CHAPTER - FRACTIONS

EXERCISE:5D

1. In Practice copy.
2. 2 and 3 excluded.

4. Fill in the place holders with the correct symbol < , > ; (BOOK WORK)

i. > ii. > iii. < iv. > v. > vi. <

5. Fill in the place holders with correct symbols > or <: (BOOK WORK)

i. > ii. > iii.< iv. > v. < vi.>

Compare the fractions given below: (BOOK WORK)

6. Sol: By cross multiplying, we get:

4×7 = 28 and 5×5=25

Clearly, 28 > 25
! "
Hence , " > #

𝟑 𝟓 𝟕 𝟔 𝟓 𝟗 𝟐 𝟒 𝟔 𝟑 𝟑 𝟓
(7) < (8) < (9) > (10) > (11) < (12) <
𝟖 𝟔 𝟏𝟏 𝟕 𝟔 𝟏𝟏 𝟑 𝟗 𝟏𝟑 𝟒 𝟒 𝟔

𝟓 𝟕 𝟒 𝟓 𝟒 𝟕 𝟕 𝟗 𝟏𝟏 𝟏𝟑
(13) 𝟖
> 𝟏𝟐 (14) 𝟗
<𝟔 (15) 𝟓
> 𝟏𝟎 (16) 𝟖 < 𝟏𝟎 (17) 𝟏𝟐 < 𝟏𝟓

Arrange the following fractions in ascending order : (ALL IN COPY)

𝟐 𝟓 𝟕 𝟏𝟏
19. 𝟑 , 𝟔 , 𝟗 𝒂𝒏𝒅 𝟏𝟖
3 3 , 6 , 9 , 18

Soln: LCM of 3, 6 , 9 , 18 = 36 3 1 , 2, 3 , 6

1 , 2 , 1, 2

Convert each one of the fraction into an equivalent fraction with denominator 36.
! ! #! !$ & & % "' ( ( $ !* ## ## ! !!
Now, = " × #! = "% ; % = % × % = "% ; ) = ) × $ = "% ; #* = #* × ! = "%
"

++ +. +/ ,0
Clearly , ,- < ,- < ,- < ,-
 11 + 2 4
Hence , 1/ < , < 3 < -

𝟑 𝟕 𝟏𝟏 𝟐𝟑
21. 𝟒 , 𝟖 , 𝟏𝟔 𝒂𝒏𝒅 𝟑𝟐
4 4 ,8 ,16 ,32
Soln : LCM of 4 , 8, 16 ,32 =32
2 1 ,2 , 4 , 8
Convert each one of the fraction into an equivalent fraction with denominator 32. 2 1 , 1 ,2 ,4
1,1,1,2

" " * !$ ( ( $ !* ## ## ! !! !" !" # !"

Now, = × = ; = × = ; = × = ; = × =
$ $ * "! * * $ "! #% #% ! "! "! "! # "!
++ +, +. +/
Clearly , ,+ < ,+ < ,+ < ,+

11 +, , 2
Hence , 1- < ,+ < . < /

Arrange the following fractions in descending order :

2 4 11 12
23. , 1+ , 1/ 𝑎𝑛𝑑 ,-
3 3 9, 12 ,18, 36
3 1, 4 , 6 , 12
Soln: LCM of 9 , 12 ,18 ,36 = 36
2 1,4,2 , 4
Convert each of the fractions into an equivalent fraction with denominator 36 2 1,2,1,2
1 , 1 , 1 ,1
2 2 . +/ 4 4 , 14 11 11 + ++ 12 12 1 12
Now , 3 = 3 × . = ,- ; 1+ = 1+ × , = ,- ; 1/ = 1/ × + = ,- ; ,- = ,- × 1 = ,-

+/ ++ 12 14
Clearly , ,- > ,- > ,- > ,-

2 11 12 4
Hence , 3 > 1/ > ,- > 1+

4 3 12 ,1
25. 2 , 1. , +1 𝑎𝑛𝑑 .+

Soln: LCM of 7 ,14 ,21 , 42 = 42 7 7 , 14, 21 ,42

3 1 , 2 , 3 ,6
Convert into equivalent fractions
2 1,2,1,2
4 4 - ,0 3 3 , 12 12 + ,. ,1 ,1 1 ,1 1,1,1,1
Now , 2 = 2 × - = .+ : 1. = 1. × , ; +1 = +1 × + = .+ ; .+ = .+ × 1 = .+
 ,. ,1 ,0 +2
Clearly , .+ > .+ > .+ > .+

12 ,1 4 3
Hence , +1 > .+ > 2 > 1.

28 . Lalitha read 30 pages of a book containing 100 pages………..more?

Soln: No. of pages in the book = 100

No. of pages Lalita read = 30

+ +
No. of pages Sarita read = 4
i.e., 4 × 100 = 2 × 20 = 40

Clearly 40>30; Therefore Sarita read more number of pages.

29.Rafiq exercised for……………………..longer time?

Soln: No. of hours in a day = 24

+
No. of hours Rafiq exercised = , × 24 = 2 × 8 = 16ℎ𝑜𝑢𝑟𝑠

,
No. of hours Rohit exercised =. × 24 = 3 × 6 = 18ℎ𝑜𝑢𝑟𝑠

Clearly , 18 > 16 ; Therefore Rohit exercised more.

30. In a school 20 students…………………………………….better result?

+0 .
Soln: Fraction of students passed in VI A = +4 = 4 ( 𝑜𝑛 𝑠𝑖𝑚𝑝𝑙𝑖𝑓𝑖𝑐𝑡𝑖𝑜𝑛)

+. .
Fraction of students passed in VI B = ,0 = 4 ( 𝑜𝑛 𝑠𝑖𝑚𝑝𝑙𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛)

Therefore both the sections have the same result.

Exercise: 5E
Find the sum:

Problem 1 to 9 in Practice copy.

+ 4
10. 3 , + 1 - + 2 (ALL IN COPY)
 + 4 6
Soln: 3 , + 1 - + 2 (Convert mixed fraction in to improper fraction using 𝑄 7 𝑟𝑢𝑙𝑒 )

11 11 + 3 3 ,6 ,1
=, + + 1 (LCM of 3, 6, 1 is 6)
- 1 ,2 , 1
++ 11 1+ .4 1
=- + -
+ -
= -
=7 +

+ 1 + 4
13. , + 3 - + 4 3 + 2 1/

+ 1 + 4 6
Soln: , + 3 - + 4 3 + 2 1/ (Convert mixed fraction into improper fraction using 𝑄 7 𝑟𝑢𝑙𝑒 )
𝟐 13 ,/ .1
𝟑
+ -
+ 3
+ 1/ (LCM of 3, 6, 9, 18 =18) 3 3, 6, 9, 18
1+ 42 2- .1 1/- 1
3 1,2,3,6
1/
+ 1/ + 1/ + 1/ = 1/
= 10 , 2 1,2,1,2
1,1,1,1

16. Rohit bought a pencil………………………….articles?

+ 12
Soln: Cost of pencil = Rs 3 4 = 𝑅𝑠 4

2 +2 5 5 , 10
Cost of eraser = Rs 2 10 = 𝑅𝑠 10
1, 2
12 +2
Total cost = 𝑅𝑠 4
+ 𝑅𝑠 10 = LCM=5×2=10

𝟑𝟒 𝟐𝟕 𝟔𝟏 1
+ = = Rs 6
𝟏𝟎 𝟏𝟎 𝟏𝟎 10

1
17. Sohini bought 4 + 𝑚 of cloth…………………………………..in all?

1 3
Soln: Cloth for kurta = 4+𝑚 = +𝑚

3 3,2
1,2
 + /
Cloth for or pyjamas =2 , 𝑚 = , 𝑚 LCM=2×3=6

3 / +2 1- ., 1
Total cloth = + + , = -
+ -
= -
= 7-𝑚

18. While coming …………………………………………………………the school?

, 13
Soln: Distance covered by rickshaw = 4 . 𝑘𝑚 = 𝑘𝑚 2 2,4
.
1,2
1 ,
Distance covered on foot = 1 𝑘𝑚 = 𝑘𝑚 LCM=2×2=4
+ +

13 , 13 - +4 1
Therefore , distance of his house from school= .
++= .
+.= .
= 6 . 𝑘𝑚

19. The weight……………………………………………with gas?

. /.
Soln: Weight of empty gas cylinder = 16 4 𝑘𝑔 = 4
𝑘𝑔

+ .. 3 3,5
Weight of gas =14 , 𝑘𝑔 = 𝑘𝑔
, 1,5
LCM =3×5=15

Therefore , weight of cylinder with gas = weight of cylinder + weight of gas

/. .. +4+ ++0 .2+ 2
=4 + ,
= 14
+ 14
= 14
= 31 14 𝑘𝑔

Exercise : 5F
Find the difference (All problems in practice copy):

Simplify : (All in copy)

4 . + 3 6 ,9 , 3
13. −3+,
- 3 2 , 3 ,1
2, 1 , 1
Soln: LCM of (6 , 9 , 3 ) = 18

3×3×2=18
4 . + 14 / 1+ 13 1
Therefore , - − 3 + , = 1/ − 1/ + 1/ = 1/ = 1 1/
 & " ( 4 8 , 4 , 12
14. + $ − #!
* 2 2, 1 , 3
Soln: LCM of (8 , 4 , 12)= 24 1, 1 , 3

" / # 0" 0. 0! 02
Therefore , . + ! − 01 = 1! + 1! − 1! = 1! 4×2×3=24

2 1.
17. 2 + 5 10 − 3 14
5 1 , 10 , 15
Soln: Convert mixed fractions into improper fractions. 2 1, 2 , 3
1, 1 , 3
+ 42 43
= 1
+ 10 − 14 LCM =5×2×3=30

-0 121 11/ +,1 11/ 11, +,

=,0 + ,0
− ,0
= ,0
− ,0
= ,0
= 3 ,0

1 1 2 1, 2 , 4
18. 8 − 3+ − 2.
1 , 1, 2
/ 2 3
Soln: 1
− + − . = LCM=2×2=4

,+ 1. 3 ,+ +, 3 1
=. − .
−.= .
− .
= . = 2.

22. what should be ………19?

+
Soln: 9 , + 𝑠𝑒𝑐𝑜𝑛𝑑 𝑛𝑜. = 19

+ 13 +3
second no. =19 − 9 , = 1
− ,
= (LCM = 3)

42 +3 +/ 1
=, − ,
= ,
=9 ,

1
Therefore the number is 9 ,

1
23. What should ………….8 4 ?

2 1 32 .1 5 15 , 5
Soln: 6 14 + 𝑠𝑒𝑐𝑜𝑛𝑑 𝑛𝑜. = 8 4 = 14 + 𝑠𝑒𝑐𝑜𝑛𝑑 𝑛𝑜 = 4 3, 1
.1 32
𝑠𝑒𝑐𝑜𝑛𝑑 𝑛𝑜. = 4
− 14 = LCM=5×3=15

1+, 32 ,, 11
= 14 − 14 = 14 = 1 14
 11
Therefore the number is 1 14

24. Practice copy.

25. Practice copy

26.Mrs Soni……………………………………………………………………………….with her?

1 14
Soln: Milk bought = 7 + 𝑙 = 𝑙 2 2,4
+
1,2
, +,
Milk consumed = 5 . 𝑙 = .
𝑙 LCM=2×2=4

14 +, ,0 +, 2 ,
Therefore milk left = +
− .
= .
− .
= . = 1.𝑙

27. A film………………………………………………………………………………………of the film?

1 10 3 3,4
Soln: Duration of film show = 3 , ℎ𝑜𝑢𝑟𝑠 = ℎ𝑜𝑢𝑟𝑠
, 1,4
, 2
Duration of advertisement =1 . ℎ𝑜𝑢𝑟𝑠 = . ℎ𝑜𝑢𝑟𝑠 LCM=3×4=12

10 2 .0 +1 13 2
Therefore duration of actual film = , − . = 1+ − 1+ = 1+ = 1 1+ ℎ𝑜𝑢𝑟𝑠
28. In practice copy.

29. A piece………………………………………………………………………………..other piece?

, 11
Soln: Length of wire =2 𝑚 = 𝑚
. .

4 4 4,8
Length of first broken piece =/
1,2
LCM=4×2=8
11 4 ++ 4 12 1
Therefore , length of second piece = . − / = /
−/= /
= 2 / 𝑚