Ex-6.7, Fractions, Class 6, Maths RD Sharma Solutions | RD Sharma Solutions for Class 6 Mathematics PDF Download

Q1: Write each fraction. Arrange them in ascending and descending order using correct sign ‘ < ‘ , ‘ = ‘ > ‘ between the fractions:
(i)
(ii)
(iii)
Ans :
(i) Ascending Order
Descending Order

(ii) Ascending Order

Descending Order
(iii) Ascending Order

Descending Order

Q2: Mark  on the number line and put appropriate signs between fractions given below :
(i) −−−−−−−−−−
(ii) −−−−−−−−−−
(iii) −−−−−−−−−−
(iv) −−−−−−−−−−
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) −−−−−−−−−−
(ii) −−−−−−−−−−
(iii) −−−−−−−−−−
(iv) −−−−−−−−−−
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)
ii)
iii)
iv)
v)
vi)
Ans:
i) because if the numerator is the same, then the fraction with smaller denominator is greater.
ii)  because 3 < 5 and the denominator is the same.
iii)  therefore,
iv) ,therefore ( Because 3 < 4 and the denominator is the same.
Therefore,
v)  Because if the numerator is the same, then the fraction with smaller denominator is greater.
vi)
( Because 135 > 32 and the denominator is the same )
Therefore,

Q5: 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) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
(vii) 
(viii) 
(ix) 
(x) 
(xi) 
(xii) 
Ans:
(i)
HCF of 2 & 12 is 2.
Divide both the numerator & denominator by the HCF of 2 &12

(ii)
HCF of 3 &15 is 3.
Divide both the numerator & denominator by the HCF of 3 &15.

(iii)
HCF of 8 & 50 is 2.
Divide both the numerator & denominator by the HCF of 8 & 50.

(iv)
HCF of 16 & 100 is 4.
Divide both the numerator & denominator by the HCF of 16 & 100.

(v)
HCF of 10 & 60 is 10.
Divide both the numerator & denominator by the HCF of 10 & 60.

(vi)
HCF of 15 & 75 is 15.
Divide both the numerator & denominator by the HCF of 15 & 75.

(v)
HCF of 12 & 60 is 12.
Divide both the numerator & denominator by the HCF of 12 & 60.

(vii)
HCF of 16 & 96 is 16.
Divide both the numerator & denominator by the HCF of 16 & 96

(viii)
HCF of 12 & 75 is 3.
Divide both the numerator & denominator by the HCF of 12 & 75.

(ix)
HCF of 12 & 72 is 12.
Divide both the numerator & denominator by the HCF of 12 & 72

(x)
HCF of 3 & 18 is 3.
Divide both the numerator & denominator by the HCF of 3 & 18.

(xi)
HCF of 4 & 25 is 1.
Divide both the numerator & denominator by the HCF of 4 & 25

Three groups of equal fractions :


Q6: Isha read 25 pages of a book containing 100 pages. Nagma read  of the same book. Who read less ?
Ans:
Total pages in the book = 100
Fraction of the book read by Isha =
(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.

Therefore, Isha read less.

Q7: Arrange the following fractions in the ascending order:
(i) 2/9, 7/9, 3/9, 4/9, 1/9, 6/9, 5/9
(ii) 7/8, 7/25, 7/11, 7/18, 7/10
(iii) 37/47, 37/50, 37/100, 37/1000, 37/85, 37/41
(iv) 3/5, 1/5, 4/5, 2/5
(v) 2/5, 3/4, 1/2, 3/5
(vi) 3/8, 3/12. 3/6, 3/4
(vii) 4/6, 3/8, 6/12, 5/16
Ans:
(i) 2/9, 7/9, 3/9, 4/9, 1/9, 6/9, 5/9 can be written in ascending order as
1/9, 2/9, 3/9, 4/9, 5/9, 6/9, 7/9
(ii) 7/8, 7/25, 7/11, 7/18, 7/10 can be written in ascending order as
7/25, 7/18, 7/11, 7/10, 7/8
(iii) 37/47, 37/50, 37/100, 37/1000, 37/85, 37/41 can be written in ascending order as
37/1000, 37/100, 37/85, 37/50, 37/47, 37/41
(iv) 3/5, 1/5, 4/5, 2/5 can be written in ascending order as
1/5, 2/5, 3/5, 4/5
(v) 2/5, 3/4, 1/2, 3/5 can be written in ascending order as
2/5, 1/2, 3/5, 3/4
(vi) 3/8, 3/12, 3/6, 3/4 can be written in ascending order as
3/12, 3/8, 3/6, 3/4
(vii) 4/6, 3/8, 6/12, 5/16 can be written in ascending order as
5/16, 3/8, 6/12, 4/6

Q8: Arrange in descending order in each of the following using symbols > :
(i) 8/17, 8/9, 8/5, 8/13
(ii) 5/9, 3/12, 1/3, 4/15
(iii) 2/7, 11/35, 9/14, 13/28
Ans:
(i) 8/17, 8/9, 8/5, 8/13 can be written in the descending order as
8/5 > 8/9 > 8/13 > 8/17
(ii) 5/9, 3/12, 1/3, 4/15 can be written in the descending order as
5/9 > 1/3 > 4/15> 3/12
(iii) 2/7, 11/35, 9/14, 13/28 can be written in the descending order as
9/14 > 13/28 > 11/35 > 2/7

Q9: Find answers to the following. Write and indicate how you solved them.
(i) Is  equal to  ?
(ii) Is  equal to  ?
(iii) Is  equal to  ?
(iv) Is  equal to  ?
Ans:
(i) No. We know that 5 × 5 ≠ 9 × 4
(ii) No. We know that 9 × 9 ≠ 16 × 5
(iii) Yes. We know that 4 × 20 = 16 × 5
(iv) No. We know that 1 × 30 ≠ 15 × 4