Page 1
Preface
A good workbook enables the students to practice more and develop skills for
better understanding of basic mathematical concepts. This book is an attempt in
that direction.
The aim of this workbook is to elicit the complete involvement of the students,
help the students to do neat work in the prescribed time, encourage students to
develop their thinking and reasoning abilities, develop a logical and analytical
temper, and aid in their self-assessment.
The workbook is designed to make students realize that “Math is fun” and that
it has wide ranging applications in our day – to – day activities. Each concept
has been supported by various concept related activities. These workbooks will
supplement the work done in the notebooks and lead to an increase in the
quality.
Page 2
ACNOWLEDGEMENT
Our heartfelt gratitude to our Rector and Principal
Rev. Fr. Babu Varghese and Vice- Principal
Rev. Fr. Bhushan Barla for their constant guidance and
encouragement in bringing out this workbook.
Our sincere thanks to the Coordinator – Mathematics
Department, Mr. Baiju Mathew for his invaluable support and
guidance.
We gratefully acknowledge the support of our parents and look
forward to your valuable suggestions for improvement.
LIGY SEBASTIAN TESSY PAUL
STELLA JOSE VIMAL MARIA TITUS
DEPARTMENT OF MATHEMATICS
DON BOSCO SCHOOL, ALAKNANDA
NEW DELHI - 110019
Page 3
CONTENTS
1. NUMBERS AND NUMERATION
2. ROMAN NUMERALS
3. FOUR FUNDAMENTAL OPERATIONS
4. UNITARY METHOD
5. PRIME AND COMPOSITE NUMBERS
6. H.C.F AND L.C.M
7. FRACTIONS
Page 4
NUMBERS AND NUMERATION
I. Check the following number name, If it is wrong put a (X) and write the correct
answer in the column ( see the example)
Number Number
Name
Correction
Columns
Number Number Name Correction
Columns
11 Eleven 9 Nine
12 Twelfe 72 Seventy two
13 Thirteen 90 Ninty
14 Fourteen 26 Twenty six
15 Fifeteen 67 Sixtiseven
16 Sixteen 43 Fourthree
17 Sefevteen 52 Fifty-two
18 Eighteen 99 Nintnine
19 Nineteen 100 Hundred
20 Twenti 1000 Thoushand
II. Write the numeral/ write figures.
NUMBER NAME NUMBER
1 Eight lakh forty thousand
2 One crore
3 Two thousand four hundred nineteen
4 Four lakh two thousand seven hundred ninety
5 Eight lakh four thousand forty
6 Five thousand fourteen
7 Twenty crore forty thousand
8 Three lakh forty thousand
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III. Write the number names.
48,715
___________________________________________________________________________
__________________________________________________________________________
1,15,004
___________________________________________________________________________
___________________________________________________________________________
24,00,237
___________________________________________________________________________
___________________________________________________________________________
90,05,005
___________________________________________________________________________
___________________________________________________________________________
8,14,19,213
___________________________________________________________________________
___________________________________________________________________________
3,00,100
___________________________________________________________________________
___________________________________________________________________________
17,14,801
___________________________________________________________________________
___________________________________________________________________________
9,01,01,100
___________________________________________________________________________
___________________________________________________________________________
5
Page 6
IV. Put commas in Indian system and in international system and write the place value of
the squared digits.
Number Number in
Indian system
Place value Number in
international
system
Place Value
1 4 3 5 8 2
2 1 4 5 6 2 9
3 7 8 9 3
4 1 4 0 7
5 9 0 2 1 0 4 0
6 3 6 8 9 5 1 2
7 4 5 0 8 2 9
8 3 5 8 4 7 2 1 0 0
9 8 4 9 2 7 5
10 1 1 3 2 4 0 1
V. Write the number name in both Indian system and international system.
Indian System International System
13489
895345
97359823
459723
100700
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VI. Write in ascending order.
a) 21375; 1375; 375; 921375
Ascending order__________________________________________________________
b) 1375; 7375; 5375; 9375;
Ascending order____________________________________________________________
VII. Write in descending order.
a) 20175; 14875; 4875; 2375
Descending order_____________ _____________________________________________
b) 480300; 418300; 481003; 481303
Descending order___________________________________________________
VII. Write in expanded from.
14893
__________________________________________________________________________
308918
___________________________________________________________________________
1500095
__________________________________________________________________________
912010
___________________________________________________________________________
7
Page 8
MENTAL MATHS [Teacher should read out the number]
Write the number name and enter the number in the place value chart given below.
1. ___________________________________________________________________
2. ___________________________________________________________________
3. ___________________________________________________________________
4. ___________________________________________________________________
5. ___________________________________________________________________
T.TH TH H T O
THOUSANDS ONES
8
Page 9
ROMAN NUMERALS
I. Write the Roman numerals from 1 to 100.
I XI XLI LXI
II LII XCII
XXIII
LXXIV
XXXV
LXVI
VII LXXXVII
XCVIII
XIX LIX
XXX XL L LXXX XC C
II. Write the Roman numerals for the following numbers. [and also colour the
numerals in the above grid].
9 ___________________ 73 ___________________
14 ___________________ 89 ___________________
39___________________ 90___________________
40 ___________________ 95 ___________________
49___________________ 97 ___________________
51___________________ 99 ___________________
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Page 10
III. Write the Hindu Arabic numerals, perform the operation, write the answer in
Hindu Arabic numerals and Roman numerals.
Roman Numeral Hindu Arabic
Numeral
Hindu Arabic
numeral
Roman Numeral
XXVIII + XXVII
LXXXIII – XLVI
VI x V
XXV ÷ V
LXXX ÷ VIII
IX x VI
XXV + XL
LXII + XII
LXX + XXX
L - XXXIX
28 + 27 55 LV
IV. Fill in the blanks:
1. Symbols _________, ____________ and _____________ are never repeated.
2. Symbol „I‟ can be subtracted from _______________ and ________________ only
3. The symbol „X‟ can be subtracted form ___________________ and ______________ only
4. The symbols ____________________, _________________ and ________________ are
never subtracted.
5. A symbol is never repeated more than _____________________ times.
6. There are ________________ symbols in Roman Numerals.
10
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Activity
1. Correct the below statement in three different ways.
a. By moving one stick b. By removing one stick
c. By adding one stick
2. Arrange five match sticks to make fourteen.
○ ○ ○ ○ ○
X I + I = X
11
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Addition and Subtraction
Add
4 3 8 9
+ 5 2 0 1
_____________
Subtract
8 9 3 5
_ 4 5 1 4
____________
8 9 3 5 is the MINUEND
4 5 1 4 is the SUBTRAHEND
I. Add:-
a) 9 4 3 0 1 9 , 5 0 2 1 , and 4 1 5
b) 5 4 1 6 7 , 2 1 6 5 and 9 9 9 9
4 3 8 9 and 5 2 0 1 are
ADDENDS.
Is the sum.
is the
Difference.
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II. Find the difference.
a) 1 5 6 3 3 , 8 8 5 0
b) 4 2 1 0 2 , 7 4 3 6
c) 8 3 1 6 5 , 8 5 0 7
III. Find the missing digits.
a) b)
+ +
c) d)
– –
8 2 4 8
4
5
5 2
1
4
3
1
4
8 2
5
2 3 2
9
4
7
8
1 3 2
13
Page 14
MULTIPLICATION TABLES
Write and learn tables from 11 to 15
11 12 13 14 15
1
2
3
4
5
6
7
8
9
10
11
12
MENTAL MATHS
(Write the answers and then check from the above table.)
11 x 8 = ______________ 13 x 7 = ______________ 11 x 4 = ________________
12 x 9 = ______________ 14 x 5 = ______________ 12 x 7 = ________________
11 x 5 = ______________ 14 x 9 = ______________ 13 x 9 = ________________
13 x 4 = ______________ 15 x 8 = ______________ 15 x 6 = ________________
15 x 5 = ______________ 11 x 4 = ______________ 11 x 7 = ________________
14
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MULTIPLICATION
3 1 2
x 2 7 5 1 5 6 0 _________ 3 1 2 x 5
2 1 8 4 0 _________ 3 1 2 x 7 0
6 2 4 0 0 _________ 3 1 2 x 2 0 0
___________
8 5 8 0 0
___________
3 1 2 is the MULTIPLICAND
2 7 5 is the MULTIPLIER
8 5 8 0 0 is the PRODUCT.
___________________________________________________________________________
7 1 6 _________ is the Multiplicand
X 2 0 7 _________ is the Multiplier _ _________is the Product.
I. Find the Product.
1) 1 4 5 8 7 2) 8 9 3 5
X 2 3 5 X 7 1 4
______________ _______________
The number we multiply is the
MULTIPLICAND.
The number by which we multiply is the
MULTIPLIER.
The result is the PRODUCT
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3) 8 9 5 6 3 4) 1 4 3 5
X 3 4 2 X 8 7 6 ________________ _______________
II. Mental Maths
1) 4 2 3 X 10 = ___________________________
2) 3 1 X 1 0 0 0 = ________________________
3) 1 0 0 1 X 2 0 0 0 = _____________________
4) 9 9 9 X 1 0 0 = __________________________
5) 4 2 5 X 3 0 0 = __________________________
6) ! 4 3 X 9 0 0 = _________________________
7) 7 5 X 5 0 0 = ___________________________
8) 4 2 X 7 0 0 = ____________________________
9) 1 4 9 X 5 0 = ____________________________
10) 7 0 1 0 X 7 0 = ___________________________
11) 9 3 5 X 9 0 = _____________________________
12) 7 0 6 X 1 1 0 = ____________________________
16
Page 17
DIVISION
4 7 ) 2 7 6 8 5
1 5 3 ) 1 4 4 5 8 5
____________
The number that is left after
division is called the REMAINDER.
A number which is to be divided is
called DIVIDEND.
The number by which we divide is
called DIVISOR.
The result is called the QUOTIENT.
17
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WORD PROBLEMS
Solve the following word problems. Write statements also.
1. There are 17 workers, if each worker is paid Rs.1500 in a day, how much money is paid for all in 6
days?
2. Anil has a collection of 4270 stamps. He pasted 35 stamps on one page. How many pages did he
use in all?
3. 2,90,560 students appeared in an examination. If 2,56,850 students passed the examination,
how many students failed?
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4. A book has 1035 pages. If Raja read 207 pages a day, how many days he took to complete the
book.
5. Mr. Gupta has Rs. 68,82,500 in his bank account. He spent Rs. 13,50,500 to buy a new car. How
much money is left in his bank account?
6. A factory produced Rs. 17,875 screw on the first day, 20,700 on the second day, 19,758 screws on
the third day. Find the total number of screws produced in three days?
Brain teaser
In a multiplication sum a girl multiplied by 27 instead of 72. Her
answer was 3240. What was the correct answer?
The correct answer was ………………….
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Unitary Method
1. 8 fans cost Rs. 13,480. What is the cost of 13 fans?
Cost of 8 fans = ____________________________
Cost of 1 fan = _____________________________
Cost of 13 fans = ___________________________
2. 26 trucks can carry 10,894 bags of cement. How many bags of cement can be carried in 1
truck?
How many can be carried by 7 Trucks?
Number of bags carried by 13 trucks = _________________________
Number of bags carried by 1 truck = ___________________________
Number of bags carried by 7 trucks = __________________________
3. The cost of 34 books is Rs. 2890. Find the cost of 20 books?
Cost of 34 books = __________________________________
Cost of 1 book = ___________________________________
Cost of 20 books = _________________________________
4. 45 workers are paid Rs. 46,125 in a day. Find the wages paid to:
a) Each worker.
b) Wages paid to 11 workers.
Wages paid to 45 workers = _________________________
Wages paid to one worker = _________________________
Wages paid to 11 workers = _________________________
To get less value we divide To get more value we multiply
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5. The cost of 25 bags of cement is Rs. 29,500; Find the cost of 92 bags of cement.
Cost of 25 bags of cement = _____________________________
Cost of 1 bag of cement = _______________________________
Cost of 92 bags of cement = _____________________________
6. 30 note books cost Rs. 2250. Find the cost of 22 note books.
Cost of 30 note books = _____________________________
Cost of 1 note books = ______________________________
Cost of 22 note books = _____________________________
7. Mohan got Rs. 8,400 for selling 8 washing machines. Find his commission for selling
24 machines.
Commission for selling 8 machines _____________________________
Commission for selling 1 machine______________________________
Commission for selling 24 machines____________________________
21
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PRIME AND COMPOSITE NUMBERS
A number which has exactly two factors, 1 and the number itself is called a prime number.
A number which has more than two factors is called a composite number.
1 has only one factor and so it is neither prime or composite.
Write the factors, count the number of factors and then ring the numerals that are
prime and indicate in the space provided.
Number Factors Number
of
factors
Prime or Composite
1 1 1 Neither prime or composite
2
3
4
7
8
13
14
17
27
32
37
41
43
50
22
Page 23
TESTS OF DIVISIBILITY
A divisibility test is a rule for determining whether one number is divisible by another number or
not without actually dividing it.
Conditions
Examples
2 A number is divisible by 2 if its last digit is even or zero.
6 0, 2 4, 1 0 6, 7 8 6 2, 1 3 0 8
3 A number is divisible by 3 if the sum of the digits is divisible by 3.
1 3 5 9, 3 7 8, 1 0 8 0, 2 4 5 1, 7 4 5 2
4 A number is divisible by 4 if the number formed by last two digits is divisible by 4.
2 0 8, 7 1 6, 9 2 4, 8 3 2 0, 6 5 3 2
5 A number is divisible by 5 if its last digit is either 0 or 5.
4 6 0, 7 2 5, 1 9 9 5, 1 7 8 0 , 4 6 3 0
6 A number is divisible by 6 if the number is divisible by 2 as well as 3.
1 8 0, 3 6 6, 4 2 0, 2 7 0 6, 8 3 2 2
7 A number is divisible by 7 if the difference between twice the last digit and the number formed by other digits is either 0 or a multiple of 7.
3 1 5, 2 9 4, 8 8 2, 1 1 1 3. Consider 1 1 1 3. Last digit = 3. Number formed by other digits = 1 1 1. Difference = 1 1 1 – 6 = 1 0 5. There fore 1 1 1 3 is divisible by 7.
8 A number is divisible by 8 if its last three digits are divisible by 8.
2 8 6 4, 1 0 0 8, 3 0 4 0, 1 8 1 6,
9 A number is divisible by 9 if the sum of the digits Is divisible by 9.
5 6 7, 1 1 0 7, 2 0 4 3, 6 4 2 6
10 A number is divisible by 10 if its last digit is 0 5 3 0, 1 1 2 0, 4 0 0 0 , 3 6 5 0, 7 6 8 0
11 A number is divisible by 11 if the difference between the sums of alternate digits is either 0 or a multiple of 11.
7 1 6 1, 2 5 8 5, 5 0 6 0. Consider 7 1 6 1. Sum of digits in even places = 1 + 1 =2. Sum of digits in odd places = 7 + 6 = 1 3. Difference = (1 3 – 2) is 1 1. Therefore 7 1 6 1 is divisible by 1 1.
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Page 24
ERATOSTHENES SIEVE
1. To see whether a number between 1 and 100 is prime or composite, we test divisibility by
2,3,5, and 7. If the number is divisible by any of these, then it is a composite number and if it
is not divisible by 2,3,5 or 7 the it is a prime number.
2. Cross out the numbers that are divisible by 2, 3 , 5, and 7. Circle the remaining numbers.
3.The circled numbers are called Prime Numbers and the crossed out numbers are called
Composite numbers.
1 2 3 4` 5 6 7 8 9 10
11 12 13 14 15 `16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
Write P for prime number and C for composite number.
3__________ 29 ________ 53 ___________ 43 ___________
12_________ 34________ 68____________ 54___________
___________________________________________________________________________
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ACTIVITY 1
Find the factor of numbers using the illustration.
Example : Find the factors of 12.
1 x 12 = 12; 3 x 4 = 12; 6 x 2 =12; So, Factors of 12 are – 1,2, 3, 4, 6, 12
Find the factors of 18.
25
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Factors of 9.
Factors of 16.
26
Page 27
FACTORS AND MULTIPLES
Complete the Factor Trees of the numbers given below and write their prime factorization:-
EXAMPLE:-
42
2 21 2 X 21
3 7 3 X 7
4 2 = 2 X 3 X 7 is the prime factorization of 42
1) 34
2) 18
3) 45
18 = ______X______X_______
34 = _________X __________
45 = ____X______X________
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4) 64
II. Draw factor trees and write the prime factorization for the following numbers:-
a) 40 c) 42
b) 36 d) 35
64 = ___x____x____x____x____x__
28
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PRIME FACTORIZATION
60 75 96
144 175 180
72 63 90
29
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168 350 84
200 384 150
120 125 105
30
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ASSIGNMENT
I. State whether True or False:-
1. Every Natural number is either Prime or Composite……………………..
2. Every Prime number is odd……………………..
3. 1 is a Prime number……………….
4. The product of two odd numbers is always an odd number……………..
5. Sum of two odd numbers is an even number……………….
6. The smallest composite odd number is………………
7. 2 is the only even prime number……………….
8. The L.C.M of 3 and 7 is 1………………
9. The H.C.F of 3 and 7 is 1……………….
10. The L.C.M of 5 and 15 is …………….
11. The H.C.F of 5 and 15 is ……………..
12. The smallest prime number is 2…………….
___________________________________________________________________________
Think !!!
The product of the numbers and the product of their H.C.F and L.C.M are the same.
Ex. H.C.F of 3 and 5 = 1
L.C.M of 3 and 5 = 15
PRODUCT OF THE NUMBERS
PRODUCT OF THEIR H.C.F AND L.C.M
3 x 5 = 15
1 x 15 = 15
31
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Activity 2
Complete the H.C.F chart.
Numbers
Factors Common
factors
H.C.F
5
6
1, 5
1, 7
1
1
6
11
10
13
8
9
Complete the L.C.M chart.
Numbers Multiples Common Multiples L.C.M
5
3
5, 10, 15, 20, 25,
30,…
3, 6, 9, 12, 15, 18, 21,
24, 27, 30, …
15, 30,…… 15
6
7
9
8
1
11
32
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ACTIVITY 3
a) Complete the H.C.F chart. Few are done for you.
H.C.F 2 6 12 15 18 30
3
6
9
9
12
24
6
b) Complete the L.C.M chart. Few are done for you.
L.C.M
1 2 3 4 5 6 7
1
1
2
3
4
12
5
6
7
21
33
Page 34
Highest Common Factor (H.C.F )
Find the factors of the following numbers. Find the common factors and Highest Common
factor.
Ex: 1 2, 1 5
Factors of 1 2 = 1, 2, 3, 4, 6, 1 2
Factors of 1 5 = 1, 3, 5, 1 5 is the greatest
Common Factors = 1, 3
H.C.F = 3
a) 1 0, 1 6
Factors of 1 0 = ___________________
Factors of 1 6 = ___________________
Common Factors = _________________
H.C.F = ______________
b) 20, 24
c) 3 5, 2 0
d)36, 60
e)30,50
f)25,45
H.C.F of two or more
numbers is the
greatest among the
common factors.
34
Page 35
g) 42, 70
h) 12, 18
CO-PRIME NUMBERS – When two numbers have no common factors other than 1,
they are called co-prime numbers.
H.C.F of two Co- prime numbers is 1
H.C.F of 5 and 6 is ____________ H.C.F of 3 and 5 is ____________
H.C.F of 7 and 9 is ____________ H.C.F of 11 and 14 is___________
H.C.F of 18 and 13 is __________ H.C.F of 2 and 3 is _____________
H.C.F BY PRIME FACTORISATION
Find the H.C.F by Prime Factorisation.
Ex: H.C.F of 1 8 and 2 4
18 = 2 x 3 x 3
24 = 2 x 2 x 2 x 3
H.C.F OF 18 and 24 = 2 x 3 = 6
H.C.F is the product of the
smallest common prime factors.
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Example: H.C.F of 20, 28 and 36
20 = 2 x 2 x 5
28 = 2 x 2 x 7
36 = 2 x 2 x 3 x 3
H.C.F of 20, 28 and 36 = 2 x 2 = 4.
a) 48, 72, 100
b) 48, 120
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(c) 25, 60, 72
d)75, 120, 225
e)32 , 64, 176
37
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LOWEST COMMON MULTIPLE (LCM )
L.C.M of two or more numbers is the smallest number which is a multiple of each of the
numbers.
I. Write the multiples, common multiples and least common multiples of the following
numbers.
Example: 9, 1 2
Multiples of 9 = 9, 1 8, 2 7, 3 6, 4 5--------------------
Multiples of 1 2 = 1 2, 2 4, 3 6, 4 8 ----------------------
Common multiples =3 6, 7 2 ---------------
L.C.M =3 6
___________________________________________________________________________
a) 8, 1 1 b) 3, 7
Multiples of 8 = ------------- Multiples of 3 = -------------------
Multiples of 1 1 = --------------- Multiples of 7 = ------------------
-
Common multiples =---------------- Common multiples = -------------
L.C.M = ______________ L.C.M = _______________
___________________________________________________________________________
c) 6, 1 5 d) 5, 6
___________________________________________________________________________
e) 1 2, 2 0 f) 1 4, 7
___________________________________________________________________________
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II L.C.M by Prime Factorization method
Example: 3 6, 4 0
2 3 6 2 4 0 3 6 = 2 X 2 X 3 X 3
2 1 8 2 2 0 4 0 = 2 X 2 X 2 X 5
3 9 2 1 0 L.C.M of 3 6 and 4 0 = 2 X 2 X 2 X 3 X 3 X 5 =6 0
3 3 5 5 2 occurs maximum 3 times.
1 1 3 occurs maximum 2 times.
5 occurs maximum one time.
__________________________________________________________________________________
a) 1 6, 2 8
1 6 = ----------------------------------- 1 6 2 8
2 8 = ---------------------------------------
L.C.M 1 6 and 2 8 = ----------------
__________________________________________________________________________________
b) 2 4 , 7 2
2 4 = ----------------------------------- 2 4 7 2
7 2 = ----------------------------------
L.C.M of 2 4 and 7 2 = --------------------------------
__________________________________________________________________________________
C) 2 2, 1 1, 7 2
2 2 = -------------------------------------------------------- 2 2 1 1 7 2
1 1 = ----------------------------------------------------------
7 2 = -----------------------------------------------------------
L.C.M of 2 2, 1 1and 7 2 = --------------------------------------------
__________________________________________________________________________________
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d) 1 8 0, 1 4 4, 1 7 5
1 8 0 = ----------------------------------------- 1 8 0 1 4 4 1 7
5
1 4 4 = --------------------------------------------
1 7 5 = -----------------------------------------------
L.C.M of 1 8 0, 1 4 4 and 1 7 5 = ------------------------------
__________________________________________________________________________________
e) 1 2, 1 8, 4 2
1 2 = ----------------------------------------------------- 1 2 1 8 4 2
1 8 = ----------------------------------------------------------
4 2 = ----------------------------------------------------------
L.C.M of 1 2, 1 8 and 4 2 = ---------------------------------
_______________________________________________________________________________
III. Find the L.C.M by Common Division method.
Example: 4 5, 3 0 3 4 5, 3 0
L.C M = 3 X 5 X 3 X 2 = 9 0 5 1 5, 1 0
3, 2
------------------------------------------------------------------------------------------------------------------------------------
a) 1 2 0, 1 8 0 1 2 0, 1 8 0
L.C.M = ____________________
= _________________
__________________________________________________________________________________
b) 2 2 0, 4 4 0 2 2 0, 4 4 0
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__________________________________________________________________________________
c) 2 5, 3 5, 1 2 0 2 5, 3 5, 1 2 0
__________________________________________________________________________________
d) 2 4 0, 4 0 8, 3 4 2 4 0, 4 0 8, 3 4
__________________________________________________________________________________
e) 1 5 0, 1 2 5, 9 0 1 5 0, 1 2 5, 9 0
__________________________________________________________________________________
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ACTIVITY 4
Divisibility Tests
Tick the numbers that are divisible by:
Numbers 2 3 6 5 9 10
2108
4310
24800
12873
21010
89304
69031
Numbers 4 8
9300
8504
1108
98760
30800
3264
60416
Since 2 X 3 = 6 , then any
number that is divisible by 2 and
3 , is also divisible by 6.
Likewise, same rule can apply to
4 X 3 = 12 ; 3 X 5 = 15 ; 3 x 8 = 24
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Numbers Calculation Divisible by
1 1
9090
13345
8094
23598
4004
43
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Fractions
Addition and Subtraction of fractions.
Like Fractions
3
6 +1
6 = ------------- 3
6 – 1
6 = ----------
7
11 + 2
11 = ----------- 7
11 -- 2
11 = ----------
23
35 + 7
35 = ----------------- 23
35 -- 7
35 = -----------------
--
Unlike fractions.
Ex: 1
6 + 4
9
Step 1. Take the L.C.M of the denominations.
Step 2. Write equivalent fractions for the given numbers with L.C.M as the
denominators.
Step 3 : Add the numerator and write the denominator as L.C.M
L.C.M of 6 and 9 = 1 8
1
6 + 4
9 = 3
18 + 8
18
= 3+8
18
= 11
18
a) 2
3 + 9
10 b) 9
10 + 1
6
c) 2
5 + 7
15 d) 3
8 + 1
4
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e) 7
12 + 11
20 f) 1
9 + 2
3
g) 3
8 + 1
3 h) 7
10 – 2
5
i) 5
6 – 3
4 j) 8
11 – 3
10
k) 3
4 – 2
3 l) 3
2 – 1
3
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Addition and Subtraction of Mixed numbers.
Example: 5 + 3 1
2
L.C.M of 1 and 2 is 2
5 + 3 1
2 = 5
1 + 7
2 = 10+7
2
= 17
2 = 8 1
2
a) 7 + 1 3
6 b) 3 + 1 2
6
c) 5 – 4 1
3 d) 8 – 2
3
e) 8 4
5 – 2 3
15 f) 1 4 – 8
12
g) 4 2
5 + 3 1
2 h) 3 2
3 + 1
6
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i) 5 1
4 + 2 2
3 j) 9 3
7 + 5
8
k) 3 5
6 – 1 3
6 l) 7 4
5 – 2 3
5
m) 4 1
2 – 2 3
5 n) 6 3
4 – 2 1
2
47
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Fill in the empty boxes to get equivalent fractions.
1) 2
5 =
15 6) 2 = 3
6
2) 5
7 =
10 7)
28
32 =
16
3) 5
= 20
25 8)
10
30 =
5
4) 5
= 15
21 9)
12
15 =
4
5) 4
5 =
10 10) 30 = 3
4
Compare the following fractions using >, < or =.
a) 7
12 9
12 e) 7
8 3
8
b) 8
11 3
11 f) 1
3 2
6
c) 6
8 5
8 g) 14
20 30
40
d) 1
4 2
4 h) 9
12 27
36
48
Page 49
Assignment
Find
1) 1
2 of Rs. 100 = __________________________________
2) 1
4 of Rs. 100 = __________________________________
3) 1
3 of 60 minutes = ______________________________
4) 1
5 of 30 days = _________________________________
5) 1
2 of 1000g = __________________________________
6) 1
4 of 60 seconds = ______________________________
7) 1
4 of 8 = ______________________________________
8) 3
4 of 16 = _____________________________________
9) 1
9 of 99 = _____________________________________
10) 2
5 of 25 = _____________________________________
49
Page 50
ACTIVITY 5
NUMBER PATTERNS
I. Draw the diagrams in a sequence and complete the series.
1 2 3
Diagrams 1 2 3 4 5
Numbers of
Squares
1 4 9 ___ ____
II. Complete the series
a) 1, 2, 4, 8, _______, _________, _______
b) 400, 200, 100, ____, _________, ________
c) 40, 38, 35, 31, _____, _________, _______
d) 22, 31, 40, 49, _____, _________, ________
50
Page 51
ACTIVITY 6
EQUIVALENT FRACTIONS
51
Page 52
FUNNY MATH RIDDLES
Q. If two’s company and three’s a crowd, what are four and five?
Q. If there are four apples and you take away three, how many do you
have?
Q. Where do fish keep their money?
Q. Two fathers and two sons go fishing. Each of them catches one fish. So
why do they bring home only three fish?
Q. I add five to nine, and get two. The answer is correct, but how?
Q. The ages of a father and son add up to 66. The father's age is the son's
age reversed. How old could they be?
Q. What weighs more - a pound of iron or a pound of feathers?
Q. If a rooster laid 13 eggs and the farmer took eight of them and then
another rooster laid 12 eggs and four of them were rotten, how many of
the eggs were left?
Q. I am an odd number; take away an alphabet and I become even. What
number am I?
Q. Using only addition, how can you add eight 8's to get the number 1,000?
ANSWER
A. 9
A. Yo
u to
ok th
ree app
les
so o
bvio
usly yo
u h
ave th
ree.
A. In
the river b
ank.
A. B
ecause th
e fishin
g
gro
up co
mprises a
gran
dfath
er, his so
n, an
d
his so
n's so
n - h
ence ju
st
three p
eop
le.
A. W
hen
it is 9am
, add
5
ho
urs to
it and
you
will get
2p
m.
A. Th
ere are three
po
ssible so
lutio
ns fo
r this:
the fath
er-son
du
o co
uld
b
e 51
and
15
years old
, 42
and
24
years old
or 6
0 an
d
06
years old
.
A. B
oth
wo
uld
weigh
the
same - co
me o
n, a p
ou
nd
rem
ains a p
ou
nd
,
irresp
ective of th
e ob
ject!
A. R
oo
sters do
n't lay eggs!
A. Seven
(SEVEN
-S=EVEN
)
A. 8
88 +8
8 +8 +8
+8
=1,0
00
52