RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.5 PDF

RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.5 focuses on understanding and identifying equivalent fractions. This exercise helps students learn how to determine whether different fractions represent the same value by simplifying them or finding a common basis.

It includes problems on matching equivalent fractions, finding missing numerators or denominators, and creating equivalent fractions by multiplying or dividing both terms by the same number.

Through step-by-step solutions, students gain confidence in simplifying fractions and applying these concepts to real-life situations, strengthening their overall grasp of fractions and their relationships.

RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.5 Introduction

This exercise focuses on understanding and identifying equivalent fractions, which are fractions that represent the same value even though their numerators and denominators differ.

Key Concepts Covered:

1. Checking if fractions are equivalent: Simplify fractions or compare by cross-multiplication to determine equivalence.

2. Matching equivalent fractions: Match fractions in one column with their equivalent fractions in another by simplification or multiplication.

3. Finding missing numerators or denominators: Given a fraction and an equivalent fraction with one missing number (☐), calculate the missing numerator or denominator by using multiplication or division.

4. Generating equivalent fractions: Find equivalent fractions by multiplying or dividing both numerator and denominator by the same number.

5. Reducing fractions to simplest form: Divide numerator and denominator by their highest common factor (HCF) to simplify fractions.

6. Checking equivalence through calculations: Confirm if two fractions are equivalent by multiplying across numerators and denominators or by simplifying both.
   
   

RD Sharma Solutions for Class 6 Chapter 6 Fractions Exercise 6.5 Question Answers

Here are the detailed solutions for RD Sharma Class 6 Maths Chapter 6 Exercise 6.5 on Fractions.

Exercise 6.5 page: 6.15

1. Write the fractions and check whether they are equivalent or not:

Solution:

(i) We know that

Fraction = ½

Fraction = 2/4 = 1/2

Fraction = 3/6 = ½

Fraction = 4/8 = ½

Hence, they are equivalent.

(ii) We know that

Fraction = 5/15 = 1/3

Fraction = 3/9 = 1/3

Fraction = 2/6 = 1/3

Fraction = 1/3

Hence, they are equivalent.

2. Write the fractions and match fractions in Column I with the equivalent fractions in Column II.

Solution:

(i) (b)

(ii) (c)

(iii) (a)

(iv) (d)

3. Replace ☐ in each of the following by the correct number:

(i) 2/7 = 6/ ☐

(ii) 5/8 = 10/☐

(iii) 4/5 = ☐/20

(iv) 45/60 = 15/ ☐

(v) 18/24 = ☐/4

Solution:

(i) 2/7 = 6/21

(ii) 5/8 = 10/16

(iii) 4/5 = 16/20

(iv) 45/60 = 15/20

(v) 18/24 =3/4

4. Find the equivalent fraction of 3/5, having:

(i) numerator 9

(ii) denominator 30

(iii) numerator 21

(iv) denominator 40

Solution:

(i) The given fraction = 3/5

By considering numerator = 9

We know that 3 × 3 = 9

Multiply the numerator and denominator of the fraction by 3

3/5 × 3/3 = 9/15

(ii) The given fraction = 3/5

By considering denominator = 30

We know that 5 × 6 = 30

Multiply the numerator and denominator of the fraction by 6

3/5 × 6/6 = 18/30

(iii) The given fraction = 3/5

By considering numerator = 21

We know that 3 × 7 = 21

Multiply the numerator and denominator of the fraction by 7

3/5 × 7/7 = 21/35

(iv) The given fraction = 3/5

By considering denominator = 40

We know that 5 × 8 = 40

Multiply the numerator and denominator of the fraction by 8

3/5 × 8/8 = 24/40

5. Find the fraction equivalent to 45/60, having:

(i) numerator 15

(ii) denominator 4

(iii) denominator 240

(iv) numerator 135

Solution:

(i) The given fraction = 45/60

By considering numerator = 15

We know that 45 ÷ 3 = 15

Dividing the numerator and denominator of the fraction by 3

45/60 ÷ 3/3 = 15/20

(ii) The given fraction = 45/60

By considering denominator = 4

We know that 60 ÷ 15 = 4

Dividing the numerator and denominator of the fraction by 15

45/60 ÷ 15/15 = 3/4

(iii) The given fraction = 45/60

By considering denominator = 240

We know that 60 × 4 = 240

Multiply the numerator and denominator of the fraction by 4

45/60 × 4/4 = 180/240

(iv) The given fraction = 45/60

By considering numerator = 135

We know that 45 × 3 = 135

Multiply the numerator and denominator of the fraction by 3

45/60 × 3/3 = 135/180

6. Find the fraction equivalent of 35/42, having:

(i) numerator 15

(ii) denominator 18

(iii) denominator 30

(iv) numerator 30

Solution:

The given fraction = 35/42

In order to reduce the fraction, divide the numerator and denominator by the HCF of 35 and 42

We get

35/42 ÷ 7/7 = 5/6

(i) So the fraction = 5/6

By considering numerator = 15

We know that 5 × 3 = 15

Multiply the numerator and denominator of the fraction by 3

5/6 × 3/3 = 15/18

(ii) So the fraction = 5/6

By considering denominator = 18

We know that 6 × 3 = 18

Multiply the numerator and denominator of the fraction by 3

5/6 × 3/3 = 15/18

(iii) So the fraction = 5/6

By considering denominator = 30

We know that 6 × 5 = 30

Multiply the numerator and denominator of the fraction by 5

5/6 × 5/5 = 25/30

(iv) So the fraction = 5/6

By considering numerator = 30

We know that 5 × 6 = 30

Multiply the numerator and denominator of the fraction by 6

5/6 × 6/6 = 30/36

7. Check whether the given fractions are equivalent:

(i) 5/9, 30/54

(ii) 2/7, 16/42

(iii) 7/13, 5/11

(iv) 4/11, 32/88

(v) 3/10, 12/50

(vi) 9/27, 25/75

Solution:

(i) We know that

5/9 × 6/6 = 30/54

Therefore, 5/9 is equivalent to 30/54.

(ii) We know that

2/7 × 8/8 = 16/56

Therefore, 2/7 is not equivalent to 16/42.

(iii) We know that

7/13 × 5/5 = 35/65

The same way

5/11 × 7/7 = 35/77

Therefore, 7/13 is not equivalent to 5/11.

(iv) We know that

4/11 × 8/8 = 32/88

Therefore, 4/11 is equivalent to 32/88.

(v) We know that

3/10 × 4/4 = 12/40

Therefore, 3/10 is not equivalent to 12/50.

(vi) We know that

9/27 = 1/3 and 25/75 = 1/3

Therefore, 9/27 is equivalent to 25/75.

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

(i) 250/400 (a) 2/3

(ii) 180/200 (b) 2/5

(iii) 660/990 (c) ½

(iv) 180/360 (d) 5/8

(v) 220/550 (e) 9/10

Solution:

(i) 250/400

By dividing numerator and denominator by HCF of 250 and 400

= (250/50)/ (400/ 50) = 5/8

So the match is (d)

(ii) 180/200

By dividing numerator and denominator by HCF of 180 and 200

= (180/20)/ (200/20) = 9/10

So the match is (e)

(iii) 660/990

By dividing numerator and denominator by HCF of 660 and 990

= (660/90)/ (990/90) = 2/3

So the match is (a)

(iv) 180/360

By dividing numerator and denominator by HCF of 180 and 360

= (180/180)/ (360/180) = ½

So the match is (c)

(v) 220/550

By dividing numerator and denominator by HCF of 220 and 550

= (220/11)/ (550/11) = 2/5

So the match is (b)

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

Solution:

The equivalent fractions which contain all digits from 1 to 9 once only are

2/6 = 3/9 = 58/174, 2/4 = 3/6 = 79/158

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:

Number of pencils Ravish had = 20

Number of pencils Ravish used = 10

By dividing the numerator and denominator by HCF of 10 and 20

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

By dividing the numerator and denominator by HCF of 25 and 50

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

By dividing the numerator and denominator by HCF of 40 and 80

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

Yes, each has used up an equal fraction of their pencils.

RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.5 PDF Download

Students can strengthen their understanding of equivalent fractions by using the detailed RD Sharma Solutions for Class 6. Maths Chapter 6 Exercise 6.5. This exercise focuses on identifying, comparing, and finding equivalent fractions, helping learners build a solid grasp of fraction equivalence. To access clear, step-by-step solutions and improve your math skills, download the RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.5 PDF from the link below.

Preparation tips for RD Sharma Class 6 Maths Chapter 6 Exercise 6.5

1. Start by revising what equivalent fractions are and how to find them by multiplying or dividing numerator and denominator by the same number.

2. Follow the detailed solutions in RD Sharma to understand the method behind each problem before attempting on your own.

3. Draw fraction bars or circles to visualize equivalent fractions better, which helps in grasping the concept easily.

4. Practice all exercises from 6.5 regularly to build speed and accuracy.

5. Always compare your solutions with RD Sharma answers to identify and correct mistakes.

6. If any concept feels confusing, clarify it immediately by asking teachers or using additional resources.

7. Pay attention to word problems involving fractions as they improve your application skills.