RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.1 provides a clear and detailed explanation of the concept of fractions through various practical examples.
This exercise helps students understand how to represent shaded parts of a figure as fractions of the whole and simplifies these fractions where necessary.
It includes a variety of problems, such as identifying fractions from shaded diagrams, solving word problems related to fractions of quantities like time and objects, and finding fractions of prime numbers within given sets.
The solutions guide students step-by-step to accurately calculate and interpret fractions in real-life contexts, making the learning process easier and more engaging.
RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.1 Overview
RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.1 focuses on the basic concept of fractions and helps students understand how to identify and write fractions based on shaded portions of different shapes or groups.
The exercise begins with simple problems where students are shown various figures divided into equal parts, with some parts shaded. Students are asked to write the fraction representing the shaded part by counting the number of shaded parts over the total number of equal parts. This helps build a clear understanding of what a fraction represents.
The exercise also includes problems where students need to simplify fractions by dividing both numerator and denominator by their greatest common divisor.Students learn to apply fractions to real-life situations, such as calculating fractions of time (e.g., how much fraction of an hour is 20 minutes) or determining fractions of a group (like how many prime numbers are there in a given range).
Overall, Exercise 6.1 aims to strengthen foundational skills in fractions by combining visual understanding with numerical calculations and practical examples.
The step-by-step solutions in RD Sharma provide clear guidance to help students grasp these concepts confidently and accurately.
RD Sharma Solutions for Class 6 Chapter 6 Fractions Exercise 6.1 Question Answers
Here are the detailed solutions for RD Sharma Class 6 Maths Chapter 6 Exercise 6.1 on Fractions.
1. Write the fraction representing the shaded portion:
Solution:
We know that
Fraction of the shaded portion = Number of shaded parts/ Total number of parts
(i) From the figure we know that
Total number of parts = 3
Number of parts which are shaded = 2
So we get
Fraction of the shaded portion = 2/3
(ii) From the figure we know that
Total number of parts = 15
Number of parts which are shaded = 11
So we get
Fraction of the shaded portion = 11/15
(iii) From the figure we know that
Total number of parts = 9
Number of parts which are shaded = 8
So we get
Fraction of the shaded portion = 8/9
(iv) From the figure we know that
Total number of parts = 7
Number of parts which are shaded = 3
So we get
Fraction of the shaded portion = 3/7
(v) From the figure we know that
Total number of parts = 9
Number of parts which are shaded = 4
So we get
Fraction of the shaded portion = 4/9
(vi) From the figure we know that
Total number of parts = 4
Number of parts which are shaded = 2
So we get
Fraction of the shaded portion = 2/4 = 1/2
(vii) From the figure we know that
Total number of parts = 2
Number of parts which are shaded = 1
So we get
Fraction of the shaded portion = 1/2
(viii) From the figure we know that
Total number of parts = 5
Number of parts which are shaded = 1
So we get
Fraction of the shaded portion = 1/5
(ix) From the figure we know that
Total number of parts = 4
Number of parts which are shaded = 1
So we get
Fraction of the shaded portion = 1/4
2. Write the fraction representing the shaded parts:
Solution:
We know that
Fraction of the shaded portion = Number of shaded parts/ Total number of parts
(i) From the figure we know that
Total number of parts = 9
Number of parts which are shaded = 3
So we get
Fraction of the shaded portion = 3/9 = 1/3
(ii) From the figure we know that
Total number of parts = 8
Number of parts which are shaded = 4
So we get
Fraction of the shaded portion = 4/8 = 1/2
(iii) From the figure we know that
Total number of parts = 12
Number of parts which are shaded = 3
So we get
Fraction of the shaded portion = 3/12 = 1/4
(iv) From the figure we know that
Total number of parts = 10
Number of parts which are shaded = 5
So we get
Fraction of the shaded portion = 5/10 = 1/2
3. Write the fraction representing the shaded portion:
Solution:
We know that
Fraction of the shaded portion = Number of shaded parts/ Total number of parts
(i) From the figure we know that
Total number of parts = 2
Number of parts which are shaded = 1
So we get
Fraction of the shaded portion = 1/2
(ii) From the figure we know that
Total number of parts = 8
Number of parts which are shaded = 4
So we get
Fraction of the shaded portion = 4/8
4. Colour the part according to the fraction given:
Solution:
5. What fraction of an hour is 20 minutes?
Solution:
We know that
Minutes in an hour = 60
So 20 minutes of an hour = 20/ 60 = 1/3
Therefore, 1/3 of an hour is 20 minutes.
6. Write the natural numbers from 2 to 12. What fraction of them are prime numbers?
Solution:
We know that natural numbers from 2 to 12 are
2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12
The prime numbers from 2 to 12 are
2, 3, 5, 7 and 11
So 5 numbers are prime among the 11 numbers
Therefore, 5/11 of them are prime numbers.
7. Write the natural numbers from 102 to 113. What fraction of them are prime numbers?
Solution:
We know that the natural numbers from 102 to 113 are
102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112 and 113
The prime numbers from 102 to 113 are
103, 107, 109 and 113
So 4 numbers are prime among the 12 numbers
We get the fraction of prime numbers = 4/ 12 = 1/3
Therefore, 1/3 fraction of them is prime numbers.
8. Mukesh has a box of 24 pencils. He gives half of them to Sunita. How many does Sunita get? How many does Mukesh still have?
Solution:
Number of pencils Mukesh has = 24
He gives half of them to Sunita = 24/ 2 = 12
So the number of pencils Mukesh still has = 24 – 12 = 12
Therefore, Mukesh gives 12 pencils to Sunita and still has 12 pencils.
9. Kavita has 44 cassettes. She gives ¾ of them to Sonia. How many does Sonia get? How many does Kavita keep?
Solution:
Number of cassettes Kavita has = 44
She gives ¾ of them to Sonia = ¾ (44) = 33
So the number of cassettes Kavita keeps = 44 – 33 = 11
Therefore, Kavita gives 33 cassettes to Sonia and still keeps 11 cassettes.
10. Shikhas has three frocks that she wears when playing. The material is good, but the colours are faded. Her mother buys some blue dye and uses it on two of the frocks. What fraction of all of the Shikha play frocks did her mother dye?
Solution:
Number of frocks = 3
Number of frocks Shikha’s mother dyed = 2
So the fraction of dyed frocks = 2/3
Hence, Shikha’s mother dyed 2/3 fraction of all of Shika’s play frocks.
RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.1 PDF Download
Students can improve their understanding of fractions with the comprehensive RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.1.
This exercise covers identifying and writing fractions based on shaded parts, simplifying fractions, and applying fractions to real-life scenarios.
To access detailed step-by-step solutions and enhance your learning, download the RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.1 PDF from the link below.
