Well-designed AP Board Solutions Class 6 Maths Chapter 7 Fractions Exercise 7.4 offers step-by-step explanations to help students understand problem-solving strategies.
Fractions Class 6 Exercise 7.4 Solutions – 6th Class Maths 7.4 Exercise Solutions
Question 1.
Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign ‘<‘, ‘=’, ‘>’ between the fractions:
Solution:
i) Total number of divisions = 8
Number of shaded parts = 3
∴ Fraction = \(\frac { 3 }{ 8 }\)
ii) Total number of divisions = 8
Number of shaded parts = 6
∴ Fraction = \(\frac { 6 }{ 8 }\)
iii) Total number of divisions = 8
Number of shaded parts = 4
∴ Fraction = \(\frac { 4 }{ 8 }\)
iv) Total number of divisions = 8
Number of shaded parts = 1
∴ Fraction = \(\frac { 1 }{ 8 }\)
Now, the fractions are : \(\frac { 3 }{ 8 }\), \(\frac { 6 }{ 8 }\), \(\frac { 4 }{ 8 }\) and \(\frac { 1 }{ 8 }\) with same denominator.
Ascending order: \(\frac { 1 }{ 8 }\) < \(\frac { 3 }{ 8 }\) < \(\frac { 4 }{ 8 }\) < \(\frac { 6 }{ 8 }\) Descending order: \(\frac { 6 }{ 8 }\) > \(\frac { 4 }{ 8 }\) > \(\frac { 3 }{ 8 }\) > \(\frac { 1 }{ 8 }\)
Solution:
1) Total number of divisions = 9
Number of shaded parts = 8
∴ Fraction = \(\frac { 8 }{ 9 }\)
ii) Total number of divisons = 9
Number of shaded parts = 4
∴ Fraction = \(\frac { 4 }{ 9 }\)
iii) Total number of divisons = 9
Number of shaded parts = 3
∴ Fraction = \(\frac { 3 }{ 9 }\) (or) \(\frac { 1 }{ 3 }\)
iv) Total number of divisons = 9
Number of shaded parts = 6
∴ Fraction = \(\frac { 6 }{ 9 }\) (or) \(\frac { 2 }{ 3 }\)
∴ Fractions are \(\frac { 8 }{ 9 }\), \(\frac { 4 }{ 9 }\), \(\frac { 3 }{ 9 }\), \(\frac { 6 }{ 9 }\) with same denominator:
Ascending order: \(\frac { 3 }{ 9 }\) < \(\frac { 4 }{ 9 }\) < \(\frac { 6 }{ 9 }\) < \(\frac { 8 }{ 9 }\) Descending order:\(\frac { 8 }{ 9 }\) > \(\frac { 6 }{ 9 }\) > \(\frac { 4 }{ 9 }\) > \(\frac { 3 }{ 9 }\)
c) Show \(\frac { 2 }{ 6 }\), \(\frac { 4 }{ 6 }\), \(\frac { 8 }{ 6 }\) and \(\frac { 6 }{ 6 }\) on the number line. Put appropriate signs between the fractions given.
\(\frac { 5 }{ 6 }\) _____ \(\frac { 2 }{ 6 }\)
\(\frac { 3 }{ 0 }\) _____ 0
\(\frac { 1 }{ 6 }\) _____ \(\frac { 6 }{ 6 }\)
\(\frac { 8 }{ 6 }\) _____ \(\frac { 5 }{ 6 }\)
Solution:
\(\frac { 2 }{ 6 }\), \(\frac { 4 }{ 6 }\), \(\frac { 8 }{ 6 }\) and \(\frac { 6 }{ 6 }\)
Question 2.
Compare the fractions and put an appropriate sign.
a) \(\frac { 3 }{ 6 }\) ______ \(\frac { 5 }{ 6 }\)
Solution:
Here, the denominators of the two fractions are same and 3 < 5.
∴ \(\frac { 3 }{ 6 }\) < \(\frac { 5 }{ 6 }\) b) \(\frac { 1 }{ 7 }\) ______ \(\frac { 1 }{ 4 }\) Solution: Here, the numerators of the two fractions are same and 7 > 4.
∴ \(\frac { 1 }{ 7 }\) < \(\frac { 1 }{ 4 }\)
c) \(\frac { 4 }{ 5 }\) ______ \(\frac { 5 }{ 5 }\)
Solution:
Here, the denominators of the two fractions are same and 4 < 5.
∴ \(\frac { 4 }{ 5 }\) < \(\frac { 5 }{ 5 }\)
d) \(\frac { 3 }{ 5 }\) ______ \(\frac { 3 }{ 7 }\)
Solution:
Here, the numerators of the two fractions are same and 5 < 7. ∴ \(\frac { 3 }{ 5 }\) > \(\frac { 3 }{ 7 }\)
Question 3.
Make five more such pates and put an appropriate sign.
Solution:
a) \(\frac { 2 }{ 7 }\) > \(\frac { 2 }{ 1 }\)
b) \(\frac { 6 }{ 8 }\) > \(\frac { 3 }{ 8 }\)
c) \(\frac { 4 }{ 9 }\) < \(\frac { 3 }{ 9 }\)
d) \(\frac { 1 }{ 9 }\) < \(\frac { 5 }{ 9 }\)
e) \(\frac { 4 }{ 10 }\) < \(\frac { 6 }{ 10 }\)
Question 4
Look at the figures and write a between the given pairs of fractions.
Make five more such problems and solve them with your friends.
Solution:
a) \(\frac { 1 }{ 6 }\) < \(\frac { 1 }{ 3 }\)
b) \(\frac { 3 }{ 4 }\) < \(\frac { 2 }{ 6 }\) c) \(\frac { 2 }{ 3 }\) > \(\frac { 2 }{ 4 }\)
d) \(\frac { 6 }{ 6 }\) = \(\frac { 3 }{ 3 }\)
e) \(\frac { 5 }{ 6 }\) < \(\frac { 5 }{ 5 }\)
Make five more such problems yourself and solve them with your friends.
Question 5.
How quickly can you do this? Fill appropriate sign. (‘<‘, ‘=’, ‘>’)
a) \(\frac { 1 }{ 2 }\) ______ \(\frac { 1 }{ 5 }\)
Solution:
\(\frac { 1 }{ 2 }\) ______ \(\frac { 1 }{ 5 }\)
We have 1 × 5 = 5 and 1 × 2 = 2
Here, 2 < 5 ∴ \(\frac { 1 }{ 2 }\) > \(\frac { 1 }{ 5 }\)
b) \(\frac { 2 }{ 4 }\) ______ \(\frac { 3 }{ 6 }\)
Solution:
\(\frac { 2 }{ 4 }\) ______ \(\frac { 3 }{ 6 }\)
We have 2 × 6 = 12 and 3 × 4 = 12
Here, 12 = 12
∴ \(\frac { 2 }{ 4 }\) = \(\frac { 3 }{ 6 }\)
c) \(\frac { 3 }{ 5 }\) ______ \(\frac { 2 }{ 3 }\)
Solution:
\(\frac { 3 }{ 5 }\) > \(\frac { 2 }{ 3 }\)
We have 3 × 3 = 9 and 2 × 5 = 10
Here. 9 < 10
∴ \(\frac { 3 }{ 5 }\) < \(\frac { 2 }{ 3 }\)
d) \(\frac { 3 }{ 4 }\) ______ \(\frac { 2 }{ 8 }\)
Solution:
\(\frac { 3 }{ 4 }\) ______ \(\frac { 2 }{ 8 }\)
We have 3 × 3 = 9 and 2 × 5 = 10
Here. 9 < 10 ∴ \(\frac { 3 }{ 4 }\) > \(\frac { 2 }{ 8 }\)
e) \(\frac { 3 }{ 5 }\) ______ \(\frac { 6 }{ 5 }\)
Solution:
\(\frac { 3 }{ 5 }\) ______ \(\frac { 6 }{ 5 }\)
We have 3 × 5 = 15 and 6 × 5 = 30
Here, 15 < 30
∴ \(\frac { 3 }{ 5 }\) < \(\frac { 6 }{ 5 }\)
f) \(\frac { 7 }{ 9 }\) ______ \(\frac { 3 }{ 9 }\)
Solution:
\(\frac { 7 }{ 9 }\) ______ \(\frac { 3 }{ 9 }\)
We have 7 × 9 = 63 and 3 × 9 = 27
Here, 63 < 27 ∴ \(\frac { 7 }{ 9 }\) > \(\frac { 3 }{ 9 }\)
g) \(\frac { 1 }{ 4 }\) ______ \(\frac { 2 }{ 8 }\)
Solution:
\(\frac { 1 }{ 4 }\) ______ \(\frac { 2 }{ 8 }\)
We have 1 × 8 = 8 and 2 × 4 = 8
Here, 8 = 8
∴ \(\frac { 1 }{ 4 }\) = \(\frac { 2 }{ 8 }\)
h) \(\frac { 6 }{ 10 }\) ______ \(\frac { 4 }{ 5 }\)
Solution:
\(\frac { 6 }{ 10 }\) ______ \(\frac { 4 }{ 5 }\)
We have 6 × 5 = 30 and 4 × 10 = 40
Here, 30 < 40
∴ \(\frac { 6 }{ 10 }\) < \(\frac { 4 }{ 5 }\)
i) \(\frac { 3 }{ 4 }\) ______ \(\frac { 7 }{ 8 }\)
Solution:
\(\frac { 3 }{ 4 }\) ______ \(\frac { 7 }{ 8 }\)
We have 3 × 8 = 24 and 4 × 7 = 28
Here, 24 < 28
∴ \(\frac { 3 }{ 4 }\) < \(\frac { 7 }{ 8 }\)
j) \(\frac { 6 }{ 10 }\) ______ \(\frac { 3 }{ 5 }\)
Solution:
\(\frac { 6 }{ 10 }\) ______ \(\frac { 3 }{ 5 }\)
We have 6 × 5 = 30 and 10 × 3 = 30
Here, 30 = 30
∴ \(\frac { 6 }{ 10 }\) = \(\frac { 3 }{ 5 }\)
k) \(\frac { 5 }{ 7 }\) ______ \(\frac { 15 }{ 21 }\)
Solution:
\(\frac { 5 }{ 7 }\) ______ \(\frac { 15 }{ 21 }\)
We have 5 × 21 = 105 and 7 × 15 = 105
Here, 105 = 105
∴ \(\frac { 5 }{ 7 }\) = \(\frac { 15 }{ 21 }\)
Question 6.
The following fractions represent just three different numbers. Separate them into three groups of equivalent fractions, by changing each one to its simplest form.
a) \(\frac { 2 }{ 12 }\)
Solution:
\(\frac { 2 }{ 12 }\) = \(\frac{2 \div 2}{12 \div 2}\) = \(\frac { 1 }{ 6 }\) [∴ HCF of 2 and 12 is 2]
b) \(\frac { 3 }{ 15 }\)
Solution:
\(\frac { 3 }{ 15 }\) = \(\frac{3 \div 3}{15 \div 3}\) = \(\frac { 1 }{ 5 }\) [∴ HCF of 3 and 15 is 3]
c) \(\frac { 8 }{ 50 }\)
Solution:
\(\frac { 8 }{ 50 }\) = \(\frac{8 \div 2}{50 \div 2}\) = \(\frac { 4 }{ 25 }\) [∴ HCF of 8 and 50 is 2]
d) \(\frac { 16 }{ 100 }\)
Solution:
\(\frac { 16 }{ 100 }\) = \(\frac{16 \div 4}{100 \div 4}\) = \(\frac { 4 }{ 25 }\) [∴ HCF of 16 and 100 is 4]
e) \(\frac { 10 }{ 60 }\)
Solution:
\(\frac { 10 }{ 60 }\) = \(\frac{10 \div 10}{60 \div 10}\) = \(\frac { 1 }{ 6 }\) [∴ HCF of 10 and 60 is 10]
f) \(\frac { 15 }{ 75 }\)
Solution:
\(\frac { 15 }{ 75 }\) = \(\frac{15 \div 15}{75 \div 15}\) = \(\frac { 1 }{ 5 }\) [∴ HCF of 15 and 75 is 15]
g) \(\frac { 12 }{ 60 }\)
Solution:
\(\frac { 12 }{ 60 }\) = \(\frac{12 \div 12}{60 \div 12}\) = \(\frac { 1 }{ 5 }\) [∴ HCF of 12 and 60 is 12]
h) \(\frac { 16 }{ 96 }\)
Solution:
\(\frac { 16 }{ 96 }\) = \(\frac{16 \div 16}{96 \div 16}\) = \(\frac { 1 }{ 6 }\) [∴ HCF of 16 and 96 is 16]
i) \(\frac { 12 }{ 75 }\)
Solution:
\(\frac { 12 }{ 75 }\) = \(\frac{12 \div 3}{75 \div 3}\) = \(\frac { 4 }{ 25 }\) [∴ HCF of 12 and 75 is 3]
j) \(\frac { 12 }{ 72 }\)
Solution:
\(\frac { 12 }{ 72 }\) = \(\frac{12 \div 12}{72 \div 12}\) = \(\frac { 1 }{ 6 }\) [∴ HCF of 12 and 72 is 12]
k) \(\frac { 3 }{ 18 }\)
Solution:
\(\frac { 3 }{ 18 }\) = \(\frac{3 \div 3}{18 \div 3}\) = \(\frac { 1 }{ 6 }\) [∴ HCF of 3 and 18 is 3]
l) \(\frac { 4 }{ 25 }\)
Solution:
\(\frac { 4 }{ 25 }\) = \(\frac{4 \div 1}{25 \div 1}\) = \(\frac { 4 }{ 25 }\) [∴ HCF of 4 and 25 is 1]
Now, grouping the above fractions into equivalent fractions, we have
i) \(\frac { 2 }{ 12 }\) = \(\frac { 10 }{ 60 }\) = \(\frac { 16 }{ 96 }\) = \(\frac { 12 }{ 72 }\) = \(\frac { 3 }{ 18 }\) [each \(\frac { 1 }{ 6 }\)]
ii) \(\frac { 3 }{ 15 }\) = \(\frac { 15 }{ 75 }\) = \(\frac { 12 }{ 60 }\) [each \(\frac { 1 }{ 5 }\)]
iii) \(\frac { 8 }{ 50 }\) = \(\frac { 16 }{ 100 }\) = \(\frac { 12 }{ 75 }\) = \(\frac { 4 }{ 25 }\)
[each \(\frac { 4 }{ 25 }\)]
Question 7.
Find answers to the following. Write and indicate how you solved them.
a) Is \(\frac { 5 }{ 9 }\) equal to \(\frac { 4 }{ 5 }\)?
Solution:
\(\frac { 5 }{ 9 }\) and \(\frac { 4 }{ 5 }\)
By cross-multiplying, we get 5 × 5 = 25 and 4 × 9 = 36
Since 25 ≠ 36
∴ \(\frac { 5 }{ 9 }\) is not equal to \(\frac { 4 }{ 5 }\)
b) Is \(\frac { 9 }{ 16 }\) equal to \(\frac { 5 }{ 9 }\)?
Solution:
\(\frac { 9 }{ 16 }\) and \(\frac { 5 }{ 9 }\)
By cross-multiplying, we get 9 × 9 = 81 and 5 × 16 = 80
Since 81 ≠ 80
∴ \(\frac { 9 }{ 16 }\) is not equal to \(\frac { 5 }{ 9 }\)
c) Is \(\frac { 4 }{ 5 }\) equal to \(\frac { 16 }{ 20 }\) ?
Solution:
\(\frac { 4 }{ 5 }\) and \(\frac { 16 }{ 20 }\)
By cross-multiplying, we get 4 × 20 = 80 and 5 × 16 = 80
Since 80 = 80
∴ \(\frac { 4 }{ 5 }\) is equal to \(\frac { 16 }{ 20 }\)
d) Is \(\frac { 1 }{ 15 }\) equal to \(\frac { 4 }{ 30 }\) ?
Solution:
\(\frac { 1 }{ 15 }\) and \(\frac { 4 }{ 30 }\)
Bý cross-multiplying, we get 1 × 30 = 30 and 4 × 15 = 60
Since 30 ≠ 60
∴ \(\frac { 1 }{ 15 }\) is not equal to \(\frac { 4 }{ 30 }\)
Question 8.
Ila read 25 pages of a book containIng 100 pages. Lalita read \(\frac { 2 }{ 5 }\) of the same book. Who read less?
Solution:
Ila read 25 pages out of 100 pages.
∴ Fraction = \(\frac { 25 }{ 100 }\) = \(\frac{25 \div 25}{100 \div 25}\) = \(\frac { 1 }{ 4 }\)
Lalita reads \(\frac { 2 }{ 5 }\) of the same book.
Comparing. \(\frac { 1 }{ 4 }\) and \(\frac { 2 }{ 5 }\), we get
1 × 5 = 5 and 2 × 4 = 8
Hence lla read less pages.
Question 9.
Rafiq exercised for \(\frac { 3 }{ 6 }\) of an hour, while Rohit exercised for \(\frac { 3 }{ 4 }\) of an hour. Who exercised for a longer time?
Solution:
Rafiq exercised for \(\frac { 3 }{ 6 }\) of an hour.
Rohit exercised for \(\frac { 3 }{ 4 }\) of an hour.
Comparing \(\frac { 3 }{ 6 }\) and \(\frac { 3 }{ 4 }\), we get
3 × 4 = 12 and 3 × 6 = 18
Since 12 < 18 ∴ \(\frac { 3 }{ 4 }\) > \(\frac { 3 }{ 6 }\)
Question 10.
In a class A of 25 students, 20 passed with 60% or more marks; in another class B of 30 students, 24 passed with 60% or more marks. In which class was a greater fraction of students getting with 60% or more marks ?
Solution:
In class A, 20 students passed in first class out of 25 students.
∴ Fraction of students getting first class = \(\frac { 20 }{ 25 }\) = \(\frac{20 \div 5}{25 \div 5}\) = \(\frac { 4 }{ 5 }\)
In class B, 24 students passed in first class out of 30 students.
∴ Fraction of students getting first class
= \(\frac { 24 }{ 30 }\) = \(\frac{24 \div 6}{30 \div 6}\) = \(\frac { 4 }{ 5 }\)
Comparing the two fractions, we get \(\frac { 4 }{ 5 }\) = \(\frac { 4 }{ 5 }\)
Hence, both the class A and B have the same fraction.