RD Sharma Solutions Class 6 Fractions Exercise 6.7

RD Sharma Solutions Class 6 Chapter 6 Exercise 6.7

RD Sharma Class 6 Solutions Chapter 6 Ex 6.7 PDF Free Download

Exercise 6.7

Q1. Write each fraction. Arrange them in ascending and descending order using correct sign ‘ < ‘ , ‘ = ‘ > ‘ between the fractions:

Ans :

Q2. Mark \(\frac{ 2 }{ 6 } , \frac{ 4 }{ 6 } , \frac{ 8 }{ 6 } , \frac{ 6 }{ 6 }\) on the number line and put appropriate signs between fractions given below :

i) \(\frac{ 5 }{ 6 } ———- \frac{ 2 }{ 6 }\)

ii) \(\frac{ 3 }{ 6 } ———- \frac{ 0 }{ 6 }\)

iii) \(\frac{ 1 }{ 6 } ———- \frac{ 6 }{ 6 }\)

iv) \(\frac{ 8 }{ 6 } ———- \frac{ 5 }{ 6 }\)

Ans :

i) 56 > 26 because 5 > 2 and the denominator is the same.

ii) 36 > 06 because 3 > 0 and the denominator is the same.

iii) 16 < 66 because 6 > 1 and the denominator is the same.

iv) 86 > 56 because 8 > 5 and the denominator is the same.

Q3. Compare the following fractions and put an appropriate :

i) \(\frac{ 3 }{ 6 } ———- \frac{ 5 }{ 6 }\)

ii) \(\frac{ 4 }{ 5 } ———- \frac{ 0 }{ 5 }\)

iii) \(\frac{ 3 }{ 20 } ———- \frac{ 4 }{ 20 }\)

iv) \(\frac{ 1 }{ 7 } ———- \frac{ 1 }{ 4 }\)

Ans :

i) 36 < 56 because 3 < 5 and the denominator is the same.

ii) 45 > 05 because 4 > 0 and the denominator is the same.

iii) 320 < 420 because 3 < 4 and the denominator is the same.

iv) 17 < 14 because 7 > 4; if the numerator is the same, then the fraction that has smaller denominator is greater.

Q4. Compare the following fractions using the symbol > or < :

i) \(\frac{ 6 }{ 7 } \; and \; \frac{ 6 }{ 11 }\)

ii) \(\frac{ 3 }{ 7 } \; and \; \frac{ 5 }{ 7 }\)

iii) \(\frac{ 2 }{ 3 } \; and \; \frac{ 8 }{ 12 }\)

iv) \(\frac{ 1 }{ 5 } \; and \; \frac{ 4 }{ 15 }\)

v) \(\frac{ 8 }{ 3 } \; and \; \frac{ 8 }{ 13 }\)

vi) \(\frac{ 4 }{ 9 } \; and \; \frac{ 15 }{ 8 }\)

Ans :

i) \(\frac{ 6 }{ 7 } > \frac{ 6 }{ 11 }\) because if the numerator is the same, then the fraction with smaller denominator is greater.

ii) \(\frac{ 3 }{ 7 } < \frac{ 5 }{ 7 }\) because 3 < 5 and the denominator is the same.

iii) \(\frac{ 8 }{ 12 }\) = \(\frac{ 2 \times 2 \times 2 }{ 2 \times 2 \times 3 } = \frac{ 2 }{ 3 } \; therefore, \; \frac{ 2 }{ 3 } = \frac{ 8 }{ 12 }\)

iv) \(\frac{ 1 }{ 5 } = \frac{ 1 }{ 5 }\times \frac{ 3 }{ 3 } = \frac{ 3 }{ 15 } , therefore \frac{ 3 }{ 15 } < \frac{ 4 }{ 15 }\) ( Because 3 < 4 and the denominator is the same.

Therefore, \(\frac{ 1 }{ 15 } < \frac{ 4 }{ 15 }\))

v) \(\frac{ 8 }{ 3 } < \frac{ 8 }{ 13 }\) Because if the numerator is the same, then the fraction with smaller denominator is greater.

vi) \(\frac{ 4 }{ 9 } = \frac{ 4 }{ 9 }\times \frac{ 8 }{ 8 } = \frac{ 32 }{ 72 }\)

\(\frac{ 15 }{ 8 } = \frac{ 15 }{ 8 }\times \frac{ 9 }{ 9 } = \frac{ 135 }{ 72 }\frac{ 32 }{ 72 } < \frac{ 135 }{ 72 }\)( Because 135 > 32 and the denominator is the same )

Therefore, \(\frac{ 4 }{ 9 }\) < \(\frac{ 15 }{ 8 }\)

Q 5. The following fractions represent just three different numbers. Separate them in to three groups of equal fractions by changing each one to its simplest form:

i) \(\frac{ 2 }{ 12 }\)

ii) \(\frac{ 3 }{ 15 }\)

iii) \(\frac{ 8 }{ 50 }\)

iv) \(\frac{ 16 }{ 100 }\)

v) \(\frac{ 10 }{ 60 }\)

vi) \(\frac{ 15 }{ 75 }\)

vii) \(\frac{ 12 }{ 60 }\)

viii) \(\frac{ 16 }{ 96 }\)

ix) \(\frac{ 12 }{ 75 }\)

x) \(\frac{ 12 }{ 72 }\)

xi) \(\frac{ 3 }{ 18 }\)

xii) \(\frac{ 4 }{ 25 }\)

Ans :

i) \(\frac{ 2 }{ 12 }\)

HCF of 2 & 12 is 2.

Divide both the numerator & denominator by the HCF of 2 &12

\(2 \div \frac{ 2 }{ 12 } \div 2 = \frac{ 1 }{ 6 }\)

ii) \(\frac{ 3 }{ 15 }\)

HCF of 3 &15 is 3.

Divide both the numerator & denominator by the HCF of 3 &15.

\(3 \div \frac{ 3 }{ 15 } \div 3 = \frac{ 1 }{ 5 }\)

iii) \(\frac{ 8 }{ 50 }\)

HCF of 8 & 50 is 2.

Divide both the numerator & denominator by the HCF of 8 & 50.

\(8 \div \frac{ 2 }{ 50 } \div 2 = \frac{ 4 }{ 25 }\)

iv) \(\frac{ 16 }{ 100 }\)

HCF of 16 & 100 is 4.

Divide both the numerator & denominator by the HCF of 16 & 100.

\(16 \div \frac{ 4 }{ 100 } \div 4 = \frac{ 4 }{ 25 }\)

v) \(\frac{ 10 }{ 60 }\)

HCF of 10 & 60 is 10.

Divide both the numerator & denominator by the HCF of 10 & 60.

\(10 \div \frac{ 10 }{ 60 } \div 10 = \frac{ 1 }{ 6 }\)

vi) \(\frac{ 15 }{ 75 }\)

HCF of 15 & 75 is 15.

Divide both the numerator & denominator by the HCF of 15 & 75.

\(15 \div \frac{ 15 }{ 75 } \div 15 = \frac{ 1 }{ 5 }\)

v) \(\frac{ 12 }{ 60 }\)

HCF of 12 & 60 is 12.

Divide both the numerator & denominator by the HCF of 12 & 60.

\(12 \div \frac{ 12 }{ 60 } \div 12 = \frac{ 1 }{ 5 }\)

vii)

\(\frac{ 16 }{ 96 }\)

HCF of 16 & 96 is 16.

Divide both the numerator & denominator by the HCF of 16 & 96

\(16 \div \frac{ 16 }{ 96 } \div 16 = \frac{ 1 }{ 6 }\)

viii)

\(\frac{ 12 }{ 75 }\)

HCF of 12 & 75 is 3.

Divide both the numerator & denominator by the HCF of 12 & 75.

\(12 \div \frac{ 3 }{ 75 } \div 3 = \frac{ 4 }{ 25 }\)

ix) \(\frac{ 12 }{ 72 }\)

HCF of 12 & 72 is 12.

Divide both the numerator & denominator by the HCF of 12 & 72

\(12 \div \frac{ 12 }{ 72 } \div 12 = \frac{ 1 }{ 6 }\)

x) \(\frac{ 3 }{ 18 }\)

HCF of 3 & 18 is 3.

Divide both the numerator & denominator by the HCF of 3 & 18.

\(3 \div \frac{ 3 }{ 18 } \div 3 = \frac{ 1 }{ 6 }\)

xi) \(\frac{ 4 }{ 25 }\)

HCF of 4 & 25 is 1.

Divide both the numerator & denominator by the HCF of 4 & 25

\(4 \div \frac{ 1 }{ 25 } \div 1 = \frac{ 4 }{ 25 }\)

Three groups of equal fractions :

\(\frac{ 2 }{ 12 }\) , \(\frac{ 10 }{ 60 }\) , \(\frac{ 16 }{ 96 }\) , \(\frac{ 12 }{ 72 }\) , \(\frac{ 3 }{ 18 }\) ; \(\frac{ 3 }{ 15 }\) , \(\frac{ 8 }{ 50 }\) , \(\frac{ 16 }{ 100 }\) , \(\frac{ 15 }{ 75 }\) , \(\frac{ 12 }{ 60 }\) , \(\frac{ 12 }{ 75 }\) , \(\frac{ 4 }{ 25 }\)

Q 6 . Isha read 25 pages of a book containing 100 pages. Nagma read \(\frac{ 1 }{ 2 }\) of the same book. Who read less ?

ANS :

Total pages in the book = 100

Fraction of the book read by Isha = \(25 \div \frac{ 25 }{ 100 } \div 25 = \frac{ 1 }{ 4 }\)

(Dividing numerator & denominator by the HCF of 25 & 100)

Fraction of the book read by Nagma = 12

Now, compare 14 & 12.

LCM of 4 & 2 is 4.

Convert each fraction into equivalent fraction with 4 as its denominator.

\(1 \times \frac{ 1 }{ 4 } \times 1 and 1 \times \frac{ 2 }{ 2 } \times \frac{ 2 }{ 14 } and \frac{ 1 }{ 4 } = \frac{ 2 }{ 4 }\)

Therefore, Isha read less.

Q 7 . Arrange the following fractions in the ascending order :

i) \(\frac{ 2 }{ 9 }\) , \(\frac{ 7 }{ 9 }\) , \(\frac{ 3 }{ 9 }\) , \(\frac{ 4 }{ 9 }\) , \(\frac{ 1 }{ 9 }\), \(\frac{ 6 }{ 9 }\) , \(\frac{ 5 }{ 9 }\)

ii) \(\frac{ 7 }{ 8 }\) , \(\frac{ 7 }{ 25 }\) , \(\frac{ 7 }{ 11 }\) , \(\frac{ 7 }{ 18 }\) , \(\frac{ 7 }{ 10 }\)

iii) \(\frac{ 37 }{ 47 }\) , \(\frac{ 37 }{ 50 }\) , \(\frac{ 37 }{ 100 }\) , \(\frac{ 37 }{ 100 }\) , \(\frac{ 37 }{ 85 }\) ,\(\frac{ 37 }{ 41 }\)

iv) \(\frac{ 3 }{ 5 }\) , \(\frac{ 1 }{ 5 }\) , \(\frac{ 4 }{ 5 }\) , \(\frac{ 2 }{ 5 }\)

v) \(\frac{ 2 }{ 5 }\) , \(\frac{ 3 }{ 4 }\) , \(\frac{ 1 }{ 2 }\) , \(\frac{ 3 }{ 5 }\)

vi) \(\frac{ 3 }{ 8 }\) ,\(\frac{ 3 }{ 12 }\) , \(\frac{ 3 }{ 6 }\) , \(\frac{ 3 }{ 4 }\)

vii) \(\frac{ 4 }{ 6 }\) , \(\frac{ 3 }{ 8 }\) , \(\frac{ 6 }{ 12 }\) , \(\frac{ 5 }{ 16 }\)

Ans :

i) \(\frac{ 2 }{ 9 }\) , \(\frac{ 7 }{ 9 }\) , \(\frac{ 3 }{ 9 }\) , \(\frac{ 4 }{ 9 }\) , \(\frac{ 1 }{ 9 }\) , \(\frac{ 6 }{ 9 }\) , \(\frac{ 5 }{ 9 }\) , when the denominators are the same and numerators are different , then the fraction with greater numerator has a larger value.

ii) \(\frac{ 7 }{ 8 }\) , \(\frac{ 7 }{ 25 }\) , \(\frac{ 7 }{ 11 }\) , \(\frac{ 7 }{ 18 }\) , \(\frac{ 7 }{ 10 }\) , when numerator are the same and denominators are different , the fraction with greater denominator has a smaller value.

iii) \(\frac{ 37 }{ 47 }\) , \(\frac{ 37 }{ 50 }\) , \(\frac{ 37 }{ 100 }\) , \(\frac{ 37 }{ 100 }\) , \(\frac{ 37 }{ 85 }\) , \(\frac{ 37 }{ 41 }\)

When numerators are the same and denominator has a smaller value.

iv) \(\frac{ 3 }{ 5 }\) , \(\frac{ 1 }{ 5 }\) , \(\frac{ 4 }{ 5 }\) , \(\frac{ 2 }{ 5 }\)

When denominators are the same and numerators are different, then the fraction with greater numerator has a larger value.

v) LCM of 2 , 4 and 5 is 20

\(\frac{ 2 }{ 5 }\) = \(\frac{ 2 }{ 5 }\) x \(\frac{ 4 }{ 4 }\) = \(\frac{ 8 }{ 20 }\)

\(\frac{ 3 }{ 4 }\) = \(\frac{ 3 }{ 4 }\) x \(\frac{ 5 }{ 5 }\) = \(\frac{ 15 }{ 20 }\)

\(\frac{ 2 }{ 5 }\) = \(\frac{ 2 }{ 5 }\) x \(\frac{ 4 }{ 4 }\) = \(\frac{ 8 }{ 20 }\)

Q 8 . Arrange in descending order in each of the following using symbols > :

i) \(\frac{ 8 }{ 17 }\) , \(\frac{ 8 }{ 9 }\) , \(\frac{ 8 }{ 5 }\) , \(\frac{ 8 }{ 13 }\)

ii) \(\frac{ 5 }{ 9 }\) , \(\frac{ 3 }{ 12 }\) , \(\frac{ 1 }{ 3 }\) , \(\frac{ 4 }{ 15 }\)

Ans 8)

Q 9 . Find answers to the following. Write and indicate how you solved them.

i) Is \(\frac{ 5 }{ 9 }\) equal to \(\frac{ 4 }{ 5 }\) ?

ii) Is \(\frac{ 9 }{ 16 }\) equal to \(\frac{ 5 }{ 9 }\) ?

iii) Is \(\frac{ 4 }{ 5 }\) equal to \(\frac{ 16 }{ 20 }\) ?

iv) Is \(\frac{ 1 }{ 15 }\) equal to \(\frac{ 4 }{ 30 }\) ?

Ans. 9)


Practise This Question

You have a certain number of chocolates and you don't know the number of chocolates. If you receive the same number of chocolates from your friend, which of the following can represent the total number of chocolates you have?