Gujarat Board Textbook Solutions Class 6 Maths Chapter 7 Fractions Ex 7.4
Gujarat Board GSEB Textbook Solutions Class 6 Maths Chapter 7 Fractions Ex 7.4 Textbook Questions and Answers.
Gujarat Board Textbook Solutions Class 6 Maths Chapter 7 Fractions Ex 7.4
Question 1.
Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign ‘<‘, ‘=’ ‘>’between the fractions:

(c) (i) show (frac { 2 }{ 6 } ), (frac { 4 }{ 6 } ), (frac { 8 }{ 6 } ) and (frac { 8 }{ 6 } ) on the number line.
(ii) Put appropriate signs between the fractions given.

Solution:
(a) Figure (i) represents fraction = (frac { 3 }{ 8 } )
Figure (ii) represents fraction = (frac { 6 }{ 8 } )
Figure (iii) represents fraction = (frac { 4 }{ 8 } )
Figure (iv) represents fraction = (frac { 1 }{ 8 } )
These are like fractions. So we arrange them in order to their numerators.
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 } )
(b) Figure (i) represents a fraction = (frac { 8 }{ 9 } )
Figure (ii) represents a fraction = (frac { 4 }{ 9 } )
Figure (iii) represents a fraction = (frac { 3 }{ 9 } )
Figure (iv) represents a fraction = (frac { 6 }{ 9 } )
The fractions are like fractions with different numerators.
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) (i) Given fractions are: (frac { 2 }{ 6 } ), (frac { 4 }{ 6 } ), (frac { 8 }{ 6 } ) and (frac { 6 }{ 6 } )
We can have: (frac { 2 }{ 6 } ) < (frac { 4 }{ 6 } ) < (frac { 8 }{ 6 } ) < (frac { 6 }{ 6 } )

(ii) We have: (frac { 5 }{ 6 } ) > (frac { 2 }{ 6 } ); (frac { 3 }{ 6 } ) > 0
(frac { 6 }{ 6 } ) < (frac { 1 }{ 6 } ); (frac { 8 }{ 6 } ) < (frac { 5 }{ 6 } )
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Question 2.
Compare the fractions and put an appropriate sign.

Solution:
(a) Here, we have ‘like fractions’ so we compare them by their numerators only.
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(b) Here, we have ‘unlike fractions’ with same numerators, so we compare them with their denominators only.
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(c) Like fractions, so we compare by their numerators only.
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(d) ‘Unlike fractions’ with same numerators so we compare them by their denominators, only.
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Question 3.
Make five more such pairs and put appropriate signs.
Solution:
Five more examples can be given as below:

After writing the appropriate signs, we have:

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Question 4.
Look at the figures and write ‘<‘ ‘>’or ‘=’ between the given pairs of fractions.


Make five more such problems and solve them with your friends.
Solution:
(a) In the figure, (frac { 1 }{ 6 } ) is on the left of (frac { 1 }{ 3 } )

(b) In the figure, (frac { 3 }{ 4 } ) lies on the right of (frac { 2 }{ 6 } ).
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(c) In the figure, (frac { 2 }{ 3 } ) is on the right of (frac { 2 }{ 4 } )
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(d) In the figurc, (frac { 6 }{ 6 } ) is on the same point as of (frac { 3 }{ 3 } ).
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(e) In the figure, (frac { 5 }{ 6 } ) is at the same point as (frac { 5 }{ 5 } ).
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Five more examples can be given as below:
Look at the previous figure and write ‘<‘, ‘>‘
or ‘=’ between the following pairs of fractions:

After writing the appropriate signs, we have

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Question 5.
How quickly can you do this? Fill appropriate sign. (‘<‘, ‘=’, ‘>’)

Solution:
We use cross-product method for quicker calculations.
We have

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Question 6.
The following fractions represent just three different numbers. Separate them into three groups of equivalent fi-actions, by changing each one to its simplest form.

Solution:

Grouping the simplest forms, we have:

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Question 7.
Find answers to the following. Write and indicare how you solved them,
(a) Is (frac { 5 }{ 9 } ) equal to (frac { 4 }{ 5 } ) ?
(b) Is (frac { 9 }{ 16 } ) equal to (frac { 5 }{ 9 } ) ?
(c) Is (frac { 4 }{ 5 } ) equal to (frac { 16 }{ 20 } ) ?
(d) Is (frac { 1 }{ 15 } ) equal to (frac { 4 }{ 30 } ) ?
Solution:
(a) By cross product, we have
5 x 5 = 25 and 9 x 4 = 36
25 ≠ 36 i.e 5 x 5 ≠ 9 x 4
(frac { 5 }{ 9 } ) ≠ (frac { 4 }{ 5 } ) i.e (frac { 5 }{ 9 } ), is not equal to (frac { 2 }{ 7 } ).
(b) y cross product, we have
9 x 9 = 81 and 16 x 5 = 80
81 ≠ 80,i.e.9 x 9 ≠ 16 x 5
(frac { 9 }{ 16 } ) ≠ (frac { 5 }{ 9 } ), i.e. (frac { 9 }{ 16 } ) is not equal to (frac { 5 }{ 9 } ).
(c) By cross product, we have
4 x 20 = 80 and 5 x 16 = 80
4 x 20 = 5 x 16
(frac { 4 }{ 5 } ) = (frac { 16 }{ 20 } ), i.e. (frac { 16 }{ 20 } ) and (frac { 4 }{ 5 } ) are equal.
(d) By cross product, we have
1 x 30 = 30 and 4 x 15 = 60
30 ≠ 60, i.e. 1 x 30 ≠ 4 x 15
(frac { 1 }{ 5 } ) ≠ (frac { 4 }{ 30 } )
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Question 8.
Ila read 25 pages of a book containing 100 pages. Lauta read (frac { 2 }{ 5 } ) of the same book. Who read less?
Solution:
Fraction of book read by Illa = (frac { 25 }{ 100 } )
(frac{25 div 25}{100 div 25}) = (frac { 1 }{ 4 } )
Fraction of book read by Lauta = (frac { 2 }{ 5 } )
To compare (frac { 1 }{ 4 } ) and (frac { 2 }{ 5 } ) we have, 1 x 5 = 5;
4 x 2 = 8 and 5 < 8
(frac { 1 }{ 4 } ) < (frac { 2 }{ 5 } ) Thus Ila read less. 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: Fraction of an hour for which Rafiq exercised = (frac { 3 }{ 6 } ) Fraction of an hour for which Rohit exercised = (frac { 3 }{ 4 } ) To compare (frac { 3 }{ 6 } ) and (frac { 3 }{ 4 } ) we have: For ‘unlike fractions’ with same numerator, greator fraction has lesser denominator. (frac { 3 }{ 4 } ) > (frac { 3 }{ 6 } )
Rohit exercised for a longer period.
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Question 10.
In a class A of 25 students, 20 passed in first class; in another class B of 30 students, 24 passed in first class. In which class was a greater fraction of students getting first class?
Solution:
In class A, fraction of students who got 1st division
= (frac { 20 }{ 25 } ) = (frac{20+5}{25 div 5}) = (frac { 4 }{ 5 } ) ………….(i)
In class B, fraction of students who got 1st division
(frac { 24 }{ 25 } ) = (frac{24 div 6}{30 div 6}) = (frac { 4 }{ 5 } ) ……………..(ii)
From (i) and (ii), same fraction (left(frac{4}{5}right)) of students got 1st class in both the classes.