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$: Class 6 - Edugain · PDF fileClass 6 Fractions For more such ... can be converted to an improper fraction as: 4 10 27 = 4 × 27 + 10 27 = 118 27 Step 2 ... into an improper fraction,$
Class 6Fractions

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Answer the questions

(1) What f raction is represented by shaded portion of these shapes :

A)

B)

C)

D)

E)

F)

(2) Shade the images to show the f ollowing f raction addition.

4

16

+

7

16

=

and makes

(3) Add the f ollowing f ractions:

A) 14

23

26 + 4

10

27

B) 11

7

8 + 3

11

27

C) 8

26

31 + 3

16

31

D) 14

7

12 + 3

11

27

E) 10

11

15 + 2

22

23

F) 14

8

13 + 6

19

24

(4) Simplif y the f ollowing f ractions:

ID : in-6-Fractions [1]

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A) 28

51

80 - 7

7

10

B) 16

113

143 - 5

2

13

C) 23

63

380 - 2

6

19

D) 27

127

154 - 5

2

11

(5) There are 290 students in a school, and they are collecting money to improve f acilit ies at the

school. The average contribution f rom each student was Rs. 165. If 9

50 of the amount was

spent in ref urbishing the gym, then how much money are they lef t with?

(6)Convert the 8

7

8 to improper f raction

(7)A f actory makes 9113 Watches every week. How many items are manuf actured in

7

13 year?

(8) The table below shows the number of books read by f ive children in one month.Name Number of books

Ismail ?

Balvinder 24

Sunil 9

Saina 10

Pranav 9

If Ismail read 3 books more than 1

4 of the total number of books read by the other f our

children, then how many books did Ismail read in a month?

Choose correct answer(s) from given choice

(9)Priyanka is reading a story book and this book has 343 pages. Priyanka manages to read

9

49

of the book every day. Af ter 4 days, how many pages does she have lef t to read?

a. 92 b. 91

c. 93 d. 280

(10)

1894

1000 in decimal f orm gives us

a. 1.894 b. 0.894

c. 18.94 d. 0.1894



(11)The parking lot of the Mall has a capacity of 468 cars. On Saturday

8

18 of the parking lot was

occupied with cars. How many additional cars could park there?

a. 260 b. 252

c. 261 d. 259

Fill in the blanks

(12)

1

5 +

1

6 - 3

11

=

(13)The local community park has space allocated f or jogging, music, and sports.

14

34 of the park

has been allocated f or sports, and out of the sports area 7

14 has been given f or playing

f ootball. The ratio of the park is given f or playing f ootball is

.

(14) The parking lot of the Theater has a capacity of 2220 cars. On Thursdays the ratio of occupiedspots to empty spots in the parking lot was 12:25. The number of additional cars that could park

there is

(15) 23

25 of a century =

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Answers

(1) A)

8

12

Step 1

We have been asked to f ind the f raction that represents the shaded portion ofthe f ollowing shape:

Step 2

Total number of equal parts in the image = 12Number of parts that are shaded in the image = 8

Step 3

Fraction of parts of the image that are shaded = Number of shaded parts

Total number of parts

= 8

12

Step 4

Hence, the f raction that is represented by the shaded portion of the shape is 8

12 .



B)

3

6

Step 1


Step 2


Step 3



= 3

6

Step 4


6

.



C)

7

9

Step 1


Step 2


Step 3



= 7

9

Step 4


9

.



D)

4

7

Step 1


Step 2


Step 3



= 4

7

Step 4


7

.



E)

2

6

Step 1


Step 2


Step 3



= 2

6

Step 4


6

.



F)

8

12

Step 1


Step 2


Step 3



= 8

12

Step 4


12 .

(2)

4

16

+

7

16

=

+ =



(3) A) 19

179

702

Step 1

Let us f irst convert the given mixed f ractions into improper f ractions. In order to

convert the mixed f raction 1423

26 into an improper f raction, we will need to

multiply the denominator 26 by 14 and add the numerator 23 to the result. Theresulting number will be the numerator of the improper f raction and thedenominator will remain the same:

1423

26 =

14 × 26 + 23

26 =

387

26

Similarly, the mixed f raction 410

27 can be converted to an improper f raction as:

410

27 =

4 × 27 + 10

27 =

118

27

Step 2

We now need to add the f ollowing unlike f ractions: 387

26 and

118

27 .

Let us f irst convert them to like f ractions.

Step 3

Let us f ind the LCM of the denominators 26 and 27.The LCM of 26 and 27 is 702.

Step 4

What should we multiply with the denominator 26 to get the LCM 702?

It is 702

26 = 27.

So, the f irst f raction can be written as:

387 × 27

702 =

10449

702

Step 5

Similarly, the second f raction can be written as:

118 × 26

702 =

3068

702

Step 6

Let us now add the two like f ractions:

10449

702 +

3068

702



= 10449 + 3068

702

= 13517

702

= 19179

702

Step 7

Thus, the sum of the f ractions 1423

26 and 4

10

27 is 19

179

702 .



B) 15

61

216

Step 1





117

8 =

11 × 8 + 7

8 =

95

8



311

27 =

3 × 27 + 11

27 =

92

27

Step 2


8 and

92

27 .


Step 3


Step 4


It is 216

8 = 27.


95 × 27

216 =

2565

216

Step 5


92 × 8

216 =

736

216

Step 6


2565

216 +

736

216



= 2565 + 736

216

= 3301

216

= 1561

216

Step 7


8 and 3

11

27 is 15

61

216 .



C) 12

11

31

Step 1





826

31 =

8 × 31 + 26

31 =

274

31



316

31 =

3 × 31 + 16

31 =

109

31

Step 2

We now need to add the f ollowing like f ractions: 274

31 and

109

31 .

Step 3

Let us add the two like f ractions:

274

31 +

109

31

= 274 + 109

31

= 383

31

= 1211

31

Step 4


31 and 3

16

31 is 12

11

31 .



D) 17

107

108

Step 1





147

12 =

14 × 12 + 7

12 =

175

12



311

27 =

3 × 27 + 11

27 =

92

27

Step 2


12 and

92

27 .


Step 3


Step 4


It is 108

12 = 9.


175 × 9

108 =

1575

108

Step 5


92 × 4

108 =

368

108

Step 6


1575

108 +

368

108



= 1575 + 368

108

= 1943

108

= 17107

108

Step 7


12 and 3

11

27 is 17

107

108 .



E) 13

238

345

Step 1





1011

15 =

10 × 15 + 11

15 =

161

15



222

23 =

2 × 23 + 22

23 =

68

23

Step 2


15 and

68

23 .


Step 3


Step 4


It is 345

15 = 23.


161 × 23

345 =

3703

345

Step 5


68 × 15

345 =

1020

345

Step 6


3703

345 +

1020

345



= 3703 + 1020

345

= 4723

345

= 13238

345

Step 7


15 and 2

22

23 is 13

238

345 .



F) 21

127

312

Step 1





148

13 =

14 × 13 + 8

13 =

190

13



619

24 =

6 × 24 + 19

24 =

163

24

Step 2


13 and

163

24 .


Step 3


Step 4


It is 312

13 = 24.


190 × 24

312 =

4560

312

Step 5


163 × 13

312 =

2119

312

Step 6


4560

312 +

2119

312



= 4560 + 2119

312

= 6679

312

= 21127

312

Step 7


13 and 6

19

24 is 21

127

312 .



(4) A) 20

15

16

Step 1





2851

80 =

28 × 80 + 51

80 =

2291

80


10 can be converted into an improper f raction

as:

77

10 =

7 × 10 + 7

10 =

77

10

Step 2

We now need to subtract the f ollowing unlike f ractions: 2291

80 and

77

10 .

Bef ore we subtract, let us f irst convert them to like f ractions.

Step 3


Step 4


It is 80

80 = 1.


2291 × 1

80 × 1 =

2291

80

Step 5


77 × 8

10 × 8 =

616

80

Step 6

Let us now subtract the two like f ractions:

2291

80 -

616

80



= 2291 - 616

80

= 1675

80

= 1675 ÷ 5

80 ÷ 5 ...[ Dividing both numerator and denominator by their HCF to bring ]

= 335

16

= 2015

16

Step 7

Thus, the simplif ied value of the given f ractions is 2015

16 .



B) 11

7

11

Step 1





16113

143 =

16 × 143 + 113

143 =

2401

143



as:

52

13 =

5 × 13 + 2

13 =

67

13

Step 2


143 and

67

13 .


Step 3


Step 4


It is 143

143 = 1.


2401 × 1

143 × 1 =

2401

143

Step 5


67 × 11

13 × 11 =

737

143

Step 6


2401

143 -

737

143



= 2401 - 737

143

= 1664

143

= 1664 ÷ 13

143 ÷ 13 ...[ Dividing both numerator and denominator by their HCF to bring

]

= 128

11

= 117

11

Step 7


11 .



C) 20

17

20

Step 1





2363

380 =

23 × 380 + 63

380 =

8803

380



as:

26

19 =

2 × 19 + 6

19 =

44

19

Step 2


380 and

44

19 .


Step 3


Step 4


It is 380

380 = 1.


8803 × 1

380 × 1 =

8803

380

Step 5


44 × 20

19 × 20 =

880

380

Step 6


8803

380 -

880

380



= 8803 - 880

380

= 7923

380

= 7923 ÷ 19


]

= 417

20

= 2017

20

Step 7


20 .



D) 22

9

14

Step 1





27127

154 =

27 × 154 + 127

154 =

4285

154



as:

52

11 =

5 × 11 + 2

11 =

57

11

Step 2


154 and

57

11 .


Step 3


Step 4


It is 154

154 = 1.


4285 × 1

154 × 1 =

4285

154

Step 5


57 × 14

11 × 14 =

798

154

Step 6


4285

154 -

798

154



= 4285 - 798

154

= 3487

154

= 3487 ÷ 11


]

= 317

14

= 229

14

Step 7


14 .

(5) Rs. 39237

Step 1

The number of students in the school = 290

Step 2

The average contribution f rom each student = Rs. 165Theref ore, the total contribution f rom all the students = 290 × 165 = Rs. 47850

Step 3

Now, the amount spent in ref urbishing the gym = 47850 × 9

50 = Rs. 8613

Step 4

The amount spent in ref urbishing the gym = Rs. 8613Theref ore, the money lef t with them = 47850 - 8613 = Rs. 39237.

(6) 71

8



(7) 255164

Step 1

The number of weeks in a year = 52 weeks

Step 2

The number of weeks in 7

13 of a year =

7

13 × number of weeks in a year

= 7

13 × 52

= 28 weeks

Step 3

The number of Watches made by the f actory in one week = 9113

Step 4

The number of Watches manuf actured in 28 weeks ( 7

13 of a year) = 28 × 9113 = 255164.

(8) 16

Step 1

Total number of books read by Balvinder, Sunil, Saina and Pranav,= 24 + 9 + 10 + 9= 52

Step 2

It is given that Ismail reads 3 books more than 1

4 of 52. Theref ore number of books read

by Ismail,

= 1

4 × 52 + 3

= 13 + 3= 16 books



(9) b. 91

Step 1

In one day she reads ( 9

49 × 343 = 63) pages

Step 2

Theref ore in 4 days, she would read (4 × 63 = 252) pages

Step 3

Theref ore remaining number of pages to read = (Total pages - Read pages)⇒ = 343 - 252⇒ = 91 pages

(10) a. 1.894

Step 1

Let us understand the def init ion of decimal f raction and decimals:Decimal fraction: is a f raction whose denominator is a power of ten such as 10, 100, 1000etc.A decimal number, or just decimal, ref ers to any number written in decimal notation. In anumber written in decimal notation, all digits to the lef t of the decimal point have f acevalues more than one and those on the right of the decimal point have f ace values lessthan one.

Step 2

We should remember f ollowing f acts about decimal numbers:Fact 1. When a decimal number is multiplied by ten, the result is obtained by moving thedecimal point to the right by one digit.Fact 2. When a decimal number is divided by ten, the result is obtained by moving thedecimal point to the lef t by one digit.Fact 3. When a number does not have a decimal point, we can assume that there is ahidden decimal point to the right of the unit digit (right-most digit).

Step 3

Now, let us try to convert the decimal f raction 1894/1000 to a decimal number.

Step 4

Here, the number 1894 is to be divided by 1000. In other words we can say that 1894 is tobe divided by 10 three times.

Step 5

In number 1894, the decimal point can be assumed to be hidden to the right of the unit digit.When it is divided by 10 three times, the decimal point will move three digits to the lef t.Hence the decimal number we get will be:1.894

Step 6

Theref ore, the answer is 1.894.



(11) a. 260

Step 1

Total number of parking spaces = 468

Step 2

Number of occupied parking spaces = 8

18 × 468

⇒ = 208

Step 3

Number of vacant parking spaces = Total - Occupied⇒ = 468 - 208⇒ = 260



(12) 118 315

Step 1

The given expression 1

5 +

1

6 - 3

11

can be simplif ied as:

1

5 +

1

6 × 11 - 3

11

= 1

5 +

1

66 - 3

11

= 1

5 +

1

63

11

= 1

5 +

11

63

= 1 × 63 + 11 × 5

315

= 63 + 55

315

= 118

315

Step 2

Thus, the value of 1

5 +

1

6 - 3

11

is 118

315 .



(13) 7 34

Step 1

: Let the area of the f ull park be 1.

Step 2

The area allocated f or sports = 14

34 of the total park area =

14

34 × 1 =

14

34

Step 3

The area allocated f or playing f ootball out of the sports area = 7

14 of the sports area

= 7

14 ×

14

34

= 7

34

Step 4

Thus the ratio of the park given f or playing f ootball is 7

34 .

(14) 1500

Step 1

It is given that ratio of occupied spots to empty spots is 12:25, which means if there are 37( = 12 + 25) spots, 12 are occupied and 25 are empty

Step 2

But is given that total number of parking spots are 2220. Theref ore total number of spotsare 60 times ( = 2220/37) of 37

Step 3

Theref ore available spots will also be 60 times of 25. Theref ore available parking spots,= 25 × 60 = 1500



(15) 92

Step 1

The numeric term f or century is 100.

Step 2

We need to f ind the number that is 23

25 of 100. That is, we need to f ind the value of

23

25

× 100.

Step 3

The value of 23

25 × 100 = 23 × 4 ... (Dividing 100 by 25)

= 92

Step 4

Hence, 23

25 of century is 92.



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