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.

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

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

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

4

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

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

6

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

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

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 ___________________

9

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

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

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.

12

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

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

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

15

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

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

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?

18

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 ………………….

19

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

20

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

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

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.

23

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___________

___________________________________________________________________________

24

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

Factors of 9.

Factors of 16.

26

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________

27

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

PRIME FACTORIZATION

60 75 96

144 175 180

72 63 90

29

168 350 84

200 384 150

120 125 105

30

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

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

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

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

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.

35

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

36

(c) 25, 60, 72

d)75, 120, 225

e)32 , 64, 176

37

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

___________________________________________________________________________

38

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 = --------------------------------------------

__________________________________________________________________________________

39

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

40

__________________________________________________________________________________

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

__________________________________________________________________________________

41

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

42

Numbers Calculation Divisible by

1 1

9090

13345

8094

23598

4004

43

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

44

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

45

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

46

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

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

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

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

ACTIVITY 6

EQUIVALENT FRACTIONS

51

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