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.
What is the Best Study Routine for Class 6
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.
