Divine Buds English School
Worksheet For FA2 (2014-2015)
Std : 5
Sub: Maths
---------------------------------------------------------------------------------------------------------Course :
L : 1 Numbers
L : 11 Roman Numerals
L : 2 Operations of Large Numbers
L : 21 Basic Geometrical Concepts
Paper Style :
Section A
Total Marks : 40
[ 20 Marks]
Section B
Q : 2 Sol.the following (2 marks each)
Q : 3 Sol.the following (3 marks each)
[20 Marks]
(2X4=8)
(3X4=12)\
Q : 1 MCQ’s
Ch : 1 Numbers
Numbers Beyond 9,99,999
 Largest 6 digit number is 9,99,999.
 When we add 1 to 9,99,999 , we get 10,00,000 the smallest 7 digit number. We read it as
ten lakh.
 Largest 7 digit number is 99,99,999. We read it as ninety-nine lakh, ninety – nine thousand,
nine hundred ninety – nine.
 When 1 is added to 99,99,999 we get 1,00,00,000 the smallest 8 digit number. We read it
as one crore.
 The largest 8 digit number is 9,99,99,999. We read it as nine crore, ninety-nine lakh,
ninety-nine thousand, nine hundred ninety-nine.
 When 1 is added to this number, we get 10,00,00,000 the smallest 9 digit number. We read
it as Ten Crore.
Indian Place Value Chart
 To make it easy to read and write the large numbers, the Indian Place Value Chart has been
divided into periods.
 The First Period is the ONES PERIOD with three places- Once (0), Tens (T) and Hundreds
(H)
 Second period is the THOUSANDS PERIOD with two places –Thousand (Th) and Ten
Thousands (TTh)
 Third period is the LAKHS PERIOD with two places – Lakhs (L) and Ten Lakhs (TC)
 Fourth Period is the CRORES PERIOD with two places –crores (C) and Ten Crores (TC)
Indian Place Value Chart
Periods Crores
Lakhs
Thousands
Ones
Places Ten
Crores Ten
Lakhs Ten
Thousand Hundred Tens Ones
Crores
Lakhs
Thousand
TC
C
TL
L
T-Th
Th
H
T
O
3
9
8
4
5
3
2
1
8
Thirty nine
Eighty Four
Fifty three Thousand Two hundred eighteen
Crore
Lakh
 While reading a number all the digit in the same period are read together and the name of
the period(expect the ones is read along with them).
 While writing a number ,we usually put a comma after every period to separate the periods.
 The plural of periods is not written. For example instead of writing five crores, three lakhs ,
ninety –four thousands, six hundreds eighty –one, we write five crore, three lakh, ninety –
four thousand, six hundred eighty – one.
EXERCISE – 1A
A. Write the following numbers in a place value chart :
1. 3,52,46,789
2. 7,16,02,030
3. 16,25,43,434
4. 15,42,89,356
5. 42,53,62,517
6. 28,75,30,005
7. 3,83,528
8. 78,31,806
9. 79,10,29,668
10 85,43,96,345
B. Write the following numbers in words :
1. 72,38,618
2. 67,81,285
3. 38,52,906
4. 2,06,00,612
5. 2,74,38,016
6. 43,11,64,006
7. 2,26,18,396
8. 16,17,90,034
9. 74,25,637
10. 43,68,258
11. 3,69,47,891
12. 2,18,45,679
13. 35,84,217
14. 6,25,30,149
15. 8,24,62,157
16. 32,14,62,190
C . Write each of the following numbers in figures :
1. Seventy two lakh , thirty seven thousand, four hundred seventy
nine.
2. Thirty seven lakh, twenty eight thousand two hundred seventy two.
3. Ninety two lakh seventy eight thousand three hundred eighteen.
4. Five crore thirty nine lakh twenty seven thousand two hundred
seventeen.
5. Forty three crore seventy two lakh thirty eight thousand five hundred
twenty seven.
6. Seven crore fifty five lakh thirty thousand nine hundred thirty three.
7. Sixty seven crore ninety.
8. Fifty crore ninety thousand seventy five.
9. Seventy crore, five lakh.
10. Nine crore, nineteen lakh, eighty thousand.
11. Seven crore, seventy one lakh, eleven thousand one hundred one.
12. Two crore, five thousand, one hundred seventeen.
13. Fifty crore, fiftylakh, fifty thousand fifty.
14. Eighty one lakh ,sixty thousand, three hundred seven.
15. Six crore, six lakh, sixty thousand , sixty six.
16. Thirteen crore, twelve lakh, eleven thousand, one hundred one.
FACE VALUE AND PLACE VALUE
 Face Value : The face value of a digit is always the digit it self.
For example, face value of 5 in 74,58,962 is 5 only.
Face value of 2 in 42,58,973 is 2 only.
 Place Value : Place value of a digit depends on the place it occupies in the place value
chart.
Place value = Face Value X Value of the place
Place values of the digits of 92,14,67,352 are:
921467352
2x1=2
5 x 10 = 50
3 x 100 = 300
7 x 1000 = 7000
6 x 10000 = 60000
4 x 100000 = 100000
1 x 1000000 = 1000000
2 x 10000000 = 20000000
9 x 100000000 = 900000000
 Place value of 0 is always 0 whatever place it may occupy.
Successor of a number : The number that comes just after a given number is
called its successor.
Eg : Successor of 78,69,599 = 78,69,599 + 1 = 78,69,600
Predecessor of a number : The number that comes just before a given number
is called its predecessor.
Eg: Predecessor of 5,68,74,956 = 5,68,74,956 – 1 = 5,68,74,955
FORMATION OF THE GREATEST AND THE SMALLEST NUMBERS :
 To form the greatest number, arrange the given digits in the descending order.
 To form the smallest number, arrange the given digits in ascending order.
 Zero should never be the 1st digit in the extreme left. To get the smallest number, zero
should always be the 2nd digit from the left.
 Fro Eg : Form the greatest and the smallest numbers from the digits 2,0,1,7,3 and 4 .
The greatest number = 743210
The smallest number = 102347
EXERCISE – 1 B
1. Find the place value of :
1. 4 in 3,41,06,315
2. 2 in 87,34,21,301
3. 8 in 4,53,80,051
4. 9 in 20,04,13,988
5. 4 in 94,32,96,031
6. 3 in 6,25,72,623
2. Find the place value of 6 in the following numbers :
1. 60,35,41,325
2. 3,20,06,151
3. 55,36,00,140
4. 3,17,52,601
5. 6,20,31,053
6. 70,26,52,123
3. Find the difference between two 8 in 81,16,865.
4. Write the following numbers in the expanded form.
1. 3,82,865
2. 78,365
3. 1,78,328
4. 6,78,356
5. 3,56,218
6. 2,83,867
7. 28,31,628
8. 1,61,24,978
9. 4,29,00,781
10. 12,05,73,471
11. 30,94,10,367
12. 74,52,91,146
5. Write the numerals in the short form.
1. 70,00,000 + 2,00,000 + 800 + 10 + 6
2. 40,00,000 + 7,00,000 + 30,000 + 4000 + 800 + 20 + 5
3. 20,00,000 + 8,00,000 + 70,000 + 20 + 7
4. 80,00,000 + 700 + 80 + 9
5. 30,00,000 + 7,00,000 + 90,000 + 8000 + 70 + 1
6. 8,00,00,000 + 70,00,000 + 9,00,000 + 80,000 + 6000 + 800 + 90 + 7
7. 2,00,00,000 + 70,00,000 + 5,000 + 800 + 70 + 6
6. Compare the following numbers using < or > in the blanks.
1. 2,73,75,896 ___________ 3,41,95,123
2. 1,56,37,536 ___________ 15,19,758
3. 67,234 ____________ 67,534
4. 4,10,999 _____________ 4,10,898
5. 21,24,371 ____________ 2,56,721
6. 4,79,059 ____________ 4,79,056
7. 21,24,371 ____________ 42,56,721
8. 34,35,36,789 ___________ 34,35,36,879
7. Find the greatest number in each group.
1. 31,20,567 ; 31,20,167 ; 3,12,667 ; 3,21,667
2. 10,49,178 ; 17,38,758 ; 10,38,278 ; 15,39,128
3. 45,69,108 ; 45,69,206 ; 45,39,206 ; 45,69,308
4. 11,29,08,164 ; 11,29,80,164 ; 11,28,90,164 ; 11,28,90,614
5. 25,17,01,294 ; 25,71,01,294 ; 15,27,01,294 ; 25,17,40,294
8. Find the smallest number of each group.
1. 63,19,000 ; 63,00,19,251 ; 83,19,468 ; 46,10,253
2. 36,12,43,551 ; 45,16,27,142 ; 30,14,349 ; 29,18,37,156
3. 10,00,68,053 ; 39,45,12,346 ; 37,49,296; 28,21,40,183
4. 98,52,17,340 ; 40,73,89,152 ; 25,18,90,314 ; 89,25,13,704
5. 3,01,45,678 ; 4,13,08,765 ; 3,41,08,756 ; 4,30,17,865
9. Arrange the following numbers in ascending order.
1. 87,36,952 ; 87,35,952 ; 87,85,952 ; 87,65,952
2. 5,32,718 ; 67,89,542 ; 8,79,56,423 ; 12,45,78,963
3. 27,93,465 ; 2,04,05,060 ; 3,56,52,595 ; 28,63,246
4. 87,56,726 ; 8,55,77,624 ; 8,56,67,723 ; 86,75,722
10. Arrange the following numbers in descending order.
1. 25,64,056 ; 25,63,201 ; 2,56,98,530 ; 59,86,542
2. 5,26,781 ; 4,52,687 ; 45,31,071 ; 44,52,700
3. 8,78,254 ; 8,79,564 ; 82,13,475 ; 4,69,58,472
4. 76,49,866 ; 78,96,467 ; 79,84,668 ; 74,68,969
11. Write successor of each number.
1. 42,57,198
2. 17,35,000
3. 8,10,309
4. 3,16,12,319
5. 5,29,79,499
6. 9,99,99,998
7. 7,00,22,111
8. 5,12,34,000
12. Write predecessor of each number.
1. 14,32,121
2. 69,05,070
3. 8,52,008
4. 35,14,100
5. 1,00,00,000
6. 5,00,05,000
7. 9,52,34,123
8. 7,86,00,506
13. Write the greatest and the smallest 6 digit numbers (without repeating a digit) from
the following digits.
1. 1,2,0,6,3,5
2. 6,3,0,1,2,8
3. 0,8,5,2,1,6
4. 7,5,8,2,9,4
5. 3,5,2,9,4,1
6. 1,9,8,7,6,3
14. Write the greatest and the smallest 7 digit numbers using all of the following digits.
You may repeat the digits.
1. 7,2,0,8,9,3
2. 6,3,8,9,7,1
3. 3,8,5,2,1,6
4. 0,2,3,8,9,6
5. 3,0,1,5,6,7
6. 2,1,9,5,7,8
15 Observe the pattern and write next three numbers.
1. 3,50,172 ; 3,50,272 ; 3,50,372 ; ___________;_____________;____________
2. 19,25,734 ; 19,35,734 ; 19,45,734;_________;_____________;____________
3. 71,98,421;71,88,421;71,78,421 ; __________;_____________;____________
4. 58,40,934;58,40,834;58,40,734; ___________;____________;_____________
INTERNATIONAL PLACE VALUE CHART.
 The international place value chart is used all over the world to maintain uniformity.
 In the international place value system, the periods are Ones, thousands and millions. Three
digts are placed in each period.
International Place Value Chart.
Period Millions
Thousands
Ones
s
Places Hundre Ten
Millio Hundred Ten
Thousan Hundre Ten One
d
Millio n
Thousan Thousan d
d
s
s
Million n
d
d
HM
TM
M
HTH
TTH
TH
H
T
O
1
3
7
2
5
8
0
9
5
One hundred thirty seven
Two hundred fifty eight thousand Ninety Five
million
So, 137,258,095 = One hundred thirty seven million, two hundred fifty eight thousand,
ninety five.
EXERCISE 1C
1.Write the following numbers in figures using the International place value system.
a) Four hundred ten thousand seven hundred nine.
b) Eight million five hundred one thousand six hundred nine.
c) Sixty three million seven thousand five hundred four.
d) One hundred thirteen million nine hundred seven thousand eight.
e) Seven hundred nine million fifty six thousand two hundred five.
f) Fifty six million.
g) Twenty five million two thousand three hundred five.
h) Five million two thousand thirty six.
i) Sixty two million two hundred five.
j) Twenty three million thirty six thousand five hundred six.
2. Write the following numbers in words using the International place value chart.
a) 7,258,963
b) 1,135,429
c) 95,736,210
d) 34,568,951
e) 987,606,789
f) 247,556,398
g) 756,438,942
h) 248,631,970
3. Rewrite the following numbers using Indian place value system.
a) Six hundred nine thousand five hundred two.
b) Twenty five million fifteen.
c) Eight million three thousand nine.
d) Thirty six million one hundred twenty thousand four.
4. Rewrite the following using International place value system.
a) Fifty six lakh two thousand seven hundred four.
b) Twenty eight lakh twenty five thousand fifty one.
c) Three crore nine lakh one thousand five hundred two.
d) Nineteen crore forty lakh six.
Exercise 1 D
 Choose the correct answer.
1. 10 millions = ________________ crore.
(a) 1
(b) 10
(c) 100
1
2
3
4
5
(d) 1000
2. 1000 = __________________ hundreds.
(a) 1
(b) 10
(c) 100
(d) 1000
3. 1 lakh = ________________ thousand.
(a) 1
(b) 10
(c) 100
(d) 1000
4. Face value of 9 in 94,58,63,215 is _____________.
(a) 9
(b) 90
(c) 9000
(d) 90,00,00,000
5. Place value of 0 in 70,86,24,314 is _______________.
(a) 10
(b) 1,00,00,000
(c) 0
(d) 1,00,000
6. Place value of 3 in 3,24,89,652 is ______________.
(a) 3
(b) 30,000
(c) 3,00,000
(d) 3,00,00,000
7. Standard form of 9,00,00,000 + 8,00,000 + 50,000 + 3,000 + 20 + 3 is
(a) 90,00,85,323
(b) 9,85,03,023
(c) 90,08,53,023
(d) 9,08,53,023
8. Difference between the place value of two 3’s in 31,16,365 is
(a) 29,99,700 (b) 30,30,700
(c) 29,29,700 (d) 29,00,700
9. The greatest 4 digit number using the digits 4,7,6 and 2 only once is
(a) 4762
(b) 6427
(c) 7624
(d) 7642
10. The greatest number among 37,189 ; 37,918 ; 37,819 and 37981 is
(a) 37,189
(b) 37,918
(c) 37,819
(d) 37,981
11. The smallest number among 6,17,081 ; 6,18,701 ; 6,17,801 and 6,10,781 is
(a) 6,17,081
(b) 6,18,701
(c) 6,17,801
(d) 6,10,781
12. The suceessor of 17,28,999 is
(a) 17,28,000
(b) 17,29,000
(c) 17,29,999 (d) 17,39,000
13. The predecessor of 4,36,000 is
(a) 4,36,001
(b) 4,35,990
(c) 4,36,999
(d) 4,35,999
14. The smallest 7 digit number using the digits 6,2,0,1,9,4,8 only once is
(a) 98,64,210
(b) 20,14,689
(c) 10,24,689 (d) 10,04,689
15. The greatest 7 digit number using the given digits 5,4,9,2 is
(a) 99,99,542
(b) 99,95,542 (c) 95,55,542 (d) 99,55,542
16. Three hundred sixty four thousand two hundred four can be written as
(a) 3,16,204
(b) 3,61,204
(c) 6,13,204
(d) 3,64,204
 ANSWERS
EXERCISE 1A
A.
CRORES
LAKHS
THOUSANDS
ONES
TC
C
TL
L
T.TH
TH
H
T
O
3
5
2
4
6
7
8
9
7
1
6
0
2
0
3
0
1
6
2
5
4
3
4
3
4
1
5
4
2
8
9
3
5
6
4
2
5
3
6
2
5
1
7
6
2
8
7
5
3
0
0
0
7
3
8
3
5
2
8
7
8
3
1
8
0
9
7
9
1
0
2
9
6
6
10
8
5
4
3
9
6
3
4
B.1. Seventy two lakh thirty eight thousand six hundred eighteen.
2. Sixty seven lakh eighty one thousand two hundred eighty five.
3. Thirty eight lakh fifty two thousand nine hundred six.
4. Two crore six lakh six hundred twelve.
5. Two crore seventy four lakh thirty eight thousand sixteen.
6. Forty three crore eleven lakh sixty four thousand six.
7. Two crore twenty six lakh eighteen thousand three hundred ninety six.
8. Sixteen crore seventeen lakh ninety thousand thirty four.
9. Seventy four lakh twenty five thousand six hundred thirty seven.
10. Forty three lakh sixty eight thousand two hundred fifty eight.
11. Three crore sixty nine lakh forty seven thousand eight hundred ninety one.
12. Two crore eighteen lakh forty five thousand six hundred seventy nine.
13. Thirty five lakh eighty four thousand two hundred seventeen.
14. Six crore twenty five lakh thirty thousand one hundred forty nine.
15. Eight crore twenty four lakh sixty two thousand one hundred fifty seven.
16. Thirty two crore fourteen lakh sixty two thousand one hundred ninety.
C. 1.72,37,479
(2) 37,28,272
(3) 92,78,318
4. 5,39,27,217
(5) 43,72,38,527
(6) 7,55,30,933
7. 67,00,00,090
(8) 50,00,90,075
(9) 70,05,00,000
10. 9,19,80,000
(11) 7,71,00,101
(12) 2,00,05,117
13. 5,50,50,050
(14) 81,60,307
(15) 6,06,60,066
16. 13,12,11,101
EXERCISE 1B
Q:1 a) 40,00,000
(b) 20,000
(c) 80,000
(d) 900
e) 4,00,00,000
(f) 3
Q:2 a) 60,00,00,000 (b) 6,000
(c) 6,00,000
(d) 600
e) 6,00,00,000
(f) 6,00,000
Q:3 7999200
Q:4 a) 3,00,000 + 80,000 + 2,000 + 800 + 60 + 5
b) 70,000 + 8,000 + 300 + 60 + 5
c) 1,00,000 + 70,000 + 8,000 + 300 + 20 + 8
d) 6,00,000 + 70,000 + 8,000 + 300 + 50 + 6
e) 3,00,000 + 50,000 + 6,000 + 200 + 10 + 8
f) 2,00,000 + 80,000 + 3,000 + 800 + 60 + 7
g) 20,00,000 + 8,00,000 + 30,000 + 1,000 + 600 + 20 + 8
h) 1,00,00,000 + 60,00,000 + 1,00,000 + 20,000 + 4,000 + 900 + 70 + 8
i) 4,00,00,000 + 20,00,000 + 9,00,000 + 700 + 80 + 1
j) 10,00,00,000 + 2,00,00,000 + 5,00,000 + 70,000 + 3000 + 400 + 70 + 1
k) 30,00,00,000 + 90,00,000 + 4,00,000 + 10,000 + 300 + 60 +7
l) 70,00,00,000 + 4,00,00,000 + 50,00,000 + 2,00,000 + 90,000 + 1,000+100+40+ 6
Q:5 a) 72,00,819
(b) 47,34,825
(c) 28,70,027
d) 80,00,789
(e) 37,98,071
(f) 8,79,86,897
g) 2,70,05,876
Q:6 a) <
(b) >
(c) <
(d) >
e) >
(f) >
(g) <
(h) <
5
8
6
8
5
Q:7 a) 31,20,567
(b) 17,38,758
(c) 45,69,308
d) 11,29,80,164
(e) 25,71,01,294
Q:8 a) 46,10,253
(b) 30,14,349
(c) 37,49,296
d) 25,18,90,314
(e) 3,01,45,678
Q:9 a) 87,35,952 < 87,36,952 < 87,65,952 < 87,85,952
b) 5,32,718 < 67,89,542 < 8,79,56,423 < 12,45,78,963
c) 27,93,465 < 28,63,246 < 2,04,05,060 < 3,56,52,595
d) 86,75,722 < 87,56,726 < 8,55,77,624 < 8,56,67,723
Q:10 a) 2,56,98,530 > 59,86,542 > 25,64,056 > 25,63,201
b) 45,31,071 > 44,52,700 > 4,52,687 > 5,26,781
c) 4,69,58,472 > 82,13,475 > 8,79,564 > 8,78,254
d) 79,84,668 > 78,96,467 > 76,49,866 > 74,68,969
Q:11 a) 42,57,199
(b) 17,35,001
(c) 8,10,310
d) 3,16,12,320
(e) 5,29,79,500
(f) 9,99,99,999
g) 7,00,22,112
(h) 5,12,34,001
Q:12 a) 14,32,120
(b) 69,05,069
(c) 8,52,007
d) 35,14,099
(e) 99,99,999
(f) 5,00,04,999
g) 9,52,34,122
(h) 7,86,00,505
Q:13 a) 653210 , 102356
(b) 863210 , 102368
c) 865210 , 102568
(d) 987542 , 245789
e) 954321 , 123459
(f) 987631 , 136789
Q:14 a) 9987320 , 2003789
(b) 9987631 , 1136789
c) 8865321 , 1123568
(d) 9986320 , 2003689
e) 7765310 , 1003567
(f) 9987512 , 1125789
Q:15 a) 3,50,472 ; 3,50,572 ; 3,50,672
(b) 19,55,734 ; 19,65,734 ; 19,75,734
c) 71,68,421 ; 78,58,421 ; 78,48,421
(d) 58,40,634 ; 58,40,534 ; 58,40 434
EXERCISE 1 C
Q:1 a) 410,709
(b) 8,501,609
(c) 63,007,504
d) 113,907,008
(e) 709,056,205
(f) 56,000,000
g) 25,002,305
(h) 5,002,036
(i) 62,000,205
j) 23,036,506
Q:2 a) Seven million two hundred fifty eight thousand nine hundred sixty three.
b) One million one hundred thirty five thousand four hundred twenty nine.
c) Ninety five million seven hundred thirty six thousand two hundred ten.
d) Thirty four million five hundred sixty eight thousand nine hundred fifty one.
e) Nine hundred eighty seven million six hundred six thousand seven hundred
eighty nine.
f) Two hundred forty seven million five hundred fifty six thousand three hundred
ninety eight.
g) Seven hundred fifty six million four hundred thirty eight thousand nine hundred
forty two.
h) Two hundred forty eight million six hundred thirty one thousand nine hundred
seventy.
Q:3 a) Six lakh nine thousand five hundred two.
b) Two crore fifty lakh fifteen.
c) Eighty lakh three thousand nine.
d) Three crore sixty one lakh twenty thousand four.
Q:4 a) Five million six hundred two thousand seven hundred four.
b) Two million eight hundred twenty five thousand fifty one.
c) Thirty million nine hundred one thousand five hundred two.
d) One hundred ninety four million six.
EXERCISE 1 D
Q:1 (a)
Q:2 (b)
Q:5 (c)
Q:6 (d)
Q:9 (d)
Q:10 (d)
Q:13 (d)
Q:14 (c)
Q:3 (c)
Q:4 (a)
Q:7 (d)
Q:8 (a)
Q:11 (d)
Q:12 (b)
Q:15 (a)
Q:16 (d)
Ch-2 OPERATIONS ON LARGE NUMBERS
Addition :
Rule : (1) Arrange the given numbers in columns and add from extreme right.
(2) Take the carry over if any to the next column to the left and add it along with
the digits in that column.
Terms used in Addition
a) The numbers to be added are called addends.
b) The result of addition is called the sum.
71
Addend
+ 25 Addend
96
Sum
EXERCISE 2 A
Q:1
a)
585874
b)
3612375
+345678
+ 5732163
c)
123456
789987
+654321
d)
1122334
4556677
+8899112
e)
4056708
9102340
+ 218795
f)
2626520
5252620
+ 456789
g)
3045678
2908754
+ 321987
h)
234567
765432
+ 123456
Q:2 Arrange in the columns and odd.
a) 36,75,218 + 18,76,984
b) 62,57,173 + 47,53,619
c) 7,54,36,948 + 39,67,489
d) 3,82,56,714 + 27,84,236
e) 1,34,52,672 + 2,43,64,739 + 93,18,453
f) 4,74,36,127 + 2,36,55,438 + 53,16,883 + 20,71,631
EXERCISE 2 B
Q:1 Ram bought two houses, one for Rs. 6,16,435 and other for Rs.4,58,236. How much
money did he spend altogether?
Q:2 Find the sum of the largest 7 digit and the largest 6 digit number.
Q:3 A bulb manufacturer produces 1,99,725 ; 10,25,950 and 4,55,950 bulbs in three
months. How many bulbs does he produce in these three months?
Q:4 The population of town A is 82,57,865, the population of town B is 50,39,831 and
the population of town C is 4,38,651. Find the total population of the three towns.
Q:5 In a public library there are 72,19,256 books on Literature, 6,19,005 Mathematics
and 25,16,856 books on other subjects. Find the total number of books in the
library.
Q:6 People of three Villages had collected Rs.96,43,210 ; Rs.12,45,896 and Rs.
75,42,639 for earthquake victims. Find the total money collected.
SUBTRACTION
 If we have to determine the difference of two numbers, we always subtract the smaller
number from the bigger number.
 To find the difference we proceed as follows.
i) Arrange the given numbers in columns.
ii) Go on subtracting column wise from ones column,borrowing if necessary
from the next column to the left.
Terms Used in Subtraction
1.Minuend : The larger number from which we subtract the smaller number is called
minued.
2.Subtrahend : The smaller number which is subtracted from the larger number is called
Subtrahend.
3.Difference : The result we obtain after subtraction is called the difference
between the given numbers.
8 7 Minuend
- 5 6 Subtrahend
3 1 Difference
EXERCISE 2 C
Q:1
a)
8005007
b)
5030469
-3026024
-2982149
c)
8234962
- 2458654
d)
970 0770
- 8888888
e)
8912345
-6789123
f)
3003003
-1234567
g)
10000000
- 1234567
h)
98765432
-12345678
i)
81008108
-12345678
j)
1010101010
- 101010101
Q : 2 Arrange in the columns and subtract.
a) 36,98,367 from 65,47,812
(b) 27,85,745 from 78,56,429
c) 63,54,724 from 74,56,789
(d) 3,65,84,722 from 5,68,42,189
e) 5,86,92,456 from 7,58,96,125 (f) 4,85,96,235 from 9,85,64,723
g) 9,58,47,624 – 4,58,62,375
(h) 56,89,237 - 1,24,568
i) 5,69,85,245 – 2,45,89,626
(j) 60,22,55,524 – 7,89,54,222
EXERCISE 2 D
Q : 1 There were 5,47,546 mangoes in a godown. If 3,12,764 were rotten, How many
mangoes were good?
Q : 2 An exhibition had two gates A and B. In a month 6,78,54,923 people entered
through gate A and 9,35,48,697 people entered through gate B. How many more
people entered through gate B than gate A?
Q : 3 In an examination 5,67,53,951 candidates appeared. Out of these 2,98,54,632
passed. How many candidates failed in the examination?
Q : 4 Total population of a town is 18,39,150. If the number of females is 8,00,637.
Find the number of males in the town.
Q : 5 A factory produces 57,86,321 gas stones in a particular year and 7,89,75,324 in
the following year. Find the increase in production of gas stoves.
Q : 6 Mrs. Patnaik bought a computer for Rs. 32,555 and a refrigerator that was priced
Rs.7920 less than the computer. How much did she pay for the refrigerator.
Q : 7 A merchant had 78,543 sacks of potates. On Monday he sold 3748 sacks and on
Tuesday he sold 5637 sacks. How many sacks did he sell in all these two days?
How many sacks were left?
MULTIPLICATION
 Following terms are used in Multiplication.
1.Multiplicand : The number to be multiplied is called the multiplicand.
2.Multiplier : The number by which we multiply is called the multiplier.
3.Product : The result we obtain after the multiplication is called the product.
E.g.: 6 2 Multiplicand
X 5 Multiplier
3 1 0 Product
Properties of Multiplication
1.Order Property : The product of two numbers do not change when the order of the
number is changed. For Eg. 5 X 8 = 40 and 8 X 5 = 40
So, 5 X 8 = 8 X 5
2.Multiplicative property of 1 : The product of a number and 1 is the number itself .
For eg. 27 X 1 = 27, 159 X 1 = 159 , 1234 X 1 = 1234
3.Multiplicative property of 0 : The product of a number and 0 is 0.
For eg. 199 X 0 = 0, 5432 X 0 = 0
EXERCISE 2 E
Q : 1 Using the properties of Multiplication, Fill in the blanks.
a) 783526 X 7158 = 7158 X ___________.
b) 781352 X 0 = ____________.
c) 735616 X 1 = ________________.
d) 536 X ______________ = 7182 X 536
e) 683516 X _________________ = 683516
f) 715898 X _______________ = 0
g) _____________ X 53899 = 53899
Q : 2 Multiply.
a) 756 X 60
d) 32,156 X 70
g) 7,30,421 X 50
j) 4,32,904 X 20
(b) 3874 X 80
(e) 86,435 X 50
(h) 3,55,321 X 40
(c) 43,256 X 30
(f) 1,56,752 X 30
(i) 1,12,657 X 90
Q : 3 Multiply.
a) 21,355 X 300
d) 30,652 X 400
g) 18,553 X 900
(b) 92,321 X 700
(e) 93,256 X 600
(h) 20,658 X 800
(c) 19,225 X 500
(f) 25,252 X 200
Q : 4 Multiply.
a) 3261 X 4000
d) 3956 X 6000
g) 3525 X 7000
(b) 2876 X 9000
(e) 5648 X 2000
(h) 8259 X 3000
(c) 3381 X 5000
(f) 4268 X 8000
EXERCISE 2 F
Q : 1 Find the product.
a)
3804
X
26
d)
27806
X 989
Q : 2 Find the product.
a) 7225 X 167
d) 8326 X 778
g) 6009 X 475
j) 6019 X 247
b)
1267
X 157
e)
X
53805
458
(b) 1624 X 333
(e) 7059 X 263
(h) 2709 X 819
(k) 5250 X 318
c)
3924
X 641
f)
X
87012
825
(c) 2697 X 812
(f) 6240 X 742
(i) 4709 X 358
(l) 2688 X 282
EXERCISE 2 G
Q : 1 Cost of a table is Rs. 5,975. What is the cost of 864 such tables?
Q : 2 A truck can carry 4582 Kg of tomatoes. How much can 758 such trucks carry?
Q : 3 A bundle to rope measures 4,587 meters. How much rope will be there in 562
such bundles?
Q : 4 A Shopkeeper sells 459 toys every week. How many toys will be sold in 397
weeks?
Q : 5 A factory produces 4,527 bolts in a day. How many bolts will be produced in a
normal year?
DIVISION
Terms used in Division :
1.Dividend : The number to be divided is called the dividend.
2. Divisor : The number by which we divide the dividend is called the divisor.
3. Quotient : The result of division is called quotient.
4. Remainder : The number which is left undivided is called the remainder.
Divisor
9
5|47
-45
02
Quotient
Dividend
Remainder
PROPERTIES OF DIVISION
1.The following relationship holds good in a division :
Dividend = Quotient X Divisor + remainder
This relationship is used to check the division.
2.When a number expect 0 is divided by itself the quotient is 1
For Eg : 25 / 25 = 1,
339 / 339 = 1
3. When a number is divided by itself, the quotient is 1.
For Eg : 29 / 1 = 29
909 / 1 = 909
4. When 0 is divided by a number expect 0, the quotient is 0.
For Eg : 0 / 23 = 0
0 / 157 = 0
5. A number cannot be divided by 0.
EXERCISE 2 H
Q : 1 Fill in the blanks.
a) 43 / 43 = _________________
c) 1234 / 1 = _________________
e) 182115 / 1 = _______________
g) 781266 / 781266 = ____________
i) 156826 / 156826 = ____________
(b) 126 / 1 = ___________________
(d) 0 / 9456 = __________________
(f) 0 / 6549 = __________________
(h) 0 / 987654 = ________________
(j) 3672681 / 1 = _______________
Q : 2 Write down the quotient and the remainder without actual division.
a) 2600 / 100
(b) 2,54,789 / 10
c) 5,12,689 / 1000
(d) 2,34,509 / 100
e) 65,000 / 1000
(f) 7,53,021 / 10
g) 62,15,873 / 100
(h) 58,962 / 1000
i) 86,742 / 10
(j) 2,36,589 / 1000
k) 1,90,029 / 100
(l) 12,056 / 1000
Q : 3 Find the dividend.
a) Quotient = 938 ; Remainder = 25 ; Divisor = 55
b) Quotient = 5105 ; Remainder = 59 ; Divisor = 126
c) Quotient = 445 ; Remainder = 1 ; Divisor = 19
d) Quotient = 998 ; Remainder = 43 ; Divisor = 26
e) Quotient = 3020 ; Remainder = 18 ; divisor = 33
f) Quotient = 135 ; Remainder = 47 ; Divisor = 84
EXERCISE 2 I
Q : 1 Divide and check your answer
a) 1800 / 12
(b) 5328 / 51
(c) 1825 / 23
d) 14202 / 16
(e) 30395 / 27
(f) 87,486 / 26
g) 45,238 / 18
(h) 53,805 / 58
(i) 63,000 / 66
j) 87,012 / 45
(k) 75378 / 71
(l) 89380 / 59
(m) 39476 / 69
(n) 51615 / 55
EXERCISE 2 J
Q : 1 45,000m of wire is to be packed in bundles. If each bundle contains 50m of wire.
How many bundles will be made?
Q : 2 14850 books are packed equally in 25 boxes. Find the number of books in each
box.
Q : 3 The cost of 35 boxes is Rs.52500. What is the cost of one box?
Q : 4 A contractor paid Rs.11340 equally to 84 workers. How much money did each
worker received?
Q : 5 The cost of 25 games is Rs. 1,23,125. Find the cost of one game?
Q : 6 75 Biscuits are to be packed in a polypack. How many poly – pack are required to
pack 2,22,075 biscuits?
EXERCISE 2 K
Choose the correct answer.
1.10,10,940 + ___________ = 10,10,940
(a) 0
(b) 1
(c) 10
(d) 100
2. 13,56,478 + ______________ = 13,56,478
(a) 1
(b) 10
(c) 0
(d) 100
3. 4,81,50,951 + 1000 = ___________________.
(a) 4,84,60,951
(b) 4,81,51,951
(c) 4,81,50,851
(d) 4,81,50,961
4. 7463 X 1000 = _______________
(a) 74600
(b) 74630
(c) 746300
(d) 7463000
5. 7,45,986 X ______________ = 7,45,986
(a) 0
(b) 1
(c) 10
(d) 100
6. _____________________ X 48975 = 0
(a) 0
(b) 1
(c) 10
(d) 100
7. 47 X 63 = _____________ X 47
(a) 69
(b) 39
(c) 36
(d) 63
8. 896 X 100 = ______________
(a) 890
(b) 8960
(c) 89600
(d)896000
9. 73508 / 100 gives
(a) Q = 735, R = 80
(b) Q = 735, R = 8
(c) Q = 7350, R = 8
(d) Q = 37, R = 508
10. 800196 / 1000 = _________________
(a) Q = 80, R = 196
(b) Q = 8001, R = 96 (c) Q = 800, R = 196
(d) Q = 8000, R = 196
11. 19254 / 19254 = _____________
(a) 1
(b) 1
(c) 19254
(d) none
12. 0 / 73 = _______________
(a) 1
(b) 1
(c) 73
(d) 37
ANSWERS
EXERCISE 2 A
Q : 1 a) 931552
d) 14578123
(g) 6276419
Q : 2 a) 55,52,202
d) 4,10,40,950
EXERCISE 2 B
1) 10,74,671
4) 1,37,36,347
(b) 9344538
(e) 13377843
(h) 1123455
(b) 1,10,10,792
(e) 4,71,35,864
(2) 1,09,99,998
(5) 1,03,55,117
(c) 1567764
(f) 8335929
(c) 7,94,04,437
(f) 7,84,80,079
(3) 16,81,625
(6) 1,84,31,745
EXERCISE 2 C
Q : 1 a) 49,78,983
(b) 20,48,320
(c) 57,76,308
d) 8,11,882
(e) 21,23,222
(f) 17,68,436
g) 87,65,433
(h) 8,64,19,754
(i) 6,86,62,430
j) 90,90,90,909
Q : 2 a) 28,49,445
(b) 50,70,684
(c) 11,02,065
d) 2,02,57,467
(e) 1,72,03,669
(f) 4,99,68,488
g) 4,99,85,249
(h) 55,64,669
(i) 3,23,95,619
j) 52,33,01,302
EXERCISE 2 D
1) 2,34,782
(2) 2,56,93,774
(3) 2,68,99,319
4) 10,38,513
(5) 7,31,89,003
(6) Rs. 24,635
7) 9385 ; 69,158
EXERCISE 2 E
Q : 1 a) 783526
(b) 0
(c) 781352
(d) 7182
e) 1
(f) 0
(g) 1
Q : 2 a) 45360
(b) 309920
(c) 1297680
(d) 2250920
e) 4321750
(f) 4702560
(g) 36521050 (h) 14212840
i) 10139130
(j) 8658080
Q : 3 a) 6406500
(b) 64624700 (c) 9612500
(d) 12260800
e) 55953600
(f) 5050400
(g) 16697700 (h) 16526400
Q : 4 a) 13044000
(b) 25884000 (c) 16905000 (d) 23736000
e) 11296000
(f) 34144000 (g) 24675000 (h) 24777000
EXERCISE 2 F
Q : 1 a) 98,904
(b) 1,98,919
(c) 25,15,284 (d) 27,50,0134
e) 2,46,42,690 (f) 7,17,84,900
Q : 2 a) 12,06,575
(b) 5,40,792
(c) 21,89,964 (d) 64,77,628
e) 18,56,517
(f) 46,30,080
(g) 28,54,275 (h) 22,18,671
i) 16,85,822
(j) 14,86,693 (k) 16,69,500 (l) 7,58,016
EXERCISE 2 G
1) 51,62,400
(2) 34,73,156
(3) 26,00,829
4) 1,82,223
(5) 16,52,355
EXERCISE 2 H
Q : 1 a) 1
(b) 126
(c) 1234
(d) 0
e) 182115
(f) 0
(g) 1
(h) 0
i) 1
(j) 3672681
Q : 2 a) Q = 26
R=0
(b) Q = 25478
R=9
c) Q = 512
R = 689
(d) Q = 2345
R=9
e) Q = 65
R=0
(f) Q = 75302
R=1
g) Q = 62158
R = 73
(h) Q = 58
R = 962
i) Q = 8674
R=2
(j) Q = 236
R = 589
k) Q = 1900
R = 29
(l) Q = 12
R = 56
Q : 3 a) 51615
(b) 643289
(c) 8456
d) 25991
(e) 99678
(f) 11387
EXERCISE 2 I
a) Q = 150
R=0
c) Q = 79
R=8
e) Q = 1125 R = 20
g) Q = 2513 R = 4
i) Q = 954
R = 36
(b) Q = 104
(d) Q = 887
(f) Q = 3364
(h) Q = 927
(j) Q = 1933
R = 24
R = 10
R = 22
R = 39
R = 27
k) Q = 1061 R = 47
m) Q = 572
R=8
EXERCISE 2 J
1) 900
4) Rs. 135
EXERCISE 2 K
1) a
6) a
(l) Q = 1514
(n) Q = 938
(2) 594
(5) 4925
(2) c
(7) d
R = 54
R = 25
(3) Rs. 1500
(6) 2961
(3) c
(8) c
CH-11 ROMAN NUMERALS
* There are seven distinct symbols in Roman system. They are
Roman Numerals
I
V
X
L
C
D
Hindu Arabic Numerals
1
5
10
50
100 500
(4) d
(9) b
(5) b
(10) c
M
1000
 There is no zero in the Roman System.
 This system has no place value system.
RULES
1) Repetition of a symbol means addition.
For Eg. 111 = 1 + 1 + 1 = 3
XXX = 10 + 10 + 10 = 30
CC = 100 + 100 = 200
 Repetition is not allowed more than 3 times.
 V , L & D are never repeated.
2) If a smaller number is written to the right of a greater numberal then the smaller is added to
the larger one.
For Eg. VII = 5 + 1 + 1 = 7
XI = 10 + 1 = 11
LXXX = 50 + 10 + 10 +10 = 80
CLX = 100 + 50 + 10 = 160
3) If a smaller numeral is written to the left of a larger numeral the smaller is always
subtracted from the larger one.
For Eg. IV = 5 – 1 = 4
IX = 10 – 1 = 9
XL = 50 – 10 = 40
XC = 100 – 10 = 90
 The numerals V , L and D are never subtracted.
 I is never written to the left of L, C and D.
ROMAN NUMERALS FROM 1 TO 200
1
I
51
LI
2
II
52
LII
3
III
53
LIII
4
IV
54
LIV
5
V
55
LV
6
VI
56
LVI
7
VII
57
LVII
8
VIII
58
LVIII
9
IX
59
LVIX
10
X
60
LX
11
XI
61
LXI
12
XII
62
LXII
13
XIII
63
LXIII
14
XIV
64
LXIV
15
XV
65
LXV
16
XVI
66
LXVI
17
XVII
67
LXVII
18
XVIII
68
LXVIII
19
XIX
69
LXIX
20
XX
70
LXX
21
XXI
71
LXXI
22
XXII
72
LXXII
23
XXIII
73
LXXIII
24
XXIV
74
LXXIV
25
XXV
75
LXXV
26
XXVI
76
LXXVI
27
XXVII
77
LXXVII
28
XXVIII
78
LXXVIII
29
XXIX
79
LXXIX
30
XXX
80
LXXX
31
XXXI
81
LXXXI
32
XXXII
82
LXXXII
33
XXXIII
83
LXXXIII
34
XXXIV
84
LXXXIV
35
XXXV
85
LXXXV
36
XXXVI
86
LXXXVI
37
XXXVII
87
LXXXVII
38
XXXVIII
88
LXXXVIII
39
XXXIX
89
LXXXIX
40
XL
90
XC
41
XLI
91
XCI
42
XLII
92
XCII
43
XLIII
93
XCIII
44
XLIV
94
XCIV
45
XLV
95
XCV
46
XLVI
96
XCVI
47
XLVII
97
XCVII
48
XLVIII
98
XCVIII
49
XLIX
99
XCIX
50
L
100
C
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
CI
CII
CIII
CIV
CV
CVI
CVII
CVIII
CIX
CX
CXI
CXII
CXIII
CXIV
CXV
CXVI
CXVII
CXVIII
CXIX
CXX
CXXI
CXXII
CXXIII
CXXIV
CXXV
CXXVI
CXXVII
CXXVIII
CXXIX
CXXX
CXXXI
CXXXII
CXXXIII
CXXXIV
CXXXV
CXXXVI
CXXXVII
CXXXVIII
CXXXIX
CXL
CXLI
CXLII
CXLIII
CXLIV
CXLV
CXLVI
CXLVII
CXLVIII
CXLIX
CL
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
CLI
CLII
CLIII
CLIV
CLV
CLVI
CLVII
CLVIII
CLIX
CLX
CLXI
CLXII
CLXIII
CLXIV
CLXV
CLXVI
CLXVII
CLXVIII
CLXIX
CLXX
CLXXI
CLXXII
CLXXIII
CLXXIV
CLXXV
CLXXVI
CLXXVII
CLXXVIII
CLXXIX
CLXXX
CLXXXI
CLXXXII
CLXXXIII
CLXXXIV
CLXXXV
CLXXXVI
CLXXXVII
CLXXXVIII
CLXXXIX
CXC
CXCI
CXCII
CXCIII
CXCIV
CXCV
CXCVI
CXCVII
CXCVIII
CXCIX
CC
EXERCISE 11 A
Q :1 Write the Roman numeral for each of the following Hindu-Arabic Numeral.
a) 200
(b) 197
(c) 184
(d) 171
e) 136
(f) 115
(g) 109
(h) 105
i) 99
(j) 85
(k) 63
(l) 42
m) 37
(n) 29
(o) 19
(p) 13
Q : 2 Write the Hindu – Arabic Numeral for each of the following Roman numerals.
a) CXCIX
(b) CXCVIII (c) CLXXVI
(d) CLXII
e) CLVIII
(f) CXXXIX
(g) CXVI
(h) CIV
i) LXXXVI
j) XCVIII
(k) LVII
(l) XLV
Q : 3 Fill in the blanks with > or <.
a) XL __________ XXXIX
c) XLII _________ LXI
e) LXXV ___________ LXIX
g) C ________L
i) C __________XC
Q : 4 Match
1. 19
2. 27
3. 32
4. 63
5. 85
6. 99
7. 152
8. 189
9. 161
10. 134
(b) LX _________ XL
(d) XLIX _________ LIX
f) LXXIX _________ XLVIII
h) XC ____________ LXXXVIII
j) XC ____________ XLIX
a. LXIII
b. LXXXV
c. CLII
d. XIX
e. XCIX
f. CLXI
g. XXVII
h. CXXXIV
j. CLXXXIX
j. XXXII
EXERCISE 11 B
Q : 1 Choose the correct answer.
1. LXIX is equivalent to
(a) 49
(b) 59
(c) 69
(d) 79
2. CXLV is equal to
(a) 150
(b) 145
(c) 445
(d) 175
3. Which of the following is incorrect?
(a) XV
(b) VX
(c) XXV
(d) XXXV
4. In Roman numeral 137 is written as
(a) CVIIXXX
(b) XXXVIII
(c) CXVIII
(d) CXXXVII
ANSWERS
EXERCISE 11 A
Q : 1 a) CC
e) CXXXVI
i) XCIX
m) XXXVII
Q : 2 a) 199
e) 158
(b) CXCVII
(f) CXV
(j) LXXXV
(n) XXIX
(b) 198
(f) 139
(c) CLXXXIV
(d) CLXXI
(g) CIX
(h) CV
(k) LXIII
(l) XLII
(o) XIX
(p) XIII
(c) 176
(d) 162
(g) 116
(h) 104
i) 86
Q : 3 a) >
f) >
Q : 4 (1) d
(6) e
(b) >
(g) >
(2) g
(7) c
(j) 98
(c) <
(h) >
(3) j
(8) i
(k) 57
(d) <
(i) >
(4) a
(9) f
(l) 45
EXERCISE 11 B
(1) c
(2) b
(3) b
(4) d
(e) >
(j) >
(5) b
(10) h
CH : 21
BASIC GEOMETRICAL CONCEPTS
1. POINT : A small dot made by a sharp pencil on a piece of paper represents a point.

A
 A point has no length no breath and no thickness.
 It has only position.
 It is represented by capital letters such as A, B, C, X, Y, Z etc.
2.LINE SEGMENT : The straight path between two given points is called line
segment.
 A line segment has a fixed length.
 A line segment AB is denoted as AB.
 Points A & B are end points of AB.
 Line segment AB is same as BA.
3.LINE : A line segment extended endlessly in both the directions is called a line.
 It has no end points.
 It is denoted by AB.
 AB is same as BA.
 A line has no definite length.
4. RAY : A line segment extended endlessly in one direction is called a Ray.
 It has one end point. In the fig.A is the end point of Ray AB. It is also called the initial
point of AB.
 It is denoted as AB.
 It has no definite length.
 Ray AB is different from BA.
5. INTERSECTING LINES : When two lines meet at a point, then they are called intersecting
lines and the point at which they meet is called point of intersection.
Here AB and CD are intersecting
Lines and O is the point of intersection.
6. COLLINEAR POINTS: When three or more points lie on the same line, then they are said to be
collinear.
In the fig A, B, C are collinear but
D, E, F are not collinear.
EXERCISE 21 A
Q : 1 Classify the following as Point, Ray, Line and Line Segment.
Q : 2 Name the points marked between X and Y.
Q : 3 Name all the line segment in the following figure.
Q : 4 Name the line segments in the following figure.
Q : 5 In the figure name the following.
a) 4 line segments
b) 3 rays
c) 2 lines
d) 4 collinear Points
Q : 6 In the figure name
a) 2 Pair of intersecting lines
b) 4 collinear points
c) 3 non collinear points.
Q : 7 Fill in the blanks.
1) A line segment has _____________________ end points.
2) A ray has ___________________ end point.
3) A ____________________ has a fixed length.
4) A ________________________ have no fixed length.
5) A __________________________ can be extended on both sides.
6) Point at which two lines meet is called _________________________.
EXERCISE 21 B
A. Measure each of the following line segments.
B. Draw line segments of following lengths.
1) 2.3 cm
(2) 4.7 cm
4) 9.7 cm
(5) 5.8 cm
7) 8.3 cm
(8) 3.4 cm
C. Choose the correct option.
1. A line has _______________ end points.
a) 1
b) 2
c) 3
d) no
2. A ray has _______________ end points.
a) 1
b) 2
c) 3
d) no
3. Which of the following has a definite length?
a) Point
b) Line
c) Line segment
d) Ray
(3) 10.7cm
(6) 8 cm
(9) 7.9 cm
4. A geometrical figure which has no size but has position is:
a) Line
b) angle
c) Point
d) ray
5. A Line Segment has __________ end points.
a) 1
b) 2
c) 3
d) 4
ANSWERS
EXERCISE 21 A
Q : 1 a) Point L
(b) Line segment XY
(c) Point R
d) Line RS
(e) Line MN
(f) Ray AB
Q : 2 P,B,Q,D & F
Q : 3 PQ, PR, PT, PS, QR, QT, QS, RT, RS, TS
Q : 4 i) AB, BC, CD, DA
ii) PQ, QR, RS, ST, TP
iii) MN, NO, OS, SP, PQ, QM
Q : 5 a) HF, FD, CD, DE
(b) FH , CA, CB
Q : 6 a) (XW and PS) (QR and TU)
(b) X, P, Q and W
Q : 7 a) two
d) Line and Ray
EXERCISE 21 B
A. 1) 8 cm
4) 3.6 cm
C. 1) d
(2) a
(b) one
(e) Line
(c) Line segment
(f) Point of intersection
(2) 4.8 cm
(5) 12.9 cm
(3) c
(3) 6.4 cm
(4) c
**************
(5) b
(c) B, C, D, E
(c) T, Q, R