RD Sharma Solutions Class 6 Maths Chapter 6 Fractions

Solution 4: 

Question 7:  Check whether the given fractions are equivalent:

Solution 7: 

Question 8:  Match the equivalent fractions and write another 2 for each:

Solution 8: 

Question 9:  Write some equivalent fractions which contain all digits from 1 to 9 once only. 

Solution 9:   There are those equivalent fractions which contain all digits from 1 to 9 once only are:

Question 10:  Ravish had 20 pencils, Shikha had 50 pencils and Priya had 80 pencils. After 4 months, Ravish used up 10 pencils, Shikha used up 25 pencils and Priya used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of their pencils? 

Solution 10: 

Number of pencils Ravish had = 20 pencils

Number of pencils Ravish used = 10 pencils

We take HCF of 10 and 20 by dividing the numerator and denominator

We get the fraction of pencils used = (10 ÷ 10)/ (20 ÷ 10) = 1/2

Number of pencils Shikha had = 50

Number of pencils used by Shikha = 25

We take HCF of 25 and 50 by dividing the numerator and denominator

We get the fraction of pencils used = (25 ÷ 25)/ (50 ÷ 25) = 1/2

Number of pencils Priya had = 80

Number of pencils used by Priya = 40

We take HCF of 40 and 80 by dividing the numerator and denominator

We get the fraction of pencils used = (40 ÷ 40)/ (80 ÷ 40) = 1/2

Yes, Ravish, Shikha and Priya has used an same fraction of their pencils.

 Exercise 6.6

Question 1:  Reduce each of the following fractions to its lowest term (simplest form):

Solution 1:

Question 2:  Simplify each of the following to its lowest term:                        

Solution 2:

Exercise 6.7

 

Question 1:  Write each fraction. Arrange them in ascending and descending order using correct sign <, =, > between the fractions:

Solution 1: 

 

 

 

 

Question 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:

Solution  5:

Question 6:   Isha read 25 pages of a book containing 100 pages. Nagma read ½ of the same book. Who read less? 

Solution 6:    Number of pages in the book = 100

 

Question 7:  Arrange the following fractions in the ascending order:

Solution 7: 

 

Question 8:  Arrange in descending order in each of the following using the symbol >:

Solution 8:

 

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

Solution 9: 

 

 Exercise 6.8

Question 1:  Write these fractions appropriately as additions or subtractions:

Solution 1: 

 

Question 2:  Solve:

Solution 2: 

 

Question 3:  Shikha painted 1/5 of the wall space in her room. Her brother Ravish helped and painted 3/5 of the wall space. How much did they paint together? How much the room is left unpainted?

 

Solution 3: 

 

 

Question 4:   Ramesh bought 2 ½  kg sugar whereas Rohit bought 3 ½kg of sugar. Find the total amount of sugar bought by both of them. 

Solution 4: 

Question 7: Savita bought 2/5 m of ribbon and Kavita 3/4 m of the ribbon. What was the total length of the ribbon they bought?

 

Solution 7: 

Length of ribbon Kavita bought = 3/4 m

Length of ribbon Savita bought = 2/5 m

So, the total length of ribbon Kavita and Savita bought = 2/5 + 3/4

We know that the LCM of 5 and 4 is 20

So, we get

= [(2 × 4)/ (5 × 4)] + [(3 × 5)/ (4 × 5)]

On further calculation

= 8/20 + 15/20

We get

= (8 + 15)/20 = 23/20  m

Hence, the total length of the ribbon Kavita and Savita bought is 23/20 m.

Question 8:  Ravish takes 2 ¹/₅ minutes to walk across the school ground. Rahul takes 7/4  minutes to do the same. Who takes less time and by what fraction?

 

Solution 8: 

Time taken by Ravish = 2 ¹/₅ minutes = ¹¹/₅ minutes

Time taken by Rahul = ⁷/₄   minutes

By comparing ¹¹/₅  and ⁷/₄   minutes

We know that LCM of 4 and 5 is 20

In order to convert fraction into equivalent fraction having 20 as denominator

[(11 × 4)/ (5 × 4)], [(7 × 5)/ (4 × 5)]

⁴⁴/₂₀ > ³⁵/₂₀

So, Rahul takes less time

written as

⁴⁴/₂₀ – ³⁵/₂₀= (44 – 35)/20 = 9/20minutes

Hence, Rahul takes less time by 9/20 minutes.

 

 

Question 9:  A piece of a wire ⁷/₈ meters long broke into two pieces. One piece was ¹/₄ meter long. How long is the other piece?

 

Solution 9: 

Given:

Length of wire = ⁷/₈ m

Length of first piece = ¹/₄ m

Consider x m as the length of second piece

It can be written as

Length of wire = Length of first piece + Length of second piece

By substituting the values

⁷/₈ = ¹/₄ + x

On further calculation

x = ⁷/₈ – ¹/₄

We know that the LCM of 8 and 4 is 8

x = [(7 × 1)/ (8 × 1)] – [(1 × 2)/ (4 × 2)]

We get

x = ⁷/₈  – ²/₈

By subtraction

x = (7 – 2)/ 8 = ⁵/₈ m

Hence, the length of second piece of wire is 5/8m.

Question 10:  Shikha and Priya have bookshelves of the same size Shikha’s shelf is 5/6full of book and Priya’s shelf is 2/5full. Whose bookshelf is more full? By what fraction?

 

Solution 10: 

Fraction of Shikha’s shelf filled with books = ⁵/₆

Fraction of Priya’s shelf filled with books = ²/₅

We know that LCM of 5 and 6 is 30

In order to convert fraction into equivalent fraction having 30 as denominator

= [(5 × 5)/ (6 × 5)], [(2 × 6)/ (5 × 6)]

 

Question 11:   Ravish’s house is ⁹/₁₀ km from his school. He walked some distance and then took a bus for ¹/₂ km up to the school. How far did he walk?

 

Solution 11: 

Given:

Distance of Ravish’s house from his school = ⁹/₁₀ km

Distance covered by bus = ¹/₂ km

written as

Distance between house and school = Distance covered by walking + Distance covered by bus

So, we get

Distance covered by walking = Distance between house and school – Distance covered by bus

 

 

 

Exercise 6.10  

Mark the correct alternative in each of the following:

 

Question 1:  Which of the following is a proper fraction?

(a)  4/3  

(b) 3/4 

(c) 13/4 

(d) 21/5 

 

Solution 1: The correct answer is (b).

We know that in a proper fraction, the numerator is less than the denominator.

 

Question 2:  Which of the following is an improper fraction?

(a) 1/2

(b) 3/7

(c) 7/3

(d) 3/15

 

Solution 2:  The correct answer is (c).

We know that in an improper fraction, the numerator is more than the denominator.

 

Question 3:  Which of the following is a fraction equivalent of 2/3?

(a) 4/5

(b) 8/6

(c)  10/25

(d) 10/15

 

Solution 3:  The correct answer is (d).

¹⁰/₁₅ = ²/₃

By cross multiplication

10 × 3 = 2 × 15

We get

30 = 30

 

Question 4:  A fraction equivalent to ³/₅  is

(a)  ⁽³⁺²⁾/₍₅₊₂₎

(b) ^(3-2)/_(5-2)

(c) ^(3×2)/_{(5 ×2)}

(d) None of these 

 

Solution 4:  The correct answer is (c).

 

We know that by dividing the numerator and denominator by 2, we obtain ³/₅.

 

Question 5:  If ⁵/₁₂ is equivalent of ^x/₃, then x =

(a) 5/4

(b) 4/5

(c) 5/3

(d) 3/5 

Solution 5: The correct answer is (a). 

Consider ⁵/₁₂ = ^x/₃ 

By cross multiplication 

5 × 3 = 12 × x 

So we get 

x = (( 5 × 3))/12  = (( 5 × 3))/((4 ×3))  =  5/4 

 

 

Question 6:   Which of the following are like fractions?

(a) 3/5, 3/7,  3/11 ,  3/16 

(b) 5/11, 7/11,  15/11 , 2/11

(c) 2/3,  3/4 , 4/5, 6/7

(d) None of these

 

Solution 6:  The correct answer is (b).

 

We know that like fractions are the fractions with the same denominator.

 

Question 7:  If 11/4 =77/x, then x =

(a) 28

(b)  77/28

(c) 44

(d) 308

 

Solution 7:  The correct answer is (a).

11/4 =77/x

By cross multiplication

11 × x = 77 × 4

x = (77 × 4)/ 11 = (7 × 11 × 4)/ 11

Dividing both the numerator & denominator by 11, we obtain 28.

 

 

 

 

Question 11:  Which of the following fractions is the smallest?

1/2,  3/7,  3/5,  4/9

(a) 4/9

(b) 3/5

(c) 3/7

(d) 1/2

 

Solution 11:  The correct answer is (c).

We know that the LCM of numerator is 12

By converting each fraction to an equivalent fraction having 12 as numerator

 

We know that if the denominator is same the fraction having larger numerator is the greatest.

Hence, 7/8 is the greatest fraction.

 

Question 13:  What is the value of a+b/ a−b, If a/b=4?

(a) 3/5

(b) 5/3

(c) 4/5

(d) 5/4

 

Solution 13:  The correct answer is (b).

It is given that a/b = 4

We can write it as a = 4b

By substituting the value of a in a+b/a-b

a+b/a-b = 4b+b/4b-b = 5b/3b

Dividing numerator and denominator by b, the value is 5/3.

 

Question 14:  If a/b = 4/3, then the value of 6a+4b/ 6a-5b is

(a) −1

(b) 3

(c) 4

(d) 5

 

Solution 14:  The correct answer is (c).

It is given that a/b = 4/3

We can write it as a = 4b/3

By substituting the value of a in 6a+4b/6a-5b

 

 

 

 

 

 

Question 17:  If ⁴⁵/₍₆₀₎ is equivalent to ³/_x, then x =

(a) 5

(b) 4

(c) 6

(d) 20

 

Solution 17:  The correct answer is (b).

Given:

45/60 = 3/x

By cross multiplication

45 × x = 3 × 60

x = (3 × 60)/45 = ¹⁸⁰/₄₅

Dividing the fraction by HCF

(180 ÷ 45)/(45÷45) = 4