STD: 82

EXAMPLE 3. What fractton of a day is 8 hours Solutton We know that 1 day 24 hours.

8 the required fraction=4 EXAMPLE 4.

What fraction of an hour is 40 mtnutesr We know that 1 hour = 60 minutes

Solution

40 the required fraction=en 60

n the given figure, if we say that the shaded reglon is ue

whole, then what is the error in it?

EXAMPLE 5.

the given figure, the shaded region is not equal to ne

unshaded region. Solution

shaded region is not equal toof the whole.

EXERCISE 5A 1. Write the fraction representing the shaded portion:

A (i)

() )

(iv) (V) (vi)

2. Shadeof the given figure.

3. In the given figure, if we say that the shaded reglon is then identify the error in it.

4. Write a fraction for each of the following: (1) three-fourths (11) four-sevenths

(Iv) three-tenths (11) two-fifths

(vi) five-sixths (v) one-elghth (vi) eight-ninths (vilil) seven-twelfths

Frnctionw

6. Write down the numerator and the denominator of each of the fractions 9Ven elgW 12

(V) 7 (1)

9 (11) (11) 15

(V)

6. Write down the fraction in whlch

(1) numerator = 3, denominator = 8 (111) numerator » 7, denominator- 16

7, Write down the fractlonal number for cach of the following:

(11) numerator = 5, denominator= 12 (1v) numerator - 8, denominator = 15

2 (1)

3 (11)

9 7

(Iv) 10

(V) 3 5

6 3 (vi) (vi)

8 vIt) 14

5 (1x)

11

8. What fraction of an hour Is 24 minutes?

9. How many natural numbers are there from 2 to 10? What fraction of them are prime

numbers?

10. Determine:

2 2 (1)of 15 pens (11)of 27 balls 3 (11)of 36 balloons

11. Determine:

3 of 16 cups (11)of 28 rackets4

(11)of 32 books 4

12. Neclam has 25 penclls. She gves of them to Meena. How many pencils does Meena get? 5

How many penclls are left with Neelam?

13. Represent cach of the following fracttons on the number Ine:

3 () ()9

5 (1v) ( (111)

PROPER, IMPROPER AND MIXED FRACTIONSs

PROPER FRACTIONS A fractlon whose numerator ls less than tts denominator ls called a

proper fractlon. 2 5 7 0 8 3' 8' 11 4' 15:ec., are all proper fractions. EXAMPLES

NOTE Each proper fraction is less than 1.

IMPROPER FRACTIONS A fractlon whose numerator ls greater than or equal to lts

denomtnator ls called an tmproper fractlon.

5 7 8 10 12 etc., are all tmproper jractlons. Thus 5' 10' 6 9

MIXED FRACTIONS A combtnatton of a whole number and a proper fractlon is called a

mixed fractlon. , etc., are all mixed fractions.

EXAMPLES

85 Fractions

EXAMPLE 4. Convert each of the followtng tnto a mixed fractlon: 23

(0 ty 37 6 50 lty 45 (t)

Solution i) On dividing 23 by 5, we get quotient = 4 and remainder = 3.

5) 23 (4 23 44 5

(ii) On dividing 37 by 6, we get 6)37 (6 quotient = 6 and remainder = 1.

36

656 (ii) On dividing 45 by 8, we get

quotient = 5 and remainder = 5. 8) 45 (5 40

55 (iv) On dividing 50 by 7, we get 7)50 (7

quotient = 7 and remainder = 1.

7 EXERCISE 5B

1. Which of the following are proper fractions?

13 10216 11 10 15 16 10 23

2. Which of the following are improper fractions?

3 5 9 8 27 23 19 10 26

2'6' 4'8 16' 31 18' 13' 26

3. Write six improper fractions with denominator 5.

4. Write six improper fractions with numerator 13.

5. Convert each of the following into an improper fraction: 5

(ti) 9 8

(11) 6 10

(iv) 3 11 ()5

(v) 10 (vi) 12 8

(vil) 8 (vii) 51 5 13

6. Convert each of the following into a mixed fraction:

95 10

(i8 62 (v3

117 (vn)7

16

103 (vii)

12 (vii)

20 81

7. Fill up the blanks with '>', '<'or '=':

(IN 3016 (v) 3016

FOUIVAL FNT FHAGTION

hul mmultplyng thu muneutn at thu tuumatun u Ju man ny hu sama

y idmg thw manurutn at tw teumatm f n fua tum ny thw sumn wnm

ullunl unulualent fru tua

FHULE 1uyul a frnutun uutualunt nn qglmun fru th, 1um ltlty n lu m uln me

soLVED EXAMPLES IAM& Wrltu fun fru tMns uugutununt u uuh nf thu fllntug

Sdutunn A

Heue,te nu twmtuams nguvuaet 4

89 Fractions

FXAMPLE9. Reduceto the stmplest form. 35

Solution Here, numerator 21 and denominator = 35. Factors of 21 are 1, 3, 7, 21.

Factors of 35 are 1, 5, 7, 35.

Common factors of 21 and 35 are 1,7. HCF of 21 and 35 is 7.

21 21+7

35 35.7 5 Hence, the simplest form of is

35

EXERCISE 5C 1. Write five fractions equivalent to each of the following:

() 2

( (4v)10 7

(vii) 5 (vii) ( (vi) 12

2. Which of the following are the pairs of equivalent fractions?

15 20 (0and (ii)and 8 40 ii)and 16

33 2 14 (iv)and 63 tand24 (vi)and 22 24 3 9

3. Find the equivalent fraction of having

(i) numerator 24 (1) denominator 30

4. Find the equivalent fraction of having

(i) numerator 35 (1) denominator 54

5. Find the equivalent fraction of ,having 11 (ii) numerator 60 () denominator 77

24 6. Find the equivalent fraction ofhaving numerator 4.

30

36 7. Find the equivalent fraction ofwith 48

(ii) denominator 4 (i) numerator 9 56

8. Find the equivalent fraction ofwith 70 (1i) denominator 100 (1) numerator 4

9. Reduce each of the following fractions into its simplest form:

i) 60 8 (lil)

98 (v) 50

60 72 (v) 90

( 15 10. Show that each of the following fractions is in the simplest form:

9 25

36 21 (iv) (v)0 8

(i4

90

Mathematics for Class 6

11. Replace by the correct numberu C COrrect number in each of the following:

5 20 (ii)

35

(iv) 9 40 (vi) 60 (v)

LIKE AND UNLIKE FRACTIONS

ACIONS Fractions having the sane denominator are called like jractions. Thus, are all like fractions. ONLIKE FRACTIONS Fractions having different denominators are called unlike jractions Thus, 2 4' 6' are all unlike fractions.

CONVERTING UNLIKE FRACTIONS INTO LIKE FRACTIONS RULE Suppose some unlikefractions are given. Convert each one of them into an equivalent Jraction having a denominator equal to the LCM of all the denominators f the given fractions.

5 Convert the fractions andinto ltke fractions. EXAMPLE 1.

2 3 6 9 l 2 5 The given fractions are and 4 Solution

2 2,3,6.9 LCM of 2, 3, 6, 9 = (2 x3x 3) = 18. So,we convert each of the given fractions into an equivalent fraction with 18 as the denominator.

3 13,3,9 1, 1,1,3

Thus, we have:

11x9-.2 2 x9 18 3 3x6 18

12

5 5 x3 66x3 18 and**28

9x2 18 9 12 15 Hence, the required like fractions are 18 18 1R and

cOMPARISON OF FRACTIONS

COMPARIsON OF LIKE FRACTIONS

Dll E1 Among two fractions with the Same denominator, the one with the areater numerator is the greater of the two.

EXAMPLES 10 10

Fractions 93

Clearly, 24,21 17 16 30 30 30 30

8 510 30 15 4 7 17 8 Hence, the given fractions in descending order are 10'30'5

EXERCISE 5D 1. Define like and unlike fractions and give five examples of each.

3 7 8 2. Convert5 10' 5and into like fractions.

30

7 3. Convert R 1nd into like fractions.

24

4. Fill in the place holders with the correct symbol > or <

tvi2 17

5. Fill in the place holders with the correct symbol> or <

(0 Compare the fractions given below:

7 6 735 8'6 5 8 11 7 .

2 4 10. 1. 3 11 13 4 9

12 13.7 13. 8' 12

45 14g6 7

15,5 10 11 13

17 12' 15 16.10 Arrange the following fractions in ascending order:

19 2 5 and 1 and 20.015and 30

18

and 21. 21 4' 8' 1632

Arrange the followving fractions in descending order:

5 and 36 2312 18 and 36 7 and 24

17 25. and 42

3 26. 1

12' 23 7 9 17 50 27. 5 13' 4' 17 11 1 1

28. Lalita read 30 pages of a book contatning 100 pages while Sarlta readof the hoe

2

94 Mathematics

for Class 6

k. Who

43. Rafiq exercised forhour. while Rohit exercised forhour. Who exerclsed for a longer.

0. In a school 20 students out of 25 passed in VI A, while 24 out of 30 passed in

read more?

time? 3

VI B. Whlch

section gave better result?

Do all work inwiaths Copy-ADDITION OF FRACTIONS