

31

B1. 203 r 2 2. 91 r 61 3. 161 r 314. 447 r 45 5. 606 r 10

C

1. 520 2. 80 3. 1,0804. 2,342 5. 650

D

1. 104,136 r 20 2. 118,245 r 18 3. 133,793 r 204. 116,895 r 28 5. 109,603 r 32

Page 25 A

1. 131 r 73 2. 138 r 155 3. 157 r 54. 104 r 238 5. 113 r 337

B

1. 119 r 332 2. 125 r 169 3. 116 r 3894. 75 r 121 5. 54 r 42 6. 33 r 4097. 78 r 357 8. 78 r 182 9. 1,242 r 810. 1258 r 256

C

1. 1750 2. 1800 3. 12004. 1000 5. 4000 6. 7387. 323 8. 30

Page 26 A

1. 70 2. Rs 91,728 3. Rs 41,86,7204. Rs 78 r Rs 115 5. Rs 6,36,528 ; Rs 76,38,336

B

1. 3165 km 2. 121,100 3. 71,288 mm4. 1,038,345 ; 10,38,000 5. 2,655.55 kg

32

A

Pupils to do this.

B

1. 900,000 + 60,000 + 2000 + 400 + 302. 4,00,000 + 80,000 + 9000 + 20 + 53. 2,000,000 + 400,000 + 30,000 + 8000 + 500 + 90 + 24. 10,000,000 + 600,000 + 20,000 + 400 + 80 + 25. 20,00,000 + 2,00,000 + 40,000 + 6000 + 300 + 80 + 9

C

1. 43,29,561 2. 60,50,038 3. 7,24,86,0174. 8,53,29,861 5. 5,09,972

D

1. 4,732,691 2. 618,572 3. 15,016,7924. 28,403,141 5. 8,659,002

E

1. 4,65,20,002 2. 5,871,016 3. 7,00,86,145

F

1. 4,697,165 2. 6,00,66,835 3. 6,721,2604. 7,082,864 5. 6,99,95,882

G

1. 1204 r 55 2. 859 r 407 3. 820 r 3844. 463 r 522 5. 808 r 4

H

1. 438,000 2. 57,000 3. 8,27,0004. 6,825,000 5. 10,05,000

33

A

1. 9 2. 25 3. 274. 12 5. 16 6. 97. 15 8. 20

Page 29 A

1. 24 2. 120 3. 214. 55 5. 60 6. 457. 55 8. 16 9. 11710. 25

B

1. 9 2. 92 3. 334. 51 5. 17 6. 30

C

1. 61 2. 74 3. 1114. 19 5. 6 6. 857. 15 8. 56

D

1. 21 2. 34 3. 314. 19 5. 66 6. 957. 9 8. 233

Page 31 A

1. 33 2. 78 3. 544. 224 5. 124

B

1. 35 2. 4 3. 364. 12 5. 2 6. 32

34

C1. 58 2.2

10 3.86

4. 57 5.1315

D

1. 9 2. 15.2 3. 15.34. 4 5. 9.5

E

1. 2 x 2 x (2 2) = 0 2. 2 + 2 + (2 2) = 53. (18 6) 3 = 4

Page 32 A

1. 14 2. 18 3. 724. 101 5. 200 6. 278

B

1. 2 124 2. 11

20 3.1130

4. 1 12 5. 11

30 6.1518

Page 33 A

1. 5 38 2.78 3. 2

25

4. 12 1920 5. 3940

B

1. 28 2. 600 3. 184. 1890 5. 15,200 6. 238.2

35

C1. 512 2. Rs 123

Page 34 A

1. 7 sq. cm 2. 3@

sq. cm 3. 9 sq. cm4. 4 sq. cm

B

Pupils to do this.

C

160 sq. cm ; 52 cm 63 sq. cm ; 48 cm270 sq. cm ; 66 cm 216 sq. cm ; 66 cm954 sq. cm ; 142 cm

D

perimeter 21 m1. area = 15.0 sq. m ; perimeter = 17 m2. area = 26 sq. m ; perimeter = 21 m3. area = 52.5 sq. m ; perimeter = 31 m

E

1. 8 m 2. 18 m

Page 35 A

1. 37.0 sq. m 2. 42 sq. m 3. 38.5 sq. m4. 26.5 sq. m

B

Playroom = 410 sq. mClassroom A = 144 sq. mClassroom B = 166.5 sq. mBathroom = 35 sq. mTotal = 755.5 sq. m

36

A

1. 10 sq. m 2. 15 sq. m

Page 38 A

3 cm ; 2 cm a = 6 sq. cm3 cm ; 5 cm b = 15 sq. cm2 cm ; 3 cm c = 6 sq. m

B

1. 3 cm ; 2 cm ; area = 6 sq. cm2. 2 cm ; 1 cm ; area = 2 sq. cm3. 3 cm ; 2.5 cm ; area = 7.5 sq. cm4. 2 cm ; 2 cm ; area = 4 sq. cm

C

1. 2 cm ; 3 cm ; 6 sq. cm and 3 sq. cm2. 2 cm ; 4 cm ; 8 sq. cm and 4 sq. cm3. 1 cm ; 3 cm ; 3 sq. cm and 1.5 sq. cm4. 2 cm ; 4 cm ; 8 sq. cm and 4 sq. cm

Page 39 A

1. 5 sq. cm 2. 10.5 sq. cm 3. 6 cm ; 7.5 sq. cm

Page 40 B

1. 5 2. 4 3. 164. 10 5. 18 6. 20

C

1. No a = 40 ; b = 32 2. No a = 36 ; b = 323. No a = 24 ; b = 32

Page 42 A

1. 25 2. 5 3. 125

37

Bb. 10 ; 4 ; 40 c. 15 ; 3 ; 45

Page 43 A

1. 9 cu. cm 2. 10 cu. cm 3. 12 cu. cm4. 16 cu. cm

B

1. 27 cu. cm 2 36 cu. cm 3. 30 cu. cm4. 24 cu. cm

C

1. 120 cu. cm 2. 360 cu. cm 3. 528 cu. cm4. 1080 cu. cm 5. 288 cu. cm 6. 600 cu. cm

D

1. 120 cu. cm 2. 112 cu. cm 3. 168 cu. cm

Page 44 A

1. 54 cu. cm 2. 120 cu. cm 3. 693 cu. cm4. 190 cu. cm 5. 129.6 cu. cm 6. 117.6 cu. cm

B

h = 6 cm, b = 5 cm, l = 12 cm

C

1. 1500 cu. cm 2. 1008 cu. cm 3. 1120 cu. cm4. 2 m 5. 20 cm

Page 45 A

1. Vol. = 30 cu. cm ; Cap. = 300 ml2. Vol. = 48 cu. cm ; Cap. = 48 ml3. Vol. = 315 cu. cm ; Cap. = 315 ml4. Vol. = 288 cu. cm ; Cap. = 288 ml

38

A

1. 56 2. 9 3. 534. 28 5. 31 6. 12

B

1. 200 2. 1 36 = 112 3. 10.5

4. 10.8 5. 18 6. 67

7. 76 + 89 =

3718 = 2

118 8. 1

38

C

1. 12 x 6 sq. m = 3 sq. m 2. 14.0 sq. m3. 2 m ; 8 sq. m + 24 sq. m = 32 sq. m

D

1. 357 cu. cm ; 357 ml 2. 1232 cu. cm ; 1232 ml3. 441 cu. m ; 441 ml 4. 644 cu. cm ; 644 ml

Page 47

1. multiples 2. prime 3. composite4. coprime 5. remainder 6. two ; twelve7. itself 8. factor 9. six ; seven10. four

Page 48 A

1. 24 2. 99 3. 284. 80 5. 21 6. 36

B

28 ; 2 ; 7 ; 4 ; 14 ; 11, 2, 4, 7, 14, 28

39

C1. 1, 2, 3, 4, 6, 8, 12, 24 8 factors2. 1, 5, 25 3 factors3. 1, 2, 3, 5, 6, 10, 15, 30 8 factors4. 1, 2, 4, 7, 8, 14, 28, 56 8 factors5. 1, 2, 4, 5, 10, 20, 25, 50, 100 9 factors6. 1, 3, 9, 27, 81 5 factors7. 1, 3, 5, 15, 25, 75 6 factors8. 1, 7, 13, 91 4 factors9. 1, 2, 4, 17, 34, 68 6 factors

D

1. 15 : 1, 3 , 5, 1539 : 1, 3 , 13, 39 H.C.F. = 3

2. 12 : 1, 2, 3, 4 , 6, 1260 : 1, 2, 3, 4 , 5, 6, 10, 12, 15, 20, 30, 60 H.C.F. = 12

3. 22 : 1, 2, 11 , 2255 : 1, 5, 11 , 55 H.C.F. = 11

4. 21 : 1 , 3, 7, 2117 : 1 , 17 H.C.F. = 1

5. 14 : 1, 2, 7 , 1449 : 1, 7 , 49 H.C.F. = 7

6. 40 : 1, 2, 4, 5, 8 , 10, 20, 3032 : 1, 2, 4, 8 , 16, 32 H.C.F. = 8

E

18 and 19 ; 23 and 27 ; 81 and 71

Page 49 A

1. units 2. even 3. 34. 9 5. 20

40

B2. 306 3. 5,481 5. 82,602

C

48,16495 ; 17, 03,760

D

4892742 9035109 52963831049850 3278934 6279876

E

4960 ; 11,000 ; 11,624,340

F

3496 ; 17,504 ; 23,656 ; 280,072 ; 3,645,064

Page 50 A

8622 ; 53,622 ; 4626 ; 39,582

B

4707 ; 84,903 ; 9645 ; 270,063

Page 51 A

1. 56 = 2 x 2 x 2 x 7 2. 94 = 2 x 473. 48 = 2 x 2 x 2 x 2 x 3 4. 100 = 2 x 2 x 255. 118 = 2 x 59 6. 212 = 2 x 2 x 537. 66 = 2 x 3 x 11 8. 164 = 2 x 2 x 41

B

1. 12 2. 45 3. 204. 42 5. 28 6. 1407. 36 8. 105 9. 4010. 75

41

193 105

93 712 93

84 19 12

9 33 9

90

C

1. 9 2. 6 3. 54. 7 5. 9 6. 6

Page 52 A

1. 4 2. 2 3. 2 4. 365. 2 6. 35 7. 9 8. 19. 28 10. 4

B

1. 10 2. 6 3. 20 4. 95. 8 6. 15 7. 22 8. 309. 75 10. 21

C

1. 2 2. 10 3. 2

Page 53 A

1. 44 2. 36 3. 24 4. 125. 22 6. 7 7. 56 8. 79. 30 10. 25

Page 54 A

1.

H.C.F. = 3

42

2.

H.C.F. = 37

3.

H.C.F. = 46

4.

H.C.F. = 11

1851 999

851 5148 851

740 1111 148

111 337 111

1110

1460 598

460 3138 460

414 346 138

1380

1649 913

649 2264 649

528 2121 264

242 522 121

110 211 22

220

43

5.

H.C.F. = 38

Page 54 B

1.

H.C.F. = 10

1380 418

380 1038 380

3800

11100 1490

1100 2390 1100

780 1320 390

320 470 320

280 140 70

40 130 40

30 310 30

300

44

2.

H.C.F. = 53

3.

H.C.F. = 142

4.

H.C.F. = 235

1901 1272

901 2371 901

742 2159 371

318 353 159

1590

11278 2272

1278 1994 1278

994 3284 994

852 2142 284

2840

21175 3055

2350 1705 1175

705 1470 705

470 2235 470

4700

45

5.

H.C.F. = 38

Page 55 A

1. 126 2. 165 3. 844. 392 5. 225

B

1. 84 2. 24 3. 1004. 36 5. 50 6. 1207. 60 8. 90

C

1. 12 and 14 2. 8 and 12 3. 20 and 254. 18 and 12 5. 50 and 10 6. 30 and 407. 60 and 12 8. 18 and 30

D

1. 48 2. 135 3. 724. 330 5. 160 6. 3757. 490 8. 120

Page 56 A

1. 90 2. 120 3. 904. 90 5. 60

1722 1406

722 1684 722

684 1738 684

646 138 38

380

46

B1. 20 2. 12

L.C.M. = 60 L.C.M. = 24

3. 90 4. 42

L.C.M. = 90 L.C.M. = 84

C

1. 2.

L.C.M. = 60 L.C.M. = 120

3. 4.

L.C.M. = 315 L.C.M. = 140

230 3 2

5

224 2 2

3

318 2 5

3

228 2 3

7

4 2 3 62

5

10

2 108 2

253

30

9 3 5 153

7

20 5 7 702

2

4

47

A

1. H.C.F = 5L.C.M. = 75H.C.F. x L.C.M. = 5 x 75 = 3755 x 75 = 375

2. H.C.F = 2L.C.M = 330H.C.F x L.C.M = 2 x 330 = 66022 x 30 = 660







9. H.C.F = 32L.C.M = 160H.C.F x L.C.M = 32 x 160 = 5120

48


B

1. 70 2. 3 3. 244. 1,845 5. 75

Page 58

A 624 ; 3,060 ; 57,312B 1572 ; 18,060 ; 480,504C 3021 ; 1239 ; 5013

D

1. 360 2. 126 3. 1260 4. 660

E

1. 2 x 2 x 37 2. 2 x 3 x 5 x 73. 5 x 73 4. 2 x 2 x 3 x 5 x 135. 2 x 11 x 19 6. 2 x 2 x 2 x 2 x 2 x 3 x 7

F

1. 36 = 2 x 2 x 3 x 3 2. 56 = 2 x 2 x 2 x 7108 = 2 x 2 x 3 x 3 x 3 120 = 2 x 2 x 2 x 3 x 5H.C.F. = 36 H.C.F. = 8

3. 24 = 2 x 2 x 2 x 3 4. 38 = 2 x 19112 = 2 x 2 x 2 x 2 x 7 95 = 5 x 1972 = 2 x 2 x 2 x 3 x 3 114 = 2 x 3 x 19H.C.F. = 8 H.C.F. = 19

336 108

1080

256 120

112 78 56

560

49

1368 506

368 2138 368

276 192 138

92 246 92

920

11457 1612

1457 9155 1457

1395 262 155

124 231 62

620

G

1.

H.C.F. = 14

2.

H.C.F. = 46

3.

H.C.F. = 31

1182 308

182 1126 182

126 256 126

112 414 56

560

50

5.

H.C.F. = 35

H

1. 24 2. 315 3. 300 4. 350

I

1. 126 2. 240 3. 210 4. 120

J

1. 126 2. 21

Page 59(Tent of Transformation)

1. 203 2.378 3.

689

4. 4711 5.757

Wheel of Reduction

1. 914 2.79 3.

79 4.

911

5. 103 6.218 7.

72

1731 1204

731 1473 731

473 1258 473

258 1215 258

215 543 215

2150

51

Addition Hoopla

1. 5 23 2.1615 = 1

115 3. 5

56

4. 7 1730 5. 83463

Common Denominator Corner

1. 1520 ; 820 2.

1518 ;

418 3.

1421 ;

1221

Subtraction Shooting

1. C 2. D 3. A 4. G

Page 60 A

1. 56 2.511 3.

89 4.

2129

B

1. 2035 2.4956 3.

58

C

1. 8 13 2. 625 3. 2

47

4. 5 79 5. 4411 6. 7

58

D

1. 378 2.517 3.

9111

4. 7112 5.7011 6.

5215

E

1. 8496 2.112126 3.

34

52

F1. 3816 = 198 = 2

38 2.

5621 =

83 = 2

23

3. 3220 = 85 = 1

35 4.

4424 =

116 = 1

56

5. 7530 = 52 = 2

12 6.

8138 =

94 = 2

14

G

1. 414 ; 3

14 2.2540 ;

640 3.

1527 ;

1627

H

1. 1320 2.1724 3. 4

815 4. 7

120

I

1. 3 34 2.7

12 3. 17

12 4. 41130

Page 61 A

1. 52 2.44 3.

35

4. 36 5.54 6.

43

B

1. 2 23 2. 214 3. 1

78

4. 56 5. 245 6. 1

17

C

1. 4 2. 6 3. 3 34 4. 313

5. 35 6. 312 7.

12 8. 1

12

53

A

2. 1 12 3. 1 4.12 5.

14

B

1. 2.

12 15 of

12

12

34 of

12

3. 4.

13 14 of

13

13

13 of

13

5. 6.

14 12 of

14

23

12 of

23

Page 63 A

1. 14 ; 13 of

14 2.

12 ;

12 of

12 3.

15 ;

12 of

15

54

B1. 2.

12 12 x

34

38 =

13

13 x

14

112 =

3. 4.

13 13 x

34

312 =

14

14 x

25

220 =

5.

15 15 x

23

215 =

6.

15 15 x

14

120 =

C

1.

15 15 x

23

215 =

55

2.

14 14 x

34

316 =

3.

13 13 x

35

315 =

4.

17 17 x

34

328 =

5.

16 16 x

45

430 =

C

1. 215 2.3

16 3.3

15

4. 328 5.430

56

D1. 227 2.342 3.

344

4. 548 5.3

70

E

1. 484 2.590 3.

356

4. 690 5.435 6.

532

Page 64 A

1. 2.

23 23 x

14

212 =

34

34 x

23

612 =

3.

35 35 x

23

615 =

4.

45 45 x

12

410 =

57

5.

56 56 x

23

1018 =

B

1. 56 x25 2.

56 x

38 3.

23 x

57

4. 12 x49 5.

37 x

34

C

1. 2.

25 25 x

23

415 =

34

34 x

23

612 =

3.

23 23 x

45

815 =

4.

56 56 x

23

1018 =

58

5.

45 45 x

34

1220 =

D

1. 1221 2.1532 3.

3590

4. 2890 5.2132

Page 65 A

1. 59 2.58 3.

35 4.

1427

5. 14 6.14 7.

715 8.

318

9. 310 10.1835

B

1. 6380 2.13 3.

2027 4.

720

5. 1627 6.5

27 7.15 8.

935

9. 955 10.928

C

1. 140 2.1

30 3.1

30 4.1

60

59

A

1. 1120 2.1

280 3.1

270

4. 1252 5.1

96 6.1

350

B

1. 115 2.14 3.

110

4. 18 5.1027 6.

425

C

1. 27 2.7

100 3.15128

4. 13 5.221 6.

18125

D

1. 25108 2.38 3.

54175

4. 1635 5.1588 6.

3596

Sids Magic Fraction Corner

(a) 110 (b)536

Page 67 A

1. 7 15 2. 2058 3. 20

14 4. 11

35

5. 1112 6.23 7.

710 8. 1

127

9. 31516 10. 143

10

60

A

1. 6 2. 2 13 3. 412 4. 18

5. 12 1235 6. 20 7. 1334 8. 8

9. 45 10. 15

B

1. 565 = 1115 2. 12

37 3. 5

2335

4. 14 712 5. 1125

Page 69 A

1. 7 15 cm 2. 33 3. Rs 330

4. 12 cm 5. 2018 kg.

B

1. 16

Page 71 A

1. How many eights make 112? 142. How many fifties make 250? 53. How many fours make 324? 814. How many seventeens make 391? 235. How many fifteens make 270? 18

B

1. 3 (third) 2. 5 (fifths) 3. 7 (seventh)4. 8 (eighths) 5. 8 (quarters) 6. 12 (sixths)7. 9 (thirds) 8. 15 (fifths) 9. 12 (quarters)

61

A

1. How many sevenths make 3 wholes? 212. How many eights make 5 wholes? 403. How many thirds make 8 wholes? 244. How many sixths make 7 wholes? 425. How many tenths make nine wholes? 90

B

1. 4 13 = 12 2. 5 12 = 10 3. 3

15 = 15

4. 4 14 = 16 5. 5 16 = 30 6. 4

110 = 40

C

1. 54 2. 84 3. 110 4. 1825. 270 6. 92 7. 196 8. 1829. 323 10. 600

Page 73 A

1. 32 2.65 3.

109

4. 87 5.125 6.

92

7. 121 8.138 9.

185

B

1. 23 2.4

13 3.521

4. 38 5.625 6.

27

7. 813 8.7

17 9.725

62

A

1. 41 2.71 3.

81

4. 121 5.171 6.

221

7. 1001 8.302

1 9.1000

1

B

1. 101 ; 1

10 2.181 ;

118 3.

251 ;

125

4. 381 ; 1

38 5.511 ;

151 6.

641 ;

164

7. 1031 ; 1

103 8.1211 ;

1121

C

1. 6 2. 2 3. 2 4. 35. 4 6. 50 7. 40 8. 4

Page 75 A

1. 36 2. 75 3. 147 4. 2565. 270 6. 1000 7. 192 8. 5289. 216 10. 648

B

1. 4 2. 10 3. 6 23 4. 12

5. 12 12 6. 30 7. 4623 8. 126

9. 58 45 10. 76

63

A

1. 16 2.1

20 3.1

10 4.1

48

5. 140 6.1

88 7.1

63 8.1

36

9. 1130 10.1

220

B

1. 13 2.14 3.

320 4.

524

5. 215 6.542 7.

118 8.

316

9. 421 10.581

Page 77 A

1. 1 12 2.12 3. 2 4.

23

5. 2 12 6. 1 7. 112 8. 2

12

9. 4 10. 2 13

B

1. 56 2.58 3.

49 4. 1

315

5. 1 14 6. 115 7. 1

120 8.

37

9. 1 15 10. 156

C

1. 21 2. multiplying

64

65

Page 78 A

1. 2 110 2. 11330 3. 2

1417 4. 5

25

5. 5 112 6. 327 7. 2

110 8. 2

1117

9. 1 1114 10. 21021

B

1. 3 325 2. 11755 3. 2

2425 4. 1

523

5. 5 2326 6. 4831 7. 2

827 8. 1

56

9. 2 829 10. 11314

C

1. T 2. T 3. F 4. F5. F 6. T 7. T 8. T

Page 79

1. 1 2. 811 3.94 4. 1

5. 4039 6.5

14 7. 1 8.103

9. 1 10. 47

Page 80 A

1. 12 2. (a) 25 m (b) 40 cm 3. 450

Page 81 A

1. 8 112 2.3

16 3. 1734 4. 12

117245

5. 16 13 6. 1578 7. 24

15 8. 28

6869

66

B

1. 22 6172 2. 2245 3. 13

34

4. 23 13 5. 5.0

Page 82

1. 0.7 ; 0.15 ; 0.5 ; 0.99

2. 0.2 ; 47100 ; 0.003 ; 8

10 ; 38

1000 ; 0.019 ; 0.245 ; 69

100 ; 0.143.1. Ten ; two 2. thousandths 3. right4. tens 5. zero zero 6. hundredths7. half 8. factor ; fractional 9. ten

10. nine 11. point

Page 83 A

1. 2.3 2. 16.1 3. 8.9 4. 12.5

B

1. 3.5 2. 4.2 3. 10.6 4. 22.4

C

1. 10 1100 2. 2422

100 3. 185

100 4. 29

10

D

1. 6.5 cm 2. 10.1 cm 3. 15.9 4. 8.7 cm

E

1. 50 12 2. 2514 3. 18

15 4. 100

920

67

F

1. 0.06 x 10 = 0.6 2. 0.75 x 10 = 7.53. 5.91 10 = 0.591

G

1. 49.06 2. 9.005 3. 260.74

H

1. 2.005 2. 4.021 3. 8.094. 6.117 5. 7.035 6. 18.3

I

1. 3 hundredths 2. 4 thousandths 3. 0 tenths4. 4 hundredths 5. 5 tenths 6. 4 units

J

1. 6.012 2. 3.16 3. 2.44. 8.035 5. 6.36 6. 99.8

Page 84 A

H T u . t h th1. 3 9 . 5 12. 1 1 0 . 0 6 43. 1 4 . 54. 2 6 0 . 8 3 35. 8 6 . 6 06. 1 4 . 9 5

B

1. 701.160 2. 86.09 3. 196.3964. 571.956 5. 585.06

C

1. Rs 158.15 2. Rs 204.70 3. Rs 26.604. Rs 117.20

68

D

1. 94.24 2. 278.046 3. 110.8144. 52.117

Page 85 A

1. 6.09 ; 7.40 2. 15.11 ; 16.32 3. 4.200 ; 14.6634. 8.190 ; 7.321 5. 41.50 ; 6.95

B

1. 32.67 2. 1136.048 3. 91.0844. 6,278.137 5. 39.964

C

1. 40.64 2. 703.178 3. 82.764. 217.011 5. 56.316

Page 86 A

1. 55.2 2. 199.5 3. 113.754. 391.2 5. 152.25 6. 217.6

B

1. Rs 164.65 2. 169.23 3. 158.724. 77.70 5. 32.55 6. 78.311

Page 87 A

1. 3.2 2. 1.35 3. 1.98 4. 20.805. 0.28 6. 46.322 7. 148.464 8. 227.552

B

1. 5.2 2. 1.8 3. 0.25 4. 1.225. 14.2 6. 0.45 7. 2.1 8. 0.31

69

C

1. 2.08 2. 4.39 3. 14.06 4. 18.215. 6.153 6. 5.98 7. 9.49 8. 7.639. 8.54 10. 9.99

Page 88 A

1. 48 2. 0.3 3. 56.5 4. 1275. 0.02 6. 14.63 7. 104.9 8. 45.21

B

1. 530 2. 1900 3. 465 4. 82005. 7 6. 80 7. 103 8. 12509. 1280 10. 6450

Page 89 A

1. 180 2. 6400 3. 8694. 21.13 5. 5170

B

1. 695 2. 48.11 3. 507.64. 3490 5. 1112

C

1. 10 2. 100 3. 104. 100 5. 1000

D

1. 5.317 2. 1.6 3. 1.8934. 7.762 5. 3.842

Page 90 A

1. 0.318 2. 0.624 3. 1.194. 0.075 5. 0.083

70

B

1. 0.0037 2. 0.0028 3. 0.00414. 0.0072 5. 0.0103

C

1. 10 2. 100 3. 104. 100 5. 10

Page 91 A

1. 672 sq mm; 6.72 sq cm 2. 1596 sq mm; 15.96 sq cm3. 5460 sq mm; 54.60 sq cm 4. 2511 sq mm; 25.11 sq cm5. 2808 sq mm; 28.08 sq cm

B

1. 0.28 sq cm; 28 sq mm100 2. 0.10 sq cm; 10 sq mm

100


100


100

C

1. 0.42 2. 0.36 3. 0.784. 2.88 5. 2.72

Page 92 A

1. 3.792 2. 15.566 3. 4.0954. 23.37 5. 13.038

B

1. 85.68 2. 85.485 3. 25.5154. 54.52 5. 4.536

71

C

1. 85861000 = 8.586 2.293361000 = 29.336

3. 228151000 = 22.815 4.8772100 = 87.72

5. 223021000 = 22.302

Page 93 A

1. 5.5518 2. 0.8232 3. 9.81474. 28.496 5. 5.6709

B

1. 682561000 = 68.256 2.52361000 = 5.236

3. 4871361000 = 48.7136 4.64788210000 = 64.7882

5. 19547210000 = 19.5472

Page 94 A

1. 3.456 2. 0.3776 3. 5.79314. 29.2105 5. 6.6172 6. 8.1512

B

1. 8.804 2. 79.68 3. 34.7514. 0.238 5. 8.6019 6. 83.167

Page 96 A

1. 84 12 = 7 2. 35 7 = 5 3. 219 3 = 734. 96 16 = 6 5. 63 21 = 3 6. 8.5 5 = 1.7

B

1. 4 2. 4 3. 0.84. 9 5. 5

72

C

1. 4 2. 2 3. 54. 5 5. 40

Page 97 A

1. 0.8 2. 50 3. 20 4. 605. 5 6. 8 7. 4221 8. 309. 50 10. 50

B

1. 20 2. 33 3. 18 4. 7

Page 98 A

1. 0.5 2. 0.625 3. 1.3334. 0.2 5. 0.25 6. 0.5

B

1. 0.25 2. 0.2 3. 0.3754. 0.05 5. 0.55

Page 99 A

1. 15.582 2. 107.68 3. 28.1544. 62.7 5. 213.717

B

1. 6.252 2. 88.9 3. 9.074. 1.743 5. 65.96 6. 21.1

C

1. five 2. 100 3. 1000 4. 6.0855. 0.649 6. 0.1705 7. 0.2369 8. 0.459. 13 10. 23.808

73

Page 100 A

1. 2.1 cm ; 2 cm 2. 1.5 cm ; 2 cm3. 2.6 cm ; 3 cm 4. 1.3 cm ; 1 cm

B

1. 11 2. 6 3. 74. 22 5. 19 6. 467. 17 8. 79 9. 90

Page 101 A

1. 8.7 2. 4.1 3. 5.9 4. 3.85. 2.4 6. 7.9 7. 6.8 8. 3.0

B

1. 7.0 2. 4.3 3. 10.2 4. 12.15. 15.4 6. 27.1 7. 39.5 8. 83.5

C

1. 8.5 2. 23.0 3. 56.1 4. 49.05. 64.0 6. 71.8 7. 83.9 8. 28.0

D

1. 54.2 ; 54 2. 52.8 ; 53 3. 396.2 ; 3964. 607.6; 608 5. 2,711.4 ; 2,711 6. 133.6; 134

E

1. 11.25 = 11.3 2. 2.31 = 2.3 3. 44.21 = 44.24. 47.65 = 47.7 5. 33.26 = 33.3 6. 352.81 = 352.8

Page 102 A

1. 6.13 2. 7.49 3. 8.034. 11.33 5. 14.11

74

B

1. 27.235 ; 27.24 2. 21.798 ; 21.803. 13.437 ; 13.44 4. 22.63 ; 22.365. 113.925 ; 113.93 6. 53.097 ; 53.10

Page 103

B : 310 ; C : 720 ; D :

1850 ; E :

33100

B : 310 = 30

100 ; C : 720 =

35100

D : 1810 = 36

100 ; E : 33

100 = 33

100

B , E , C , D , A

Page 104 A

1. 70100 2.80

100 3.65

100 4.28

100

5. 20100 6.42

100 7.45

100 8.58

100

9. 90100 10.74

100

B

1. 50100 2.25

100 3.94

100

4. 60100 5.95

100 6.32

100

C 8

Page 105 A

1. 6212

100 ; 62.5

1002. 87

12

100 ; 87.5

1003. 6

14

100 ; 6.25100

75

B

1. 62.5 2. 12.51 3. 37.5 km.

Page 107 A

1. 70 per cent 2. 19 per cent 3. 87 per cent4. 15 per cent 5. 25 per cent 6. 90 per cent7. 60 per cent 8. 58 per cent

B

1. 35 % 2. 80 % 3. 99 %4. 60 % 5. 56 % 6. 78 %

C

1. 310 2.625 3.

120 4.

910

5. 920 6.825 6.

27100 8.

99100

D

1. 28.57 % 2. 55.56 % 3. 23.08 %4. 63.64 % 5. 71.43 %

Page 108 A

1. 425 % 2. 160 % 3. 730 %4. 635 % 5. 380 % 6. 272 %

B

1. 316.67 2. 266.67 3. 183.334. 414.29 5. 628.57 6. 311.11

C

1. 600 % 2. 900 % 3. 1100 %4. 1700 % 5. 2300 % 6. 4500 %

76

Page 109 A

1. Rs 52 2. Rs 3400 3. Rs 47.50

B

1. Rs 5 2. 500 km 3. Rs 304. 20 5. Rs 63

C

1. 9 2. 4.5 m 3. 24 g4. 30 kg 5. Rs 48

D

1. 6 2. Rs 5,1003. Rs 3,850 ; Rs 46,200

Page 110 A

1. 50 per cent ; 53.33 per cent2. 48 per cent ; 54.167 per cent

B

1. 66 % ; 70 % : General Knowledge2. 70 % ; 67 % : English3. 49 % ; 70 % : Sara

Page 111 A

1. 15 2. 42 3. 434. 18 cm 5. Rs 28 6. 31.71

B

1. 14 2. 3 3. 3704. 44 5. 2220; 3 ; 740

Page 112 A

37.0 kg

77

B

1. Rs 9.25 2. 21.38 3. Rs 984 4. 2.79 kg5. (a) 23 girls (b) 21.57 boys (c) 312 (d) 22.29

Page 113 A

1. Sun : 25Mon : 28Tues : 27Wed : 24Thur : 21

2. 253. Mon ; Tues4. Wed ; Thur

B

13 ; Bop, Jiff, Kit

Page 114 A

1. Rs 2550 2. Rs 5925 3. Rs 35504. Rs 4650 5. Rs 11,200 6. Rs 10,650

B

1. 20 % 2. 33#

% 3. 10.59 %4. 8.85 % 5. 11.67 % 6. 2.5 %

Page 115 A

1. Rs 850 2. Rs 2775 3. Rs 5064. Rs 1750 5. Rs 311 6. Rs 3620

B

1. Rs 500 ; 20 % 2. Rs 1250 ; 27.78 %3. Rs 1250 ; 17.24 % 4. Rs 700 ; 12.5 %

78

Page 117 A

1. Rs 3600 2. Rs 1075 3. Rs 690

B

1. Rs. 12,720 2. Rs 22,500 3. Rs 19,980

Page 118 A

1. 18.49 2. 35.02 3. 70.014. 102.59 5. 143.10 6. 475.20

B

1. 725 2.1120 3.

1825 4.

920

C

1. 48100 = 0.48 2.3

100 = 0.03 3.16100 = 0.16

4. 2 5100 = 0.025 5.57

100 = 0.57 6.2

100 = 0.02

D

1. Rs 192 2. 450 L 3. 350 km4. Rs 40 5. 10.8 m

E

1. Rs 49.50 2. Rs 2080 3. Rs 212.50 4. Rs 9.30

Page 119 A

1. Straight 2. Obtuse 3. Reflex4. Acute 5. Right

B

Pupils to do this.

79

C

1. 360 2. 90 3. 1804. Obtuse 5. 270 6. 180; 360

D

1. & ABC = 40 2. & XYZ = 1803. & PQR = 130 4. & UVW= 50

Page 120 A

1. & RST = 30 2. & ABC = 553. & PQR = 120 4. & JKL = 1105. & MNO = 90 6. & XYZ = 130

B

Pupils to do this.

C

1. Acute 2. AB ; BC 3. B ; vertex 4. 73

Page 121 A

1. 310 2. 340 3. 345 4. 250

B

Pupils to do this.

Page 122 A

1. equilateral 2. scalene 3. isoceles4. equilateral 5. scalene 6. scalene

B

Equilateral Scalene Isocelesa c be d f

80

Page 123 A

3.5 ; 60 , 3.5 ; 60 , 3.5 ; 60equilateral ; They are all equal (60)

B

5 ; 66 , 5 cm ; 48 , 4 cm ; 66Isosceles ; 2 angles are equal.

Page 126 B

1. a = 45 e = 74b = 47 f = 90c = 37

C

' 2' 3' 4' 5' 6

Page 128 A

2. ( 3. ( 4. (

Page 130 A

1. Opposite 2. Parallelogram 3. Trapezium4. Sixty 5. Kite 6. Rhombus7. Rectangle 8. Ten

Page B

1. Parallelogram&s : 70 , 70 , 110, 110 Sum = 360

81

2. Kite&s : 81 , 124 , 31, 124Sum = 360

3. Trapezium&s : 101 , 130 , 50, 79 Sum = 360

4. Rhombus&s : 110 , 70 , 110, 70 Sum = 360

Page 131 A

1. parallelogram, kite, rhombus2. square, rhombus3. square, rectangle, rhombus, parallelogram4. square, parallelogram, rectangle, rhombus5. square6. rhombus

B

Pupils to do this.

Page 132 A

1. a and c = 70, b and d = 1102. a and d = 105, b and c = 753. a = 36, b = 133, c = 58, d = 1334. a and c = 60, b and d = 1205. a = 110, b = 110, c = 70, d = 706. a = 90, b = 90, c = 120, d = 60

B

Pupils to do this.

C

1. 22.4 cm 2. 19.2 cm 3. 15.6 cm 4. 25.2 cm

82

Page 133 A

CD, MN, ST

B

1. AE 2. AB, DE 3. AE 4. AE

C

PQ, TU, VW, CD

Page 136 A

1. 2.4 cm 2. 2.6 cm 3. 3 cm 4. 2.8 cm

B

1. 1.2 2. 1.3 3. 1.5 4. 1.4

C

1. 4.82 2. 11.69 3. Radius4. Quadrant 5. 180 6. Diameter ; radius7. Centre ; circumference

Page 138 B

1. 8 cm 2. 10 cm 3. 12 cm 4. 14 cm5. 13 cm 6. 4 cm 7. 7 cm 8. 11 cm9. 9 cm 10. 6.6 cm

C

1. XA, XB, XC, XD2. AB = 2.5 cm ; CD = 2.5 cm3. Arc ASC ; arc CQB ; arc BRD,

Arc DPA ; arc SCQ ; arc QBR,Arc RDP ; arc PAS

83

Page 139 C

E, F, H, I, M, N, W, Z

Page 140 : 1

1. 56,72,318Fifty six lac, seventy two thousand, three hundred andeighteen.

2. 60,09,053Sixty lac, nine hundred and fifty three.

3. 7,40,28,301seven crores, forty lac, twenty eight thousand, three hundredand one.

4. 9,07,55,620Nine crores, seven lac, fifty five thousand, six hundred andtwenty.

2.

1. 4,203,721Four million, two hundred and three thousand, seven hundredand twenty one.

2. 5,047,834Five million, forty seven thousand, eight hundred and thirtyfour.

3. 31,672,049Thirty one million, six hundred and seventy two thousand andforty nine.

4. 80,246,118Eighty million, two hundred and forty six thousand, onehundred and eighteen.

84

3

1. Six hundred thousand or 600,0002. Twenty lac or 20,00,0003. Four million or 4,000,0004. Four lac or 4,00,0005. Eighty million or 80,000,0006. Five crore or 5,00,00,000

4

(a) (b)1. 2,347,999 2,348,0012. 14,17,599 14,17,6013. 6,09,99,999 6,10,00,0014. 83,999,999 84,000,001

5

1. 10,05,155 2. 3,055,494 3. 18,96,27,1974. 488.75 5. 411.030 6. 75,067.389

6

1. 640 ; 600 2. 1870 ; 19003. 7040 ; 7000 4. 82,560 ; 82,6005. 1,29,390 ; 1,29,400 6. 4,651,020 ; 4,651,000

7

1. 2.5 ; 2.46 2. 3.7 ; 3.71 3. 6.2 ; 6.194. 13.1 ; 13.06 5. 84.1 ; 84.10 6. 100.3 ; 100.34

8

1. 508,248 2. 2,736,240 3. 4,787,8824. 134.096 5. 295.092 6. 817.125

9

1. 255 2. 4.72 3. 996.574. 902.36 5. 1111.88 6. 2162.84

85

10

1. 44 2. 148 3. 36

4. 5 712 5. 51013 6. 0.73

Page 141

11

1. 12.7056 2. 9.09 3. 5 144. 79 5. 6100 6. 98.46

12

1. 80 km2. Second hour from 11 a.m. to 12 noon.3. 70 km4. From 12 to 12.30 p.m.5. 180 km6. 60 km/hr.

13

1. 17.5 sq m 2. 18 sq m 3. 28 sq m 4. 15 sq m

14

1. 31.5 cu m 2. 150.5 cu m3. 631.35 cu m 4. 85.45 cu m

15

1. 10332 2. 2976083. 7020 4. 82,272 ; 1,06,056

16

1. 24 2. 630 3. 200 4. 16,170

86

Page 142

17

1. 6 2. 28 3. 9 4. 4

18

1. 17 2. 19 3. 234. 74 5. 459 6. 47

19

1. 420 2. 180 3. 1248 4. 270

20

1. 427 2. 7311 3.

145 4. 7

710

5. 36 2235 6. 0 7. 25 8.1

16

9. 23 10. 11516 11. 1

2533 12. 2

13

21(a) (b) (c)

1. 48 480 48002. 0.3 3 303. 14.7 147 14704. 68.7 687 68705. 30.19 301.9 30196. 45.35 453.5 4535

22

1. 1000 2. 10 3. 1000 4. 100

23

1. 0.24 2. 6 3. 3 4. 0.7805. 2410 6. 13.9095 7. 5000 8. 89. 20 10. 0.3522

87

24

1. 10787410000 = 10.7874 2.1134310000 = 1.1343

3. 62809210000 = 63.8092

25

1. 0.45 0.4552. 0.57 0.5713. 0.69 0.6924. 0.74 0.7375. 6.67 6.6676. 2.78 2.778

26

1. 70% 2. 70% 3. 94%4. 15% 5. 425% 6. 340%

27

1. 45 2.14 3.

425

28

1. 0.45 2. 0.07 3. 0.12

30

1. 602. 803. Scalene as well as obtuse angle '

33

Rs 408

88

Page 144

1. 2 1120 2. 60% 3. 504 4. 125. 86 6. 14 7. 14 8. 70%

9. 11718 10. 11718 11. 60% 12. 2

1320

13. 12 14. 14

89

Notes

90

Notes

9 780195 799781

ISBN 0-19-579978-X

math grade 5 teaching guide

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