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Frank Learning Maths Class 6 Solutions Chapter 5 Fractions
Welcome to NCTB Solution. Here with this post we are going to help 6th class students for the Solutions of Frank Learning Maths Class 6 Book, Chapter 5 Fractions. Here students can easily find step by step solutions of all the problems for Fractions. Here students will find solutions for Exercise 5.1, 5.2, 5.3, 5.4 and 5.5 also get solutions for chapter Check-up questions. Exercise wise proper solutions. All the problem are solved with easily understandable methods so that all the students can understand easily. Here in this post all Mathematic solutions are based on the CBSE latest curriculum.
Fractions Exercise 5.1 Solution
Question no – (3)
Solution :
(a) 2/3 in word,
= Two-thirds
(b) 1/4 in word,
= One-fourths
(c) 3/7 in word,
= Three-sevenths
(d) 4/15 in word,
= Four-fifteenths
Question no – (4)
Solution :
Fractions |
Numerator | Denominator | |
(a) | 2/5 | 2 | 5 |
(c) | 6/17 | 6 | 17 |
(b) | 8/15 | 8 | 15 |
(d) | 4/9 | 4 | 9 |
Question no – (5)
Solution :
As per the question,
Nidhi has = 10 chocolates.
She gives to Sarika = half of them
Chocolates she give to Sarika = ?
∴ 1/2 of 10
= 5
Thus, she gives 5 chocolates to Sarika.
Question no – (6)
Solution :
Leena has 28 stamps.
She gives 7 stamps to Meena.
Stamps Leena give to Meena = ?
Now, Leena has 28 stamps,
∴ 1 stamps = 1/18
∴ 7 stamps = 7/28 = 1/4
Thus, Leena gives Meena one-fourth of the stamps.
Question no – (7)
Solution :
(a) We know that, A day = 24 hours
∴ 1 hour = 1/24
Hence, 6 hour = 6/24 = 1/4
Therefore, 1/4 fraction of a day is 6 hours.
(b) First, we know that,
An hour = 60 minutes
∴ 1 minute – 1/60
∴ 15 minutes = 15/60 1/4
So, 1/4 fraction of an hour is 15 minutes.
(c) We all know that,
1 year = 12 months.
∴ 1 year = 1/12 months
So, 1/12 fraction of a year is 1 month.
(d) We all know that, A week = 7 days
∴ 1 day = 1/7
∴ 3 da = 3/7
Thus, 3 days of a week is 3/7 of a week.
(e) First, we know that,
Total words in English Alphabet is = 26
Total vowels in English Alphabet is = 5
Now, Fraction = 5/26
Thus, 5/26 of English alphabet is the set of vowels.
(f) We know that,
Prime numbers between 1 and 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53,
59, 61, 67, 71, 73, 79, 83, 89, 97.
Total Prime numbers = 25
Now, Fraction,
= 25/100
= 1/4
Hence, 1/4 fraction of numbers between 1 and 100 is prime numbers.
Question no – (8)
Solution :
(a) fresh?
= Total mangoes = 60
∴ Fresh mangoes,
= 60 – 12
= 48
∴ Fraction
= 48/60
= 4/5
Thus, 4/5 fraction of the mangoes is fresh.
(b) rotten?
Total mangoes = 60,
∴ rotten = 12
∴ Fraction,
= 12/60
= 1/5
So, 1/5 fraction of the mangoes is rotten.
Question no – (9)
Solution :
(a) Three (3) 1/3 s’ will make one whole.
(b) Total 6 (six) 1/6 will make one whole.
Question no – (10)
Solution :
As per the given question,
A bag contains 20 balls of which 3 balls are green,
10 balls are red and the remaining are blue.
∴ Total balls = 20,
Green = 3
Red = 10
Blue = 20 – (3 + 10)
= 20 – 13
= 7
∴ Fractions of Green balls = 3/20,
∴ Fractions of Red balls = 1/2,
∴ Fractions of Blue balls = 7/20
Question no – (11)
Solution :
We know that, The all natural numbers are 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45,
∴ The number of all numbers
= (45 – 30) + 12
= 16
∴ The number of odd numbers = 8
Now, The required fraction,
= 8/16
= 1/2
Thus, 1/2 fraction of these numbers is odd.
Question no – (12)
Solution :
We know,
The Natural numbers are 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113
Prime numbers = (113, 107, 109, 113)
∴ Total numbers,
= (113 – 102) + 1
= 12
Prime numbers = 4
Now, the required fraction,
= 4/12
= 1/3
Thus, 1/3 fraction of them are prime numbers.
Question no – (13)
Solution :
According to the question,
The total girls = 6
In first team = 3
∴ The required fraction,
= 3/6
= 1/2
So, 1/2 fraction of the girls is in the first team.
Try These 5 (i) :
Question no – (1)
Solution :
(a) 1/3 on the number line
(b) 1/4 on the number line
(c) 3/4 on the number line
(d) 2/7 on the number line
Question no – (2)
Solution :
Five more such fractions are,
1/7, 2/7, 3/7, 4/7, 5/7, 6/7
On the number line,
Question no – (3)
Solution :
There are infinite fractions between 0 and 1.
Question no – (4)
Solution :
A = 1/6,
B = 2/6
C = 3/6
D = 4/6
E = 5/6
Question no – (5)
Solution :
Since, the denominator is 7, 1, have to divide the line in 7 parts.
Try These 5 (ii) :
Question no – (1)
Solution :
(a) 2/3
= 2/3 it is a proper fraction.
(b) 8/6
= 8/6 it is a improper fraction.
(c) 27/13
= 27/13 it is a improper fraction.
(d) 52/117
= 52/117 it is a proper fraction.
Question no – (2)
Solution :
5/5 + 3
= 5/8
And 5/8, it is a proper fraction.
Question no – (3)
Solution :
According to the question,
= 5 + 6/5 × 6
= 11/30
And, 11/30 it is a proper fraction.
Question no – (4)
Solution :
1/6, 2/5, 3/4, 4/3, 5/2, 6/1 are the fractions,
Whose numerator and denominator add up to 7.
There are 6 such fractions.
Question no – (5)
Solution :
If N > D then N/D > 1,
If N = D then N/D, then N/D = 1
If N < D then n/d < 1.
Question no – (6)
Solution :
(a) 1/2 ≤ 1
(b) 2/3 ≥ 1
(c) 1 ≥ 4/9
(d) 7/7 ≤ 8/3
(e) 17/5 ≥ 200/200
(f) 0/5 ≤ 1
(g) 6/11 ≤ 305/305
Fractions Exercise 5.2 Solution
Question no – (1)
Solution :
(a) Whose numerator is 5 and denominator is 74.
= 5/7
(b) Whose denominator is 9 and numerator is 5.
= 5/9
(c) Whose numerator and denominator add up to 10. How many fractions of this kind can you make?
Total nine fractions,
= 1/9, 2/8, 3/7, 4/6, 5/5, 6/4, 7/3, 8/2, 9/1
(d) Whose denominator is 4 more than the numerator.
= 5/9, 6/10, 7/11, 100/104, 1000/1004
Question no – (2)
Solution :
(a) 1/2 < 1
(b) 3/5 < 1
(c) 1 > 7/8
(d) 4/4 = 1
(e) 2005/20005 = 1
Question no – (3)
Solution :
(a) 18/5 into mixed fraction
= 3 3/5
(b) 46/7 into mixed fraction
= 6 4/7
(c) 25/3 into mixed fraction
= 8 1/3
(d) 19/8 into mixed fraction
= 2 3/8
Question no – (4)
Solution :
(a) 8 2/5 into improper fraction,
= (5 × 8)+ 2/5
= 42/5
(b) 6 1/2 into improper fraction,
= (2 × 6) + 1/2
= 13/2
(c) 7 3/20 into improper fraction,
= (20 × 7) + 3/20
= 143/20
(d) 11 3/8 into improper fraction,
= (8 × 11) + 3/8
= 91/8
Question no – (5)
Solution :
(a) 5/7 on the number line
(b) 2 1/4 on the number line
(c) 4/3 on the number line
(d) 8/5 on the number line
Question no – (6)
Solution :
(a) 1/4, 1/2, 3/4, 4/4, and 5/4
(b) 1/6, 1/3, 1/2, 2/3, 5/6, 6/6 and 7/6.
Try These 5 (iii) :
Question no – (1)
Solution :
(a) Four equivalent fractions of 4/11 is,
= 8/22, 12/33, 16/44, 20/55
(b) Four equivalent fractions of 4/5 is,
= 8/10, 12/15, 16/20, 20/25
(c) Four equivalent fractions of 3/7 is,
= 6/14, 9/21, 12/28, 15/35
(d) Four equivalent fractions of 2/5 is,
= 4/10, 6/15, 8/20, 10/25
Question no – (2)
Solution :
Equivalent fraction of 7/11 with numeration 28 is = 28/44
Question no – (3)
Solution :
Equivalent fraction of 18/27 with denominator 3 is = 2/3
Question no – (4)
Solution :
All equivalent fractions of 32/104 with lesser denominator and numerator are –
16/52, 8/26, and 4/13
Try These 5 (iv) :
Question no – (1)
Solution :
(a) 4/19 and 12/57
= Since, 4 × 57 = 19 × 12,
The fraction 4/19 and 12/57 are equivalent.
(b) 3/8 and 18/48
= Since 3 × 48 = 8 × 18,
The fraction 3/8, 18/48 are equivalent.
(c) 7/15 and 4/9
= Since, 7 × 9 ≠ 15 × 4,
The fraction 7/15 and 4/9 are not equivalent
(d) 36/56 and 9/14
= Since, 36 × 14 = 56 × 9,
The fraction 36/56, 9/14 are equivalent.
Question no – (2)
Solution :
(a) 2/5 = ____/15
= 2/5 = 6/15
(b) ____/18 = 5/6
= 15/18 = 5/6
(c) 1/8 = ____/32
= 1/8 = 4/32
(d) 4/7 = ____/21
= 4/7 = 5/21
(e) 5/12 = 60/___
= 5/12 = 60/114
Fractions Exercise 5.3 Solution
Question no – (2)
Solution :
(a) 3/4 and 21/28
= Since, 3 × 28 = 4 × 21,
Therefore, 3/4 and 21/28 are equivalent.
(b) 8/9 and 8/10
= Since, 8 × 10 ≠ 8 × 9, 8/9 and 8/10 are not equivalent.
(c) 3 1/5and 32/10
= 3 1/5 = 10/5 and 32/10,
Since 16 × 102 = 5 × 323 1/5 and 32/10 are equivalent.
Question no – (3)
Solution :
(a) Five equivalent fractions of 6/7 are,
= 12/14, 18/21, 24/28, 30/35, 36/42
(b) Five equivalent fractions of 9/13 are,
= 18/26, 27/39, 36/52, 45/65, 54/78
(c) Five equivalent fractions of 3/5 are,
= 6/10, 9/15, 12/20, 15/25, 18/30
Question no – (4)
Solution :
(a) Here, numerator 1000
So, 4 × denominator = 7 × 100
or, denominator = 7 × 100/4 = 175
∴ The required fraction is = 100/175
(b) Given, numerator 180
= So, 4 × denominator = 7 × 100
or, denominator = 7 × 180/4 = 315
∴ The required fraction is = 180/315
(c) denominator 48
= 48/84
(d) denominator 49
= 28/49
Question no – (6)
Solution :
(a) 4/5 and 28/35
Here, 4 × 35 = 5 = 5 × 28 and
HCF of 4 and 5 is 1.
Therefore, 8/9 is the simplest form of 28/35.
(b) 8/9 and 40/45
Since, 8 × 45 = 9 × 40 and HCF of 8 and 9 is 1.
Therefore, 8/9 is the simplest form of 40/45.
(c) 4/7 and 24/56
Since 4 × 56 ≠ 7 × 24,
Therefore, 4/7 is not the simplest form of 24/56.
Question no – (7)
Solution :
(a) 36/144
We, have to find the HCF of 36, 144
The simplest form is,
= 36 ÷ 36/144 ÷ 36
= 1/4
(b) 65/117
Since HCF of 65 and 117 is 13,
The simplest form,
= 65 ÷ 13/117 ÷ 13
= 5/9
(c) 180/120
We, have to find the HCF of 180 and 120
∴ The simplest form is
= 180 ÷ 60/120 ÷ 60
= 3/2
(d) 440/990
We, have to find the HCF of 400 and 990
∴ The smallest form is,
= 440 ÷ 110/990 ÷ 110
= 4/9
Question no – (8)
Solution :
From the question we get,
Stuti had 40 toffees,
Arunima had 60 toffees
Alisha had 80 toffees.
After one week, Stuti was left with 20 toffees
Arunima with 30 and Alisha with 40
Now, After one week, Stuti had 20/40 = 1/2 fraction of the toffees.
Arunima had 30/60 = 1/2 fraction of the toffees.
Alisha had 40/80 = 1/2 fraction of the toffees.
Therefore, each of them consumed an equal fraction of their toffees.
Question no – (9)
Solution :
(i) 250/400 → (a) 2/3
Two more equivalent fractions = 10/16, 15/24
(ii) 180/200 → (b) 2/5 ;
Two more equivalent fractions = 18/20, 27/12
(iii) 660/990 → (c) 1/2 ;
Two more equivalent fractions = 6/9, 8/12
(iv) 180/360 → (d) 5/8 ;
Two more equivalent fractions = 3/6, 4/8
(v) 220/550 → (e) 9/10 ;
Two more equivalent fractions = 4/10, 6/15
Question no – (10)
Solution :
The fractions 1/4 and 16/number of parts, are equivalent
∴ 1 × number of pars
= 4 × 16
= 64
Therefore, the rectangles has been divided in 64 parts.
Try These 5 (vi)
Question no – (1)
Solution :
(a) 1/5, 5/12, 4/9 …(Given fractions)
Let’s compare 1/5 and 5/12
Since 5 × 5 > 1 × 12 therefore, 5/12 > 1/5
Now, Let’s compare 5/12 and 4/9
Since 4 × 12 > 5 × 9
∴ 4/9 > 5/12
Now writing the fractions in ascending order,
We got 1/5, 5/12, 4/5
(b) 5/4, 6/5, 3/8 …(Given fractions)
Let’s compare 5/4 and 6/5
Since, 5 × 5 > 4 × 6 therefore, 5/4 > 6/5
Now, Let’s compare 6/5 and 3/8
Since, 6 × 8 > 5 × 3, therefore, 6/5 > 3/8
Now writing the fractions in ascending order,
We get, 3/8, 6/5, 5/4
Question no – (2)
Solution :
(a) 2/9, 8/15, 6/9, 4/5 …(Given fraction)
Let’s compare 2/9 and 8/15
Since 2 × 15 < 5 × 3, therefore 8/15 > 2/9
Now, Let’s compare 8/15 and 6/9
Since 15 × 6 > 8 × 9, therefore 6/9 > 8/15
Now, Let’s compare 6/9 and 4/5
Since, 9 × 4 > 6 × 5, therefore 4/5 > 6/9
∴ Writing the fractions in descending order, we get 4/5, 6/9, 8/15, 2/9.
(b) 5/9, 2/3, 8/10 …(Given fraction)
The LCM of 9, 3, 10 is
3 × 3 × 10 = 90
∴ 5 × 10/9 × 10
= 50/90, 2 × 30/3 × 30
= 60/90, 8 × 9/10 × 9
= 72/90
Now, writing the fractions in descending order,
We get 8/10, 2/3, 5/9
(c) 4/10, 11/5, 4/15, 7/90 …..(Given fraction)
The LCM of 10, 5, 15, 90, is
∴ 4 × 9/10 × 9
= 36/90, 11 × 18/5 × 18
= 198/90, 4 × 6/15 × 6
= 24/90, 7 × 1/90 × 1
= 7/90
∴ Writing the fractions in descending order, we get 11/5, 4/10, 4/15, 7/90
(d) 3/10, 3/15, 3/17, 3/9, 3/5 (given fraction)
Since, all the numerator are same, the fraction with smallest denominator will be the greatest and the fractions with greatest denominator will be the smallest
∴ Writing the fractions in descending order we get
= 3/5, 3/9, 3/10, 3/1, 3/17
Question no – (3)
Solution :
(a) 1/5, 1/2, 1/7, 1/9
The Smallest = 1/9
The Greatest = 1/2
(b) 12/11, 3/11, 9/11, 10/11
The Smallest = 3/11
The Greatest = 12/11
Fractions Exercise 5.4 Solution
Question no – (1)
Solution :
2/5, 3/5, 4/5, 5/5, 7/5 on the number line,
(a) 4/5 _ 2/5
= 4/5 > 2/5
(b) 5/5 _ 7/5
= 5/5 < 7/5
(c) 1/5 _ 5/5
= 1/5 < 5/5
(d) 3/5 _ 0/5
= 3/5 > 0/5
Question no – (2)
Solution :
(a) 4/7 __ 6/7
= 4/7 < 6/7
So, here the appropriate sign is <
(b) 1/9 __ 1/4
= 1/9 < 1/4
Hence, here the appropriate sign is <
(c) 4/5 __ 3/5
= 4/5 > 3/5
Thus, here the appropriate sign is >
(d) 8/25 __ 11/25
= 8/25 < 11/25
Therefore, here the appropriate sign is <
Question no – (3)
Solution :
(i) 1/5 < 2/5,
(ii) 7/10 > 3/5,
(iii) 8/15 < 12/16 ,
(iv) 3/9 > 2/9,
(v) 3/10 > 3/11,
(vi) 4/15 > 4/18,
(vii) 5/20 < 6/21,
(viii) 3/4 < 4/5
(ix) 5/3 > 5/4,
(x) 5/6 < 8/9
Question no – (4)
Solution :
(a) 3/4 _ 7/8
Since, 4 × 7 > 8 × 3
Therefore, 3/4 < 7/8
(b) 6/10 _ 12/15
Since, 6 × 15 < 10 × 12
Therefore 6/10 < 12/15
(c) 1/3 _ 1/4
= Since, 3 × 1 < 4 × 1
Therefore, 1/3 > 1/4
(d) 5/7 _ 4/9
Since, 5 × 9 > 7 × 4
Therefore, 5/7 > 4/9
Question no – (5)
Solution :
As per the question,
Parul and Tanu ran a 200 m race.
Parul completed the race in 2/3 minutes and Tanu in 4/8 minutes
Now, Since, 3 × 4 < 2 × 8,
Therefore, 2/3 is greater than 4/8
Therefore, Parul took more time.
Question no – (6)
Solution :
Shivi read 50 pages out of 200
∴ Shivi read 50/200 or 1/4 of the book
Vidushi read 1/5 of the book
Comparing 1/4 and 1/5, we get 1 × 4 < 1 × 5, ie 1/4 > 1/5
∴ Vidushi read less.
Another method :
Shivi read 50 pages
And Vidushi read 200 × 1/5 = 40 pages
Therefore, Vidushi read less.
Question no – (7)
Solution :
According to the question,
Saurabh finished his homework in = 8/16 of an hour,
Surabhi finished her homework in = 3/4 of an hour
Now, Comparing 8/16 or 1/2 and 3/4 we get,
= 2 × 3 > 1 × 4, ie 3/4 > 1/2
∴ Saurabh took less time.
Question no – (8)
Solution :
As per the question we know,
In class VI – A, 10 students put of 40 scored more than 90 in mathematics.
In class VI – B, 6 students out of 36 scored more than 90 in mathematics.
Now, The fractions are = 10/40 or 1/4 and 6/36 or 1/6
Comparing, 1/4 and 1/6, we have 1 × 4 < 1 × 6.
Therefore, 1/4 > 1/6 So, Class VIA performed better.
Question no – (9)
Solution :
Isha ate 4 biscuits our of 8.
So, the fraction is 4/8 or 1/2
Preeti ate 7 biscuits out of 12
So, the fraction is 8/12 or 2/3
Shinky ate 10 biscuits out of 15
So, the fractions is 10/15 or 2/3
Question no – (10)
Solution :
(i) Arrange in ascending order :
(a) Given fractions, 1/6, 5/6, 7/6, 9/6, 17/6
In ascending order,
= 1/, 5/6, 7/6, 9/19, 17/6
(b) Given fractions, 3/2, 1/5, 1/4, 5/8
In ascending order,
= 1/5, 1/4, 5/8, 3/2
(c) Given fractions, 1/12, 1/23, 1/4, 1/5, 1/7, 1/50
In ascending order,
= 1/50, 1/23, 1/12, 1/7, 1/5, 1/4
(ii) Arrange in descending order :
(a) Given fractions, 5/6, 5/11, 5/8, 5/2, 5/14, 5/19
In descending order,
= 5/2, 5/6, 5/8, 5/11, 5/14, 5/19
(b) Given fractions, 1/11, 3/11, 2/11, 11/11, 15/11
In descending order,
= 15/11, 11/11, 3/11, 2/11, 1/11
(c) Given fractions, 2/7, 2/5, 6/10
In descending order,
= 6/10, 2/5, 2/7
Try These 5 (vii) :
Question no – (1)
Solution :
(a) 1/6 + 2/6 + 7/6
= 1 + 2 + 7/6
= 10/6
∴ The sum will be 10/6
(b) 1/4 + 2/4 + 9/4
= 1 + 2 + 9/4
= 12/4
∴ The sum will be 12/4
(c) 6/9 + 7/9 + 19/9
= 6 + 7 + 19/9
= 22/9
∴ The sum will be 22/9
Question no – (2)
Solution :
As per the given question,
Ravi got 1/4 kg grapes to Sonu and 3/4 kg to Monu.
Grapes distributed by Ravi = ?
∴ Total quantity,
= 1/4 + 3/4
= 1 + 3/4
= 4/4
= 1 kg
Therefore, the total quantity of grapes distributed by Ravi is 1 kg.
Question no – (3)
Solution :
According to the question,
Raju got = 1/7th part of a pizza
His brother Manoj got = 2/7th part
Sister Tina got = 3/7th part.
∴ Total amount,
= 1/7 + 2/7 + 3/7
= 1 + 2 + /7
= 6/7
Thus, total amount of pizza the three got is 6/7
Fractions Exercise 5.5 Solution
Question no – (1)
Solution :
Five pairs of fractions whose sum is 1 are,
= (3/4, 1/4) ; (4/6, 2/6), (5/10, 5/10), (3/7, 4/7), (2/8, 6/8)
Question no – (2)
Solution :
(a) 3/8
= 1/1 – 3/8
= 8 – 3/8
= 5/8
Thus, 5/8 should be added.
(b) 1/9
= 1/1 – 1/9
= 9 – 1/9
= 8/9
So, 8/9 should be added.
(c) 4/5
= 1/1 – 4/5
= 5 – 4/5
= 1/5
Hence, 1/5 should be added.
(d) 11/15
= 1/1 – 11/15
= 15 – 11/15
= 4/15
So, 4/15 should be added.
(e) 8/35
= 1/1 – 8/35
= 35 – 8/35
= 27/35
Thus, 27/35 should be added.
(f) 81/100
= 1/1 – 81/100
= 100 – 81/100
= 19/100
So, 19/100 should be added.
(g) 199/200
= 1/1 – 199/200
= 200 – 199/200
= 1/200
So, 1/200 should be added.
(h) 998/1000
= 1/1 – 998/1000
= 1000 – 338/1000
= 2/1000
Therefore, 2/1000 should be added.
Question no – (3)
Solution :
(a) 1/9 + 1/9
= 1 + 1/9
= 2/9
∴ The answer will be 2/9
(b) 1/3 + 2/3
= 1 + 2/3
= 3/3
= 1
∴ The answer will be 1
(c) 3/5 + 2/5
= 2 + 3/5
= 5/5
∴ The answer will be 5/5
(d) 4/9 + 4/9
= 4 + 4/9
= 8/9
∴ The answer will be 8/9
Question no – (4)
Solution :
(a) 1/9 + 1/3
= (1 × 1) + (1 × 3)/9
= 1 + 3/9
= 4/9 …(Solved)
(b) 1/8 + 1/24
= (1 × 3) + (1 × 1)/24
= 3 + 1/24
= 4/24
= 1/6 …(Solved)
(c) 1/4 + 1/20
= (5×1) + (1 × 1)/20
= 5 + 1/20
= 6/20
= 3/10 …(Solved)
(d) 1/6 + 1/12
= (2 × 1) + (1 × 1)/12
= 2 + 1/12
= 3/12
= 1/4 …(Solved)
Question no – (5)
Solution :
(a) 2/14, 1/7
The given fractions are 2/14 or 1/7 and 1/7
∴ 1/7 + 1/7
= 1 + 1/7
= 2/7
(b) 3/8, 4/9,
= The given fractions are 3/8, 4/9
LCM of 8 and 9 is 72
∴ 3 × 8/9 × 8
= 24/72 and 4 × 8/9 × 8
= 32/72
∴ 24/72 + 32/72 = 24
= + 32/72
= 56/72
= 7/9
(c) 3, 12/5
The given fractions are 3, 12/5
or, 3 15/5 and 12/5
∴ 15/5 + 12/5
= 15 + 12/5
= 27/5
(d) 1 1/4, 3,3/4
The given fractions are 1 1/4 and 3 3/4 or, 5/4 and 15/4
∴ 5/4 + 15/4
= 5 + 15/4
= 20/4
= 5
(e) 8 2/3, 5 1/4
The given fractions are 8 2/3 and 5 1/4 or, 26/3 and 21/4
∴ LCM of 3 and 4 is 12
∴ 26 × 4/3 × 4
= 104/12 and 21 × 3/4 × 3
= 63/12
∴ 104/12 + 63/12
= 104 + 63/12
= 167/12
(f) 11/15, 7/9, 8/10
The given fractions are 11/15, 7/9, 8/10
LCM of 15, 9, 10 is – 90
∴ 11 × 6/15 × 6
= 66/90, 7 × 10/9 × 10
= 70/90, 8 × 9/10 × 9
= 72/90
= 66/90 + 70/90 + 72/90
= 66 + 70 + 72/90
= 208/90
= 104/45
(g) 5/15, 7/18, 9/36
The given fractions are 5/15, 7/18, 9/36
The LCM of 15, 18, 36 is 180
∴ 5 × 12/15 × 12
= 60/180, 7 × 10/18 × 10
= 70/180, 9 × 5/30 × 5
= 45/180
∴ 60/180 + 70/180 + 45/180
= 60 + 70 + 45/180
= 175/180
= 35/36
(h) 1 1/3, 2 3/6, 3 4/5
The given fractions are 1 1/3, 2 3/6, 3 4/5,or 4/3 , 15/6, 19/5
The LCM of 3, 6, 5, is 30
∴ 4 × 10/3 × 10 = 40/30,
15 × 5/6 × 5 = 75/30,
19 × 6/5 × 6 = 144/30
∴ 40/30 + 75/30 + 114/30
= 40 + 75 + 114/30
= 228/30
(i) 6/7, 1 1/2, 3 4/5
The given fractions are 6/7, 1 1/2, 3 4/5, or 6/7, 3/2, 19/5
The LCM of 7, 2, 5 is = 70
∴ 6 × 10/7 × 10 = 60/70,
3 × 35/2 × 35 = 105/70
= 19 × 14/5 × 14
= 226/70
∴ 60/70 + 105/70 + 226/70
= 60 + 105 + 266/70
= 431/70
Question no – (6)
Solution :
(a) 15/15 – 1/15
= 15 – 1/15
= 14/15 …(Solved)
(b) 5/9 – 2/9
= 5 – 2/9
= 3/9 …(Solved)
(c) 7/7 – 3/7
= 7 – 3/7
= 4/7 …(Solved)
(d) 4/5 – 2/5
= 4 – 2/5
= 2/5 …(Solved)
Question no – (7)
Solution :
(a) 17/10 – 2/3
= (17 × 1) – (3 × 5)/10
= 17 – 15/10
= 2/10
∴ The answer will be 2/10
(b) 3/4 – 3/8
= (3 × 2) – (3 × 1)/8
= 6 – 3/8
= 3/8
∴ The answer will be 3/8
(c) 1/1 – 5/8
= (1 × 8) – (5 × 11)/8
= 8 – 5/8
= 3/8
∴ The answer will be 3/8
(d) 1/2 – 1/6
= (1 × 3) – 91 × 1)/6
= 3 – 1/6
= 2/6
= 1/3
∴ The answer will be 1/3
(e) 2 1/3 – 1 2/3
= 2 1/3 – 1 2/3 = 7/3 – 5/3
= 7 – 5/3
= 2/3
∴ The answer will be 2/3
(f) 3 3/4 – 2 1/5
= 15/4 – 11/5 (15 × 5) – (11 × 4)/20
= 75 – 44/20
= 31/20
∴ The answer will be 31/20
(g) 8 1/4 – 2 5/6
= 8 1/4 – 2 5/6 = 33/4 – 17/6
= (33 × 3) – (17 × 2)/12
= 99 – 24/12
= 65/12
∴ The answer will be 65/12
Question no – (8)
Solution :
According to the question,
A piece of wire = 14/15 metre long
One piece was = 1/3 metre long.
The other piece = ?
Now, The length of the other place
= 14/15 – 1/3
= (14 × 1) – 91 × 5)/15
= 14 – 5/15
= 9/15
Thus, the other piece 9/15 metre long.
Question no – (9)
Solution :
As per the question,
The weight of Heena’s book is = 4/7 kg
Nidhi’s is = 5/7 kg.
Total weight of their books = ?
∴ The total weight,
= 4/7 + 5/7
= 4 + 5/7
= 9/7 kg
Thus, the total weight of their books is 9/7 kg.
Question no – (10)
Solution :
A cup is 1/3 full of milk ….(according to the question)
∴ The full cup = 1
∴ Part of the cup to be filled is,
= 1 – 1/3
= 3 – 1/3
= 2/3
Therefore, 2/3 part of the cup is still to be filled by milk to make it full.
Question no – (11)
Solution :
As per the given question,
From a piece of 10 3/4 m long ribbon = 2 4/5 m is cut.
The length of the remaining ribbon = ?
∴ The length of remaining ribbon,
= 10 3/4 – 1 4/5
= 43/4 – 14/5
= (43 × 5) – (14 × 4)/20
= 215 – 56/20
= 159/20 m
The length of the remaining ribbon is 159/20 m.
Question no – (12)
Solution :
According to the question,
Raj studied for = 50 minutes
Shilpa studied for = 3/4 of an hour.
Now, Shilpa studied for = 3/4 hour
= 3/4 × 60
= 45 minutes
∴ Raj studied for,
= (50 – 45)
= 5 minutes more
Hence, Raj studied more time and by 5 minutes.
Question no – (13)
Solution :
According to the question,
Sarika’s house is 5 2/3 km from her college.
She covers 4 1/2 km by Metro train and the remaining by rickshaw
∴ Sarika cover by rickshaw,
= (5 2/3 – 4 1/2)
= 17/3 – 9/2
= (17 × 2) – (9 × 3)/6
= 34 – 27/6
= 7/6 km
Hence, Sarika cover 7/6 km by rickshaw.
Question no – (14)
Solution :
(a) Subtract 3 1/4 from 4 2/3 …(according to the question)
So now, 4 2/3 – 3 1/4 = 14/3 – 13/4
= (14 × 4) – 913 × 3)/12
= 56 – 39/12
= 17/12
(b) Subtract 7/18 from 15/27 ….(according to the question)
So now, 15/27 – 7/18
= (15 × 2) – (7 × 3)/54
= 30 – 21/54
= 9/54
= 1/6
Question no – (15)
Solution :
As per the given question,
The perimeter of a triangle is 15 1/7 m.
The sum of its two sides is 9 1/14 m,
The length of the third side = ?
Now, The length of the third side,
= 15 1/7 – 9 1/14
= 106/7 – 127/14
= (106 × 2) – (127 × 1)/14
= 212 – 127/14
= 85/14
Thus, the length of the third side is 85/14.
We can also solve the problem in this way,
= 15 1/7 – 9 1/14
= (15 + 1/7) – (9 + 1/14)
= (15 – 9) + (1/7 – 1/14)
= 6 + 1/14
= 6 1/14
= 85/14 m
Question no – (16)
Solution :
The bigger fractions is,
= 1/2 (7/11 + 2/11)
= 1/2 × 9/11
= 9/22
The smallest fraction is,
= 1/2 (7/11 – 2/11)
= 1/2 × 5/11
= 5/22
∴ The required pair is 9/22, 5/22
Question no – (17)
Solution :
(a) 8 2/4 + 4 1/4
= 12 3/4
(b) 6 1/2 = 6 2/4 + 2 1/4
= 8 3/4 ≠ 8 2/6
Question no – (18)
Solution :
0 is the whole number.
0, 1, 2, 3, 4, 5. = There are total 6 numbers out of 5 are natural numbers.
Fraction that represents the number of natural numbers to total numbers in the collection =
Total natural number / Total numbers = 5 / 6.
(ii) Fraction that represents the number of whole numbers to total numbers in the collection
= Total whole number / Total numbers
= 6 / 6
= 1
Question no – (19)
Solution :
The fraction representing the total number of natural numbers in the collection of numbers – 3,- 2, – 1 , 0, 1, 2, 3
Now, The fraction for natural numbers = 3/7
The fraction for whole numbers = 4/7
The fractions for integers = 7/7 = 1
Fractions Chapter Check-up Solution
Question no – (1)
Solution :
As per the question,
Sarita has a box of 88 pens.
She gave one fourth of them to her younger brother
Now, Sarita gave to her younger brother,
= 88 × 1/4
= 22 pens
∴ She had 88 – 22 = 66 pens left with her.
Question no – (2)
Solution :
(a) Given fractions are, 11/9, 11/7, 11/10, 11/6
Here, the smallest one is = 11/10
(b) Given fractions are, 9/11, 7/11, 10/11, 6/11
Here, the smallest one is, = 6/11
Question no – (3)
Solution :
(a) Three equivalent fraction of 6/7 are = 12/14, 18/21, 24/28
(b) Three equivalent fraction of 12/17 are = 24/34, 36/51, 48/68
Question no – (4)
Solution :
(a) Given fractions, 3/7, 27/56
Since, 3 × 56 ≠ 7 × 27,
Therefore, 3/7, 27/56 are not equivalent.
(b) The given fractions are 11/15, 77/90
Since, 11 × 90 ≠ 15 × 77,
Therefore, 11/15, 77/90 are not equivalent.
Question no – (5)
Solution :
Given, 7/4 + 5/2
= 7 + 5/4 + 2
= 12/6
= 2
In the addition of the fractions, we have to find the LCM the denominator first we can’t just odd the numerators separately.
Question no – (6)
Solution :
Given in the question,
(a) 2435 m to km
The result as mixed fraction.
So now,
= 2435 = (2435/1000) km
= 487/200
= 2 87/200
So, 2435 m = 2 87/200 km
Question no – (7)
Solution :
Given fractions, 3/8, 5/4, 8/5, 2/9
Now, Arrange the given fractions in descending order,
We get 8/3, 5/4, 3/8, 2/9
Question no – (8)
Solution :
(a) 1/5 + 2/25
= (5 × 1) + (2 × 1)/25
= 5 + 2/25
= 7/25 …(Simplified)
(b) 3/10 + 4/15
= 3/10 + 4/15
= (3 × 3) + (4 × 2)/30
= 9 + 8/30
= 17/30 …(Simplified)
(c) 3/4 – 1/2
= = (3 × 1) – 92 × 1)/4
= 3 – 2/4
= 1/4 …(Simplified)
(d) 3/4 + 7/12 + 1/3
= (3 × 3) + (7 × 1) + (4 × 1)/12
= 9 + 7 + 4/12
= 20/12 …(Simplified)
(e) 5/12 – 1/4
= 5 – 3/12
= 2/12
= 1/6 …(Simplified)
(f) 6 1/10 – 2 5/7
= (61 × 7) – (19 × 10)/70
= 427 – 190/90
= 237/70 …(Simplified)
Question no – (9)
Solution :
0/5 < 1/5 < 2/5 < 3/5 < 4/5 < 5/5 ;
0/6 < 1/6 < 2/6 < 3/6< 4/6 < 5/6 < 6/6
Five more such problems and solutions,
(a) 1/6 < 1/3
(b) 3/4 > 2/6
(c) 2/3 > 2/4
(d) 6/6 = 3/3
(e) 5/6 < 5/5
Question no – (10)
Solution :
(a)
2/3 | 4/3 | 2 |
1/3 | 2/3 | 1 |
1/3 | 2/3 | 1 |
(b)
1/2 | 1/3 | 5/6 |
1/3 | 1/4 | 7/12 |
1/6 | 1/12 | 1/4 |
For more better understanding :
Question no – (11)
Solution :
(a) 7/18 + 5/6 + 1 1/12
= (7 × 2) + (5 × 6) + (13 × 3)/36
= 14 + 30 + 39/36
= 83/36 …(Simplified)
(b) 5/8 + 2/5 – 1/4
= (5 × 5) + (2 + × 8) – (10 × 1)/40
= 25 + 16 – 10/40
= 31/40 …(Simplified)
Question no – (12)
Solution :
= 3/5 + 2/3 – 2/3 – 1/2 …(according to the question)
= 3/5 – 1/2
= (3 × 2) – (1 × 5)/10
= 6 – 5/10
= 1/10
Question no – (13)
Solution :
(a) 2/5 on the number line
(b) 3 1/5 on the number line
(c) 2 1/5 on the number line
Question no – (14)
Solution :
(a) I am a fraction equivalent to 4/5 with the denominator as 80.
∴ = 80 ÷ 5
= 16
∴ The fraction is,
= 4 × 16/5 × 16
= 64/80
So, I am 64/80.
(b) I am a fraction with numerator 4. The fraction is equivalent to 12/18.
∴ 12 ÷ 4
= 3
∴ The fraction is,
12 ÷ 3/18 ÷ 3
= 4/6
So, I am 4/6
(c) The sum of 2 7/9 and 1 5/18.
∴ 2 7/9 + 1 5/18 …(according to the question)
= 25/9 + 23/18
= (25 × 2) + (23 × 1)/18
= 50 + 23/18
= 73/18
Thus, I am 73/18.
(d) The difference of 915/998 and 15/998
∴ 915/998 – 15/998
= 915 – 15/998
= 900/998
So, here I am 900/998
(e) Given fractions are, 725/896, 725/846, 725/899, 725/900
Here the greater fraction is = 725/846
So, here I am 725/846
Question no – (15)
Solution :
∴ The required fraction is = 1/1 – 1/10
= (1 × 10) – (1 × 1)/10
= 10 – 1/10
= 9/10
So, 9/10 fraction of the food eaten is not available for the next level.
Question no – (16)
Solution :
Given, His age till retirement = 60 years
∴ He was in job,
= 60 – 24
= 36 years.
∴ The required fraction,
= 36/60
= 3/5
Thus, 3/5 fraction of his age till retirement was he in the job.
Question no – (17)
Solution :
As per the given question,
Estimated about 33000 tonnes of CNG, 3300 tonnes of diesel and 21000 tonnes of petrol was saved by the end of year 2007
(a) the quantity of diesel saved to the quantity of petrol saved.
= The quantity of diesel saved = 3300 tonnes
The quantity of petrol saved = 21000 tonnes.
∴ The required fraction,
= 330/21000
= 11/70
(b) the quantity of diesel saved to the quantity of CNG saved.
= The quantity of diesel saved = 3300 tonnes
The quantity of CNG saved = 33000 tonnes
∴ The required fraction,
= 3300/33000
= 1/10
Previous Chapter Solution :