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)

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