## NCERT Solutions Class 6 Maths Chapter - 7: Fractions## Exercise 7.1
i.
Shaded number of sections = 2 Total number of sections = 4 Fraction = 2/4 ii.
Shaded number of sections = 8 Total number of sections = 9 Fraction = 8/9 iii.
Shaded number of balls = 4 Total number of balls = 8 Fraction = 4/8 iv.
Shaded number of sections = 1 Total number of sections = 4 Fraction = � v.
Shaded number of sections = 3 Total number of sections = 7 Fraction = 3/7 vi.
Shaded number of flowers = 3 Total number of flowers = 12 Fraction = 3/12 vii.
Shaded number of sections = 10 Total number of sections = 10 Fraction = 10 It means that all the sections are shaded. viii.
Shaded number of sections = 4 Total number of sections = 9 Fraction = 4/9 ix.
Shaded number of sections = 4 Total number of sections = 8 Fraction = 4/8 x.
Shaded number of sections = 1 Total number of sections = 2 Fraction = 1/2
It means that 1 section is shaded out of total 6 sections. So, here we will shade only one section of the given figure.
It means that 1 section is shaded out of total 4 sections. So, here we will shade only one section of the given figure.
It means that 1 section is shaded out of total 3 sections. So, here we will shade only one section of the given figure.
It means that 3 sections are shaded out of total 4 sections. So, here we will shade only three sections of the given figure.
It means that 4 sections are shaded out of total 9 sections. So, here we will shade only four sections of the given figure.
All the figures shown above are incorrect.
Total hours in a day = 24 So, the value of fraction 8 hours of a day = 8/24
Total minutes in an hour = 60 So, the value of fraction 40 minutes an hour = 40/60
Arya needs to divide each sandwich into three equal parts so that each boy will get equal part of the vegetable and jam sandwich. Fraction = One sandwich/Total number of boys = 1/3
Total number of boys = 3 Share of each person = 2/3 Thus, each boy will received 2/3 part of a sandwich.
Number of dresses finished by Kanchan = 20 Fraction of dresses she finished = Number of dress finished/ Total number of dresses Fraction = 20/30 Dividing numerator and denominator by 10, we get: Fraction of dresses she finished = 2/3
Total number of natural numbers from 2 to 12 = 11 Prime numbers between 2 and 12 are 2, 3, 5, 7, and 11 Total number of prime numbers from 2 to 12 = 5 Thus, fraction of prime numbers = Total number of prime numbers from 2 to 12/total number of natural numbers from 2 to 12 = 5/11
Total number of natural numbers from 102 to 113 = 12 Prime numbers between 102 and 113 are 103, 107, 109, and 113 Total number of prime numbers from 102 to 113 = 4 Thus, fraction of prime numbers = Total number of prime numbers from 102 to 113 /total number of natural numbers from 102 to 113 = 4/12
Number of circles with X = 4 Fraction of circles with X = Number of circles with X/ Total number of circles Fraction of circles with X = 4/8 Dividing numerator and denominator with 4, we get: Fraction of circles with X = ½ Thus, both 4/8 and 1/2 are the answers of the above question.
Number of CDs received on birthday = 5 Total number of CD = 5 + 3 = 8 Fraction of CDs bought = Number of CDs bought/ Total number of CDs Fraction of CDs bought = 3/8 Fraction of CDs received = Number of CDs received / Total number of CDs Fraction of CDs received = 5/8 ## Exercise 7.2
(a) 1/2, 1/4, 3/4, 4/4 (b) 1/8, 2/8, 3/8, 7/8 (c) 2/5, 3/5, 8/5, 4/5
(a) 20 /3
When 20 is divided by 3 6 × 3 = 18 Remainder = 20 - 18 = 2 Quotient = 6 Mixed fraction = quotient Remainder/divisor Mixed fraction = 6 2/3 (b) 11/ 5
When 11 is divided by 5 5 × 2 = 10 Remainder = 11 - 10 = 1 Quotient = 2 Mixed fraction = quotient Remainder/divisor Mixed fraction = 2 1/5 (c) 17 /7
When 17 is divided by 7 7 × 2 = 14 Remainder = 17 - 14 = 3 Quotient = 2 Mixed fraction = quotient Remainder/divisor Mixed fraction = 2 3/7 (d) 28/ 5
When 28 is divided by 5 5 × 5 = 25 Remainder = 28 - 25 = 3 Quotient = 5 Mixed fraction = quotient Remainder/divisor Mixed fraction = 5 3/5 (e) 19 /6
When 19 is divided by 6 6 × 3 = 18 Remainder = 19 - 18 = 1 Quotient = 3 Mixed fraction = quotient Remainder/divisor Mixed fraction = 3 1/6 (f) 35/ 9
When 35 is divided by 9 9 × 3 = 27 Remainder = 35 - 27 = 8 Quotient = 3 Mixed fraction = quotient Remainder/divisor Mixed fraction = 3 8/9
Improper fraction = Dividend/Divisor Mixed fraction = quotient Remainder/divisor To convert mixed fraction to improper fraction, Improper fraction = (quotient × divisor + remainder) / divisor 7 ¾ = (7 × 4 + 3)/4 = 31/4
Improper fraction = Dividend/Divisor Mixed fraction = quotient Remainder/divisor To convert mixed fraction to improper fraction, Improper fraction = (quotient × divisor + remainder) / divisor 5 6/7= (5 × 7 + 6)/7 = 41/7
Improper fraction = Dividend/Divisor Mixed fraction = quotient Remainder/divisor To convert mixed fraction to improper fraction, Improper fraction = (quotient × divisor + remainder) / divisor 2 5/6 = (2 × 6 + 5)/6 = 17/6
Improper fraction = Dividend/Divisor Mixed fraction = quotient Remainder/divisor To convert mixed fraction to improper fraction, Improper fraction = (quotient × divisor + remainder) / divisor 10 3/5 = (10 × 5 + 3)/5 = 53/5
Improper fraction = Dividend/Divisor Mixed fraction = quotient Remainder/divisor To convert mixed fraction to improper fraction, Improper fraction = (quotient × divisor + remainder) / divisor 9 3/7= (9 × 7 + 3)/7 = 66/7
Improper fraction = Dividend/Divisor Mixed fraction = quotient Remainder/divisor To convert mixed fraction to improper fraction, Improper fraction = (quotient × divisor + remainder) / divisor 8 4/9 = (8 × 9 + 4)/9 = 76/9 ## Exercise 7.3
a.
Fraction = Shaded sections/Total number of sections in a given figure Fraction = Fraction = Shaded sections/Total number of sections in a given figure Fraction = Dividing both the numerator and denominator by 2, we get: Fraction = 1/2 Fraction = Shaded sections/Total number of sections in a given figure Fraction = Dividing both the numerator and denominator by 3, we get: Fraction = 1/2 Fraction = Shaded sections/Total number of sections in a given figure Fraction = Dividing both the numerator and denominator by 4, we get: Fraction = 1/2 Thus, we can say that all these b.
Fraction = Shaded circles /Total number of circles in a given figure Fraction = Dividing both the numerator and denominator by 4, we get: Fraction = 1/3 Fraction = Shaded circles /Total number of circles in a given figure Fraction = Dividing both the numerator and denominator by 3, we get: Fraction = 1/3 Fraction = Shaded circles /Total number of circles in a given figure Fraction = Dividing both the numerator and denominator by 2, we get: Fraction = 1/3 Fraction = Shaded circles /Total number of circles in a given figure Fraction = Fraction = Shaded circles/Total number of circles in a given figure Fraction = Dividing both the numerator and denominator by 3, we get: Fraction = 2/5 Thus, all these fractions are not equivalent because the last fraction is equal to 2/5, while the others are equal to 1/3.
(a) Fraction = Shading sections/ Total number of sections in the given figure Shading section = 1 Total number of sections = 2
(b) Fraction = Shading sections/ Total number of sections in the given figure Shading sections = 4 Total number of sections = 6
Dividing both the numerator and denominator by 2, we get: Fraction = 2/3 It is the fraction in the lowest form, i.e., both the numerator and the denominator has only (c) Fraction = Shading sections/ Total number of sections in the given figure Shading sections = 3 Total number of sections = 9
Dividing both the numerator and denominator by 3, we get: Fraction = 1/3 (d) Fraction = Shading sections/ Total number of sections in the given figure Shading sections = 2 Total number of sections = 8
Dividing both the numerator and denominator by 2, we get: Fraction = 1/4 (e) Fraction = Shading sections/ Total number of sections in the given figure Shading sections = 3 Total number of sections = 4
The above fraction is already present in its lowest form. (i) Fraction = Shading triangles/ Total number of triangles in the given figure Shading triangles = 6 Total number of triangles = 18
Dividing both the numerator and denominator by 6, we get: Fraction = 1/3 (ii) Fraction = Shading sections/ Total number of sections in the given figure Shading sections = 4 Total number of sections = 8
Dividing both the numerator and denominator by 4, we get: Fraction = 1/2 (iii) Fraction = Shading sections/ Total number of sections in the given figure Shading sections = 12 Total number of sections = 16
Dividing both the numerator and denominator by 4, we get: Fraction = 3/4 (iv) Fraction = Shading sections/ Total number of sections in the given figure Shading sections = 8 Total number of sections = 12
Dividing both the numerator and denominator by 4, we get: Fraction = 2/3 (v) Fraction = Shading triangles/ Total number of triangles in the given figure Shading triangles = 4 Total number of triangles = 16
Dividing both the numerator and denominator by 4, we get: Fraction = 1/4 To pair the equivalent fractions, let's represent all the above answers in the form of a table.
Thus, the equivalent fractions are:
Here we will consider the block as (a)
2 × A = 8 × 7 Expanding the number 8 2 × A = 2 × 4 × 7 Comparing both sides, we get: A = 4 × 7 A = (b)
5 × A = 8 × 10 Expanding the number 10 5 × A = 8 × 2 × 5 5 × A =5 × 8 × 2 Comparing both sides, we get: A = 8 × 2 A = (c)
3 × 20 = A × 5 Expanding the number 20 3 × 4 × 5 = A × 5 Comparing both sides, we get: A = 3 × 4 A = (d)
45 × A = 60 × 15 Expanding the number 60 45 × A = 3 × 20 × 15 45 × A = 3 × 15 × 20 45 × A = 45 × 20 Comparing both sides, we get: A = (e)
18 × 4 = 24 × A Expanding the number 18 6 × 3 × 4 = 24 × A 6 × 4 × 3 = 24 × A 24 × 3 = 24 × A Comparing both sides, we get: A =
Let the numerator be A. 3/5 = A/20 3 × 20 = 5 × A Expanding the number 20 3 × 5 × 4 = 5 × A 5 × 4 × 3 = 5 × A 5 × 12 = 5 × A Comparing both sides, we get: A =
Thus, the equivalent value of the fraction is
Let the denominator be A. 3/5 = 9/A 3 × A = 5 × 9 Expanding the number 9 3 × A = 5 × 9 3 × A = 5 × 3 × 3 3 × A = 3 × 3 × 5 Comparing both sides, we get: A = 3 × 5 A =
Thus, the equivalent value of the fraction is
Let the numerator be A. 3/5 = A/30 3 × 30 = 5 × A Expanding the number 30 3 × 5 × 6 = 5 × A 5 × 6 × 3 = 5 × A 5 × 18 = 5 × A Comparing both sides, we get: A =
Thus, the equivalent value of the fraction is
Let the denominator be A. 3/5 = 27/A 3 × A = 5 × 27 Expanding the number 27 3 × A = 5 × 9 3 × A = 5 × 9 × 3 3 × A = 3 × 9 × 5 Comparing both sides, we get: A = 9 × 5 A =
Thus, the equivalent value of the fraction is
Let the denominator be A. 36/48 = 9/A 36 × A = 9 × 48 Expanding the number 48 36 × A = 9 × 12 × 4 36 × A = 9 × 4 × 12 36 × A = 36 × 12 Comparing both sides, we get: A =
Thus, the equivalent value of the fraction is
Let the numerator be A. 36/48 = A/4 36 × 4 =48 × A Expanding the number 36 3 × 12 × 4 = 48 × A 12 × 4 × 3 = 48 × A 48 × 3 = 48 × A Comparing both sides, we get: A =
Thus, the equivalent value of the fraction is
To check the equivalent fractions, we will convert the fractions to their lowest form, where both the numerator and denominator of a fraction has only 1 as the common factor.
5/9 is already present in its lowest form.
Let's consider the second fraction. Factors of 30: 2 × 5 × 3 Factors of 54: 2 × 3 × 3 × 3 Common factors = 2 × 3 = 6 Dividing both the numerator and the denominator of 30/54 by 6, we get:
Thus, both the fractions are equal.
3/10 is already present in its lowest form.
Let's consider the second fraction. Factors of 12: 2 × 2 × 3 Factors of 50: 2 × 5 × 5 Common factor = 2 Dividing both the numerator and the denominator of 12/50 by 2, we get:
Thus, both the fractions are not equal. 3/10 is not equal to 6/25
7/13 is already present in its lowest form.
5/11 is also present in its lowest form. Thus, both the fractions are not equal.
Factors of 48: 2 × 2 × 2 × 2 × 3 Factors of 60: 2 × 2 × 3 × 5 Common factors: 2 × 2 × 3 = 12 Dividing both the numerator and the denominator of the given fraction by 12, we get: 4/5 Thus, 4/5 is the simplest form of 48/60.
Factors of 150: 3 × 5 × 2 × 5 Factors of 60: 2 × 2 × 3 × 5 Common factors: 2 × 3 × 5 = 30 Dividing both the numerator and the denominator of the given fraction by 30, we get: 5/2 Thus, 5/2 is the simplest form of 150/60.
Factors of 84: 2 × 2 × 7 × 3 Factors of 98: 2 × 7 × 7 Common factors: 2 × 7 = 14 Dividing both the numerator and the denominator of the given fraction by 14, we get: 6/7 Thus, 6/7 is the simplest form of 84/98.
Factors of 12: 2 × 2 × 3 Factors of 52: 2 × 2 × 13 Common factors: 2 × 2 = 4 Dividing both the numerator and the denominator of the given fraction by 4, we get: 3/13 Thus, 3/13 is the simplest form of 12/52.
Factors of 7: 1 × 7 Factors of 28: 2 × 2 × 7 Common factor: 7 Dividing both the numerator and the denominator of the given fraction by 7, we get: 1/4 Thus, 1/4 is the simplest form of 7/28.
Total number of pencils with Ramesh = 20 Number of pencils used by Ramesh = 10 Fraction = Used pencils/total pencils Fraction = 10/20 = 1/2 Thus, Ramesh used Total number of pencils with Sheelu = 50 Number of pencils used by Sheelu = 25 Fraction = Used pencils/total pencils Fraction = 25/50 = 1/2 Thus, Sheelu used Total number of pencils with Jamaal = 80 Number of pencils used by Jamaal = 40 Fraction = Used pencils/total pencils Fraction = 40/80 = 1/2 Thus, Jamaal also used
Here, we will convert the given fraction into its lowest fraction to match with the given values.
## Exercise 7.4
(a)
Ascending order: 1/8 < 3/8 < 4/8 < 6/8 Descending order: 6/8 > 4/8 > 3/8 > 1/8
Number of shaded sections = 3 Total number of sections = 8 Fraction = Shaded sections/Total number of sections Fraction = 3/8 Number of shaded sections = 6 Total number of sections = 8 Fraction = Shaded sections/Total number of sections Fraction = 6/8 Number of shaded sections = 4 Total number of sections = 8 Fraction = Shaded sections/Total number of sections Fraction = 4/8 Number of shaded section = 1 Total number of sections = 8 Fraction = Shaded sections/Total number of sections Fraction = 1/8 To compare the fractions, we need to ensure that the fractions have the same denominator. Ascending order of numbers is the order from smallest fraction to the largest fraction. 1/8 < 3/8 < 4/8 < 6/8 Descending order of numbers is the order from largest fraction to the smallest fractions. 6/8 > 4/8 > 3/8 > 1/8 (b)
Ascending order: 3/9 < 4/9 < 6/9 < 8/9 Descending order: 8/9 > 6/9 > 4/9 > 3/9
Number of shaded sections = 8 Total number of sections = 9 Fraction = Shaded sections/Total number of sections Fraction = 8/9 Number of shaded sections = 4 Total number of sections = 9 Fraction = Shaded sections/Total number of sections Fraction = 4/9 Number of shaded sections = 3 Total number of sections = 9 Fraction = Shaded sections/Total number of sections Fraction = 3/9 Number of shaded section = 6 Total number of sections = 9 Fraction = Shaded sections/Total number of sections Fraction = 6/9 To compare the fractions, we need to ensure that the fractions have the same denominator. Ascending order of numbers is the order from smallest fraction to the largest fraction. 3/9 > 4/9 > 6/9 > 8/9 Descending order of numbers is the order from largest fraction to the smallest fractions. 8/9 > 6/9 >4/9 > 3/9
Put appropriate signs between the fractions given.
Since the denominators of both the fractions are the same, fraction 5/6 is greater than the fraction 2/6.
3/6 > 0/6 We can also write 0 as 0/6. Dividing 0 by any number results in 0. Since the denominators of both the fractions are now the same, fraction 3/6 is greater than the fraction 0/6 or 0.
The fraction 6/6 is greater than the fraction 1/6.
The fraction 8/6 is greater than the fraction 5/6.
Here, the denominators are different. To compare the fractions, we need the same denominators. So, multiply the left fraction by 4. 1 × 4/ (7 × 4) = 4/28 Similarly, multiply the right fraction by 7. 1 × 7/ (4 × 7) = 7/28 Now, comparing both fractions, 4/28 < 7/28 Hence, 1/7 < 1/4
Here, the denominators are different. To compare the fractions, we need the same denominators. So, multiply the left fraction by 7. We can select any multiple to make the denominator of the fractions equal. 3 × 7/ (5 × 7) = 21/35 Similarly, multiply the right fraction by 75 3 × 5/ (7 × 5) = 15/35 Now, comparing both fractions, 21/35 > 15/35 Hence, 3/5 > 3/7
- 2/5 > 1/5
- 4/8 < 7/8
- 1/8 < 3/8
- 5/5 > 2/5
- 6/9 > 1/9
All the numbers above are present in the ascending order.
To compare, the denominators of the given fractions should be equal. Multiplying the right side fraction by 2, we get: 1 × 2/ (3 × 2) = 2/6 Comparing now, 1/6 < 2/6 Hence, 1/6 < 1/3
To compare, the denominators of the given fractions should be equal. Multiplying the left side fraction by 3, we get: 3 × 3/ (4 × 3) = 9/12 Multiplying the right side fraction by 2, we get: 2 × 2/ (6 × 2) = 4/12 Comparing now, 9/12 > 4/12 Hence, 3/4 > 2/6
To compare, the denominators of the given fractions should be equal. Multiplying the left side fraction by 4, we get: 2 × 4/ (3 × 4) = 8/12 Multiplying the right side fraction by 3, we get: 2 × 3/ (4 × 3) = 6/12 Comparing now, 8/12 > 6/12 Hence, 2/3 > 2/4
A number divided by the same number is always equal to 1. 1 = 1 Hence, 6/6 = 3/3
To compare, the denominators of the given fractions should be equal. Multiplying the left side fraction by 5, we get: 5 × 5/ (6 × 5) = 25/30 Multiplying the right side fraction by 3, we get: 2 × 3/ (4 × 3) = 6/12 Comparing now, 8/12 > 6/12 Hence, 2/3 > 2/4
To compare, the denominators of the given fractions should be equal. Multiplying the left side fraction by 5, we get: 1 × 5/ (2 × 5) = 5/10 Multiplying the right side fraction by 2, we get: 1 × 2/ (5 × 2) = 2/10 Comparing now, 5/10 > 2/10 Hence, 1/2 > 1/5
To compare, the denominators of the given fractions should be equal. Both the given fractions are not present in their lowest form. So first, we will convert both the fractions to their lowest form. Dividing the left fraction by 2, we get: 1/2 Dividing the right fraction by 3, we get: 1/2 Comparing now, 1/2= 1/2 Hence, 2/4 = 3/6
To compare, the denominators of the given fractions should be equal. Multiplying the left side fraction by 3, we get: 3 × 3/ (5 × 3) = 9/15 Multiplying the right side fraction by 5, we get: 2 × 5/ (3 × 5) = 10/15 Comparing now, 9/15 < 10/15 Hence, 1/2 > 1/5 3/5 < 2/3
To compare, the denominators of the given fractions should be equal. The second fraction can be converted to its lowest form. Dividing the right fraction by 2, we get: 1/4 The denominators of both the fractions are now the same. By comparing, 3/4 > 1/4 Thus, 3/4 > 2/8
The denominators are the same. Thus, 6/5 is greater than 3/5.
The denominators are the same. Thus, 7/9 > 3/9
To compare, the denominators of the given fractions should be equal. The second fraction can be converted to its lowest form. Dividing the right fraction by 2, we get: 1/4 The denominators of both the fractions are now the same. By comparing, � = 1/4 Thus, 1/4 = 2/8
To compare, the denominators of the given fractions should be equal. The first fraction can be converted to its lowest form. Dividing the left fraction by 2, we get: 3/5 The denominators of both the fractions are now the same. By comparing, 3/5 < 4/5 Thus, 6/10 < 4/5
To compare, the denominators of the given fractions should be equal. Multiplying the left side fraction by 2, we get: 3 × 2/ (4 × 2) = 6/8 Comparing now, 6/8 < 7/8 Hence, 3/4 < 7/8
To compare, the denominators of the given fractions should be equal. The first fraction can be converted to its lowest form. Dividing the left fraction by 2, we get: 3/5 2 × 3 = 6 2 × 5 = 10 The denominators of both the fractions are now the same. By comparing, 3/5 = 3/5 Thus, 6/10 = 3/5
To compare, the denominators of the given fractions should be equal. The second fraction can be converted to its lowest form. Dividing the right fraction by 3, we get: 5/7 3 × 5 = 15 3 × 7 = 21 The denominators of both the fractions are now the same. By comparing, 5/7 = 5/7 Thus, 5/7 = 15/21
Simplest form refers to the form of a fraction where the numerator and the denominator have only 1 as the common factor. Here, we will find the common multiple and divide the numerator and the denominator with that common multiple.
1/6 2 × 1 = 2 2 × 6 = 12
1/5 3 × 1 = 3 3 × 5 = 15
4/25 2 × 4 = 8 2 × 25 = 50
4/25 4 × 4 = 16 4 × 25 = 100
1/6 10 × 1 = 10 10 × 6 = 60
1/5 15 × 1 = 15 15 × 5 = 75
1/5 12 × 1 = 12 12 × 5 = 60
1/6 16 × 1 = 16 16 × 6 = 96
4/25 3 × 4 = 12 3 × 25 = 75
1/6 12 × 1 = 12 12 × 6 = 72
1/6 3 × 1 = 3 3 × 6 = 18
The above fraction is already present in its lowest form. The three groups of equivalent fractions are shown in the below table:
Multiplying the left fraction by 5, we get: 5 × 5/ (9 × 5) = 25/45 Multiplying the right fraction by 9, we get: 9 × 4/ (5 × 9) = 36/45 By comparing, 25/45 < 36/45 Thus, 5/9 is not equal to 4/5.
Multiplying the left fraction by 9, we get: 9 × 9/ (9 × 16) = 81/144 Multiplying the right fraction by 16, we get: 16 × 5/ (16 × 9) = 80/144 By comparing, 81/144 > 80/144 Thus, 9/16 is not equal to 5/9.
Dividing the numerator and the denominator by 4, we get: (4 × 4)/(4 × 5) = 4/5 By comparing with the first fraction, 4/5 = 4/5 Thus, 4/5 is equal to 16/20.
Dividing the numerator and the denominator by 2, we get: (2 × 2)/(2 × 15) = 2/15 By comparing with the first fraction, 1/15 < 2/15 Thus, 1/15 is not equal to 4/30.
Number of pages read by Lalita = Fraction × Total number of pages = 2/5 × 100 = 200/5 = 40 Number of pages read by Lalita = 40 Thus, Lalita read 40 pages and Ila read 25 pages.
Number of minutes exercised by Rafiq = Fraction × Number of minutes = 3/6 × 60 = 30 minutes Number of minutes exercised by Rohit = Fraction × Number of minutes = 3/4 × 60 = 45 minutes Thus, Rohit exercised for 45 minutes and Rafiq exercised for 30 minutes.
Number of students passed with 60% or more marks in class A = 20 Fraction of passed students = Number of students passed/Total students = 20/25 = 4/5 Fraction of students passed in class A = 4/5 Number of students in class B = 30 Number of students passed with 60% or more marks in class b = 24 Fraction of passed students = Number of students passed/Total students = 24/30 = 4/5 Fraction of students passed in class B = 4/5 Thus, equal fraction of students passed in both the classes. ## Exercise 7.5
Here, we will first find the value of fraction of each block. Fraction = Shaded section/Total number of sections Shaded section = 1 Total number of sections = 5 Fraction = Fraction = Shaded section/Total number of sections Shaded section = 2 Total number of sections = 5 Fraction = Fraction = Shaded section/Total number of sections Shaded section = 3 Total number of sections = 5 Fraction = It shows that, 1/5 + 2/5 = 3/5 Thus, it signifies addition.
Fraction = Shaded section/Total number of sections Shaded section = 5 Total number of sections = 5 Fraction = Fraction = Shaded section/Total number of sections Shaded section = 3 Total number of sections = 5 Fraction = Fraction = Shaded section/Total number of sections Shaded section = 2 Total number of sections = 5 Fraction = It shows that, 5/5 - 3/5 = 2/5 Thus, it signifies subtraction.
Fraction = Shaded section/Total number of sections Shaded section = 2 Total number of sections = 6 Fraction = Fraction = Shaded section/Total number of sections Shaded section = 3 Total number of sections = 6 Fraction = Fraction = Shaded section/Total number of sections Shaded section = 5 Total number of sections = 6 Fraction = Thus, 2/6 + 3/6 = 5/6 The above fraction signifies addition.
For addition, the denominators should be same. 1/18 + 1/18 = (1 + 1)/18 = 2/18 Both the numerator and the denominator have 2 as the common factor. Let's divide the fraction by 2 to convert to its lowest form.
2 × 1 = 2 2 × 9 = 18 Thus, 1/18 + 1/18 = 1/9
For addition, the denominators should be same.
= (8 + 3)/15 = 11/15 The fraction is already present in its lowest form.
= (7 - 5)/7 = 2/7 The fraction is already present in its lowest form.
= (1 + 21)/22 = 22/22 Both the numerator and the denominator have 22 as the common factor. Let's divide the fraction by 22 to convert to its lowest form.
22 × 1 = 22 Thus, 1/22 + 21/22 = 1
= (12 - 7)/15 = 5/15 Both the numerator and the denominator have 5 as the common factor. Let's divide the fraction by 5 to convert to its lowest form.
5 × 1 = 5 5 × 3 = 15 Thus, 12/15 - 7/15 = 1/3
= (5 + 3)/8 = 8/8 Both the numerator and the denominator have 8 as the common factor. Let's divide the fraction by 8 to convert to its lowest form.
8 × 1 = 8 Thus, 5/8 + 3/8 = 1
To subtract, the denominators should be equal. We can write any number with denominator as 1. For example, 1 can be written as 1/1 Multiplying the fraction (1/1) by 3, we get: 3/3 1 × 3/ 1 × 3 = 3/3 Now subtracting, 3/3 - 2/3 = (3 - 2)/3
= (1 + 0)/4 = 1/4
We can write any number with denominator as 1. For example, 3 can be written as 3/1 Multiplying the fraction (3/1) by 5, we get: 5 × 3/ 1 × 5 = 15/5 Now subtracting, 15/5 - 12/5 = (15 - 12)/5
Fraction of wall painted by Madhavi = 1/3 Total wall painted together = 2/3 + 1/3 = (2 + 1)/3 = 3/3 Dividing the numerator and the denominator by 3, we get: 1/1 Thus, Shubham and Madhavi painted together
= (7 - 3)/10 = 4/10 The numerator and the denominator of the above fraction have 2 as the common factor. Dividing the fraction by 2, we get: 2/5 2 × 2 = 4 2 × 5 = 10
Let the blank space be A.
A = 5/21 + 3/21 A = (5 + 3)/21 A = 8/21 = (7 - 3)/10 = 4/10 The numerator and the denominator of the above fraction have 2 as the common factor. Dividing the fraction by 2, we get: 2/5 2 × 2 = 4 2 × 5 = 10
Let the blank space be A.
A = 3/6 + 3/6 A = (3 + 3)/6 A = 6/6
Let the blank space be A.
A = 12/27 - 5/27 A = (12 - 5)/27 A = 7/27
The fraction of oranges with Javed = 5/7 Total oranges in the basket = 1/1 The complete fraction is always represented as 1 or 1/1. Fraction of oranges left in the basket = 1/1 - 5/7 To subtract, the denominator should be equal. Multiplying the fraction by 7, we get: (1× 7)/ (1 × 7) = 7/7 Now subtracting, 7/7 - 5/7 = (7 - 5)/7 = 2/7 Thus, 2/7 fraction of oranges was left in the basket. ## Exercise 7.6
So, we will multiply both the fractions by a number to make the denominators equal. 7 × 3 = 21 Multiplying the fraction (2/3) by 7, we get: (2 × 7)/ (3 × 7) = 14/21 Multiplying the fraction (1/7) by 3, we get: (1 × 3)/ (7 × 3) = 3/21 Now, adding = 14/21 + 3/21 = 17/21 We can also convert the fraction to its lowest form. But, the above fraction is already present in its lowest form as the numerator and the denominator has only 1 as the common factor.
So, we will multiply both the fractions by a number to make the denominators equal. Multiplying the fraction (3/10) by 3, we get: (3 × 3)/ (10 × 3) = 9/30 Multiplying the fraction (7/15) by 2, we get: (7 × 2)/ (15 × 2) = 14/30 Now, adding = 9/30 + 14/30 = 23/30
So, we will multiply both the fractions by a number to make the denominators equal. 9 × 7 = 63 Multiplying the fraction (4/9) by 7, we get: (4 × 7)/(9 × 7) = 28/63 Multiplying the fraction (2/7) by 9, we get: (9 × 2)/ (7 × 9) = 18/63 Now, adding = 28/63 + 18/63 = (28 + 18)/63 = 46/63
So, we will multiply both the fractions by a number to make the denominators equal. 7 × 3 = 21 Multiplying the fraction (5/7) by 3, we get: (5 × 3)/ (3 × 7) = 15/21 Multiplying the fraction (1/3) by 7, we get: (1 × 7)/ (7 × 3) = 7/21 Now, adding = 15/21 + 7/21 = (15 + 7)/21 = 22/21
So, we will multiply both the fractions by a number to make the denominators equal. 5 × 6 = 30 Multiplying the fraction (2/5) by 6, we get: (2 × 6)/ (5 × 6) = 12/30 Multiplying the fraction (1/6) by 5, we get: (1 × 5)/ (6 × 5) = 5/30 Now, adding = 12/30 + 5/30 = (12 + 5)/30 = 17/30
So, we will multiply both the fractions by a number to make the denominators equal. 5 × 3 = 15 Multiplying the fraction (4/5) by 3, we get: (4 × 3)/ (3 × 5) = 12/15 Multiplying the fraction (2/3) by 5, we get: (2 × 5)/ (5 × 3) = 10/15 Now, adding = 12/15 + 10/15 = (12 + 10)/15 = 22/15
So, we will multiply both the fractions by a number to make the denominators equal. 4 × 3 = 12 Multiplying the fraction (3/4) by 3, we get: (3 × 3)/ (4 × 3) = 9/12 Multiplying the fraction (1/3) by 4, we get: (1 × 4)/ (4 × 3) = 4/12 Now, subtracting = 9/12 - 4/12 = (9 - 4)/12 = 5/12
2 × 3 = 6 Here, we will multiply the fraction (1/3) by 2 to make both the denominators equal. Multiplying the fraction (1/3) by 2, we get: (1 × 2)/ (3 × 2) = 2/6 Now, subtracting, = 5/6 - 2/6 = (5 - 2)/6 = 3/6 Let's divide the above fraction by 2 to convert to its lowest form. 1/2 3 × 1 = 3 3 × 2 = 6
To make the denominators equal, we will find the LCM of all the denominators. LCM (3, 4, 2) = 12 So, we will multiply the three fractions by a number to make the denominators equal to 12. Multiplying the fraction (2/3) by 4, we get: (2 × 4)/ (3 × 4) = 8/12 Multiplying the fraction (3/4) by 3, we get: (3 × 3)/ (4 × 3) = 9/12 Multiplying the fraction (1/2) by 6, we get: (1 × 6)/ (2 × 6) = 6/12 Now, adding 8/12 + 9/12 + 6/12 = (8 + 9 + 6)/12 = 23/12
To make the denominators equal, we will find the LCM of all the denominators. LCM (2, 3, 6) = 6 So, we will multiply the three fractions by a number to make the denominators equal to 6. Multiplying the fraction (1/2) by 3, we get: (1 × 3)/ (2 × 3) = 3/6 Multiplying the fraction (1/3) by 2, we get: (1 × 2)/ (3 × 2) = 2/6 The third fraction has already 6 as the denominator. Now, adding 3/6 + 2/6 + 1/6 = (3 + 2 + 1)/6 = 6/6 Dividing the above fraction by 6, we get: 1/1 or 1
(1 + 3) + (1/3 + 2/3) = 4 + (3/3) = 4 + 1 = 5
(4 + 3) = 7
2/3 + 1/4 To add, the denominator of the fraction should be equal to 12. 3 × 4 = 12 Multiplying the fraction (2/3) by 4, we get: (2 × 4)/ (3 × 4) = 8/12 Multiplying the fraction (1/4) by 3, we get: (1 × 3)/ (4 × 3) = 3/12 Adding now, 8/12 + 3/12 = (8 + 3)/12 = 11/12 Let's add fraction part and whole part, 7 + 11/12 7/1 + 11/12 Multiplying the fraction (7/1) by 12, we get: 7 × 12/ 1 × 12 = 84/12 Adding now, 84/12 + 11/12
= 16/5 - 7/5 = (16 - 7)/5 = 9/5
To make the denominators equal, we will find the LCM of all the denominators. LCM (3, 2) = 6 So, we will multiply the two fractions by a number to make the denominators equal to 6. Multiplying the fraction (4/3) by 2, we get: (2 × 4)/ (3 × 2) = 8/6 Multiplying the fraction (1/2) by 3, we get: (1 × 3)/ (2 × 3) = 3/6 Now subtracting, 8/6 - 3/6 = (8 - 3)/6 = 5/6
Length of ribbon bought by Sarita = 2/5 meter Length of ribbon bought by Lalita =3/4 meter Total length = Length bought by Sarita + Length bought by Lalita = 2/5 + 3/4 Let's multiply the fraction (2/5) by 4 and the fraction (3/4) by 5 to make the denominators equal to 20. (2 × 4)/ (5 × 4) = 8/20 (3 × 5)/ (4 × 5) = 15/20 Total length = 8/20 + 15/20 = 23/20 Thus, Sarita and Lalita bought together 23/20 meter of the ribbon.
Piece of cake given to Naina = 1 1/2 Piece of cake given to Najma = 1 1/3 Total amount of cake = 1 1/2 + 1 1/3 Let's add whole and fraction part separately, we get: (1 + 1) + (1/2 + 1/3) Multiplying the fraction (1/2) by 3 and the fraction (1/3) by 2, we get: 2 + ((1 × 3)/(2 × 3) + (1 × 2)/ (3 × 2)) = 2 + (3/6 + 2/6) = 2 + 5/6 = 2 5/6 Thus, the total amount of cake was given to both of them is2 5/6.
Let the blank space be A. A - 5/8 = 1/4 A = 1/4 + 5/8 Multiplying the fraction (1/4) by 2, we get: (1 × 2)/ (4 × 2) = 2/8 Adding now, A = 2/8 + 5/8
Let the blank space be A. A - 1/5 = 1/2 The negative sign becomes positive when taken on the other side. A = 1/2 + 1/5 Multiplying the fraction (1/2) by 5 and the fraction (1/5) by 2 to make the denominator equal to 10, we get: A = 5/10 + 2/10 A = (5 + 2)/10 A = 7/10
Let the blank space be A. 1/2 - A = 1/6 A = 1/2 - 1/6 Multiplying the fraction (1/2) by 3, we get: A = 3/6 - 1/6 A = (3 - 1)/6 A = 2/6 Dividing the numerator and the denominator by the common factor (2), we get: A = 1/3
Total length of the wire = 7/8 meter Length of one piece = 1/4 meter Length of the other piece = Total length - Length of one piece = 7/8 - 1/4 Multiplying the fraction (1/4) by 2, we get: = 7/8 - 2/8 = (7 - 2)/8
Thus, the length of the other piece is 5/8 meter.
Total distance of the Nandini's house from her school = 9/10 km Distance taken by a bus = 1/2 km Distance Nandini walked = 9/10 - 1/2 Multiplying the second fraction by 5, we get: 9/10 - 5/10 = (9 - 5)/10 = 4/10 Dividing the above fraction by 2, = 2/5 Thus, Nandini walked 2/5 km to reach the school.
The fraction of Asha's shelf filled with books = 5/6 The fraction of Samuel's shelf filled with books = 2/5 To compare, let's make their denominators equal. Multiplying the fraction (5/6) by 5, we get: (5 × 5)/ (6 × 5) = 25/30 Multiplying the fraction (2/5) by 6, we get: (2 × 6)/ (5 × 6) = 12/30 By comparing, 25/30 > 12/30 Thus, Asha's book shelf is fuller than the Samuels' book shelf. Difference = 25/30 - 12/30 = (25 - 12)/30 = 13/30 Thus, Asha's book shelf is fuller than the Samuels' book shelf by 13/30.
Time taken by Jaidev to walk across the school ground = 2 1/5 = 11/5 Time taken by Rahul to walk across the school ground = 7/4 Multiplying the fraction (11/5) by 4, we get: (11 × 4)/ (5 × 4) = 44/20 Multiplying the fraction (7/4) by 5, we get: (7 × 5)/ (4 × 5) = 35/20 By comparing, 35/20 < 44/20 Thus, Rahul takes less time. Difference = 44/20 - 35/20 = (44 - 35)/20 = 9/20 Rahul takes 9/20 minutes less than the Jaidev. Next TopicClass 6 Maths Chapter 8 |