RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.6 PDF

RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.6 focuses on reducing fractions to their simplest form. This exercise helps students strengthen their understanding of factors and the concept of HCF (Highest Common Factor).

By solving these problems, students learn how to divide both the numerator and denominator by their common factor to simplify fractions. The questions are straightforward and give plenty of practice to build confidence in basic fraction skills.

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These solutions guide learners step by step, making it easier to understand and apply the method of simplification in real-life math problems.

RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.6 Introduction

Chapter 6 of RD Sharma for  Class 6 focuses on Fractions, an important topic in understanding parts of a whole and how numbers relate in division form.

Exercise 6.6 specifically deals with reducing fractions to their simplest form, which means expressing fractions in the lowest possible terms where the numerator (top number) and denominator (bottom number) have no common factors other than 1.

In this exercise, students learn the process of simplifying fractions by finding the Highest Common Factor (HCF) of the numerator and denominator. The HCF is the largest number that divides both the numerator and the denominator exactly without leaving any remainder.

The exercise involves:

• Identifying factors of both the numerator and denominator.

• Finding their common factors.

• Determining the highest of these common factors (HCF).

• Dividing both numerator and denominator by the HCF to get the fraction in its simplest form.

RD Sharma Solutions for Class 6 Chapter 6 Fractions Exercise 6.6

Here are the detailed solutions for RD Sharma Class 6 Maths Chapter 6 Exercise 6.6 on Fractions.

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

1. (i) 40/75

(ii) 42/28

(iii) 12/52

(iv) 40/72

(v) 80/24

(vi) 84/56

Solution:

(i) 40/75

We know that

Factors of 40 are

1, 2, 4, 5, 8, 10, 20 and 40

Factors of 75 are

1, 3, 5, 15 and 75

So the common factors are 1 and 5

We get HCF = 5

By dividing the numerator and denominator by 5

40/75 ÷ 5/5 = 8/15

Hence, the simplest form of 40/75 is 8/15.

(ii) 42/28

We know that

Factors of 42 are

1, 2, 3, 6, 7, 14, 21 and 42

Factors of 28 are

1, 2, 4, 7, 14 and 28

So the common factors are 1, 2 and 14

We get HCF = 14

By dividing the numerator and denominator by 14

42/28 ÷ 14/14 = 3/2

Hence, the simplest form of 42/28 is 3/2.

(iii) 12/52

We know that

Factors of 12 are

1, 2, 3, 4, 6 and 12

Factors of 52 are

1, 2, 4, 13, 26 and 52

So the common factors are 1, 2 and 4

We get HCF = 4

By dividing the numerator and denominator by 4

12/52 ÷ 4/4 = 3/13

Hence, the simplest form of 12/52 is 3/13.

(iv) 40/72

We know that

Factors of 40 are

1, 2, 4, 5, 8, 10, 20 and 40

Factors of 72 are

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72

So the common factors are 1, 2, 4 and 8

We get HCF = 8

By dividing the numerator and denominator by 8

40/72 ÷ 8/8 = 5/9

Hence, the simplest form of 40/72 is 5/9.

(v) 80/24

We know that

Factors of 80 are

1, 2, 4, 5, 8, 10, 16, 20, 40 and 80

Factors of 24 are

1, 2, 3, 4, 6, 8, 12 and 24

So the common factors are 1, 2, 4 and 8

We get HCF = 8

By dividing the numerator and denominator by 8

80/24 ÷ 8/8 = 10/3

Hence, the simplest form of 80/24 is 10/3.

(vi) 84/56

We know that

Factors of 84 are

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84

Factors of 56 are

1, 2, 4, 7, 8, 14, 28 and 56

So the common factors are 1, 2, 4, 7, 14 and 28

We get HCF = 28

By dividing the numerator and denominator by 28

84/56 ÷ 28/28 = 3/2

Hence, the simplest form of 84/56 is 3/2.

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

(i) 75/80

(ii) 52/76

(iii) 84/98

(iv) 68/17

(v) 150/50

(vi) 162/108

Solution:

(i) 75/80

We know that

Factors of 75 are

1, 3, 5, 15, 25 and 75

Factors of 80 are

1, 2, 4, 5, 8, 10, 12, 16, 20, 40 and 80

So the common factors are 1 and 5

We get HCF = 5

By dividing the numerator and denominator by 5

75/80 ÷ 5/5 = 15/16

Hence, the simplest form of 75/80 is 15/16.

(ii) 52/76

We know that

Factors of 52 are

1, 2, 4, 13, 26 and 52

Factors of 76 are

1, 2, 4, 19, 38 and 76

So the common factors are 1, 2 and 4

We get HCF = 4

By dividing the numerator and denominator by 4

52/76 ÷ 4/4 = 13/19

Hence, the simplest form of 52/76 is 13/19.

(iii) 84/98

We know that

Factors of 84 are

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84

Factors of 98 are

1, 2, 7, 14, 49 and 98

So the common factors are 1, 2, 7 and 14

We get HCF = 14

By dividing the numerator and denominator by 14

84/98 ÷ 14/14 = 6/7

Hence, the simplest form of 84/98 is 6/7.

(iv) 68/17

We know that

Factors of 68 are

1, 2, 4, 17, 34 and 68

Factors of 17 are

1 and 17

So the common factors are 1 and 17

We get HCF = 17

By dividing the numerator and denominator by 17

68/17 ÷ 17/17 = 4/1

Hence, the simplest form of 68/17 is 4/1.

(v) 150/50

We know that

Factors of 150 are

1, 2, 3, 5, 6, 10, 15, 25, 50 and 150

Factors of 50 are

1, 2, 5, 10, 25 and 50

So the common factors are 1, 2, 5, 10, 25 and 50

We get HCF = 50

By dividing the numerator and denominator by 50

150/50 ÷ 50/50 = 3/1

Hence, the simplest form of 150/50 is 3/1.

(vi) 162/108

We know that

Factors of 162 are

1, 2, 3, 6, 9, 18, 27, 54, 81 and 162

Factors of 108 are

1, 2, 3, 4, 6, 9, 12, 18, 27 and 54

So the common factors are 1, 2, 3, 6, 9, 18, 27 and 54

We get HCF = 54

By dividing the numerator and denominator by 54

162/108 ÷ 54/54 = 3/2

Hence, the simplest form of 162/108 is 3/2.

RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.6 PDF Download

Students can enhance their understanding of simplifying fractions by using the detailed RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.6.

This exercise emphasizes reducing fractions to their simplest form by finding the highest common factor (HCF) of the numerator and denominator.

To get clear, step-by-step explanations and improve your fraction skills, you can download the RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.6 PDF from the link below.

Preparation Tips for RD Sharma Class 6 Maths Chapter 6 Exercise 6.6

• Begin by revising the concept of factors and how to find the Highest Common Factor (HCF) of two numbers as per the latest CBSE syllabus.

• Understand the method of dividing both numerator and denominator by their HCF to simplify fractions.

• Use visual aids like fraction strips or diagrams to see how fractions get simplified and what the simplest form looks like.

• Practice all questions in Exercise 6.6 carefully to build accuracy and confidence in simplifying fractions.

• Compare your answers regularly with the RD Sharma solutions to spot errors and improve.

• Apply the simplification skill in word problems and real-life scenarios to strengthen your understanding.