RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.7 provides a detailed approach to understanding the comparison and ordering of fractions.
This exercise helps students learn how to arrange fractions in ascending and descending order, mark fractions on a number line, and simplify fractions to their lowest terms.
It includes practical problems that enhance the ability to compare fractions with the same or different denominators using various methods like cross-multiplication and equivalent fractions.
By working through these solutions, students build a strong foundation in fraction concepts, which are essential for higher-level math, and develop confidence in solving both theoretical and real-life fraction problems effectively.
RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.7 Introduction
This exercise focuses on understanding and comparing fractions by arranging them in ascending and descending order, marking them on a number line, simplifying fractions to their lowest terms, and solving word problems involving fractions.
Key Concepts Covered:
-
Ordering Fractions:
-
Arrange fractions in ascending and descending order using comparison signs (<, >, =).
-
Compare fractions with the same denominator by comparing numerators.
-
Compare fractions with different denominators by converting to equivalent fractions or using cross-multiplication.
-
Number Line Representation:
-
Mark fractions such as 2/8, 4/8, 8/6, and 6/4 on a number line.
-
Use the number line to visually compare and order fractions.
-
Simplifying Fractions:
-
Word Problems:
-
Fraction Equality and Comparison:
Access Answers to Maths RD Sharma Solutions for Class 6 Chapter 6 Fractions Exercise 6.7
Here are the detailed solutions for RD Sharma Class 6 Maths Chapter 6 Exercise 6.7 on Fractions.
1. Write each fraction. Arrange them in ascending and descending order using correct sign <, =, > between the fractions:
Solution:
2. Mark 2/6, 4/6, 8/6 and 6/6 on the number line and put appropriate signs between fractions given below:
(i) 5/6 …….. 2/6
(ii) 3/6 ……. 0/6
(iii) 1/6 …… 6/6
(iv) 8/6 …… 5/6
Solution:
(i) We know that
5/6 > 2/6 as 5 > 2 and the denominator is same.
(ii) We know that
3/6 > 0/6 as 3 > 0 and the denominator is same.
(iii) We know that
1/6 < 6/6 as 6 > 1 and the denominator is same.
(iv) We know that
8/6 > 5/6 as 8 > 5 and the denominator is same.
3. Compare the following fractions and put an appropriate sign:
(i) 3/6 …… 5/6
(ii) 4/5 …… 0/5
(iii) 3/20 …… 4/20
(iv) 1/7 ……. 1/4
Solution:
(i) We know that
3/6 < 5/6 as 3 < 5 and the denominator is same.
(ii) We know that
4/5 > 0/5 as 4 > 0 and the denominator is same.
(iii) We know that
3/20 < 4/20 as 3 < 4 and the denominator is same.
(iv) We know that
1/7 < 1/4 as 7 > 4 and the fraction having smaller denominator is larger.
4. Compare the following fractions using the symbol > or <:
(i) 6/7 and 6/11
(ii) 3/7 and 5/7
(iii) 2/3 and 8/12
(iv) 1/5 and 4/15
(v) 8/3 and 8/13
(vi) 4/9 and 15/8
Solution:
(i) We know that
6/7 > 6/11 as the fraction having smaller denominator is larger.
(ii) We know that
3/7 < 5/7 as 3 < 5 and the denominator is same.
(iii) We know that
8/12 = (2 × 2 × 2)/ (2 × 2 × 3) = 2/3
Hence, 2/3 = 8/12
(iv) We know that
1/5 = (1/ 5) × (3/3) = 3/15 which is lesser than 4/15
Hence, 1/5 < 4/15
(v) We know that
8/3 > 8/13 as the fraction having smaller value of denominator is larger.
(vi) We know that
4/9 = (4/9) × (8/8) = 32/72
15/8 = (15/8) × (9/9) = 135/72
So we get 32/72 < 135/72
Hence, 4/9 < 15/8.
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:
(i) 2/12
(ii) 3/15
(iii) 8/50
(iv) 16/100
(v) 10/60
(vi) 15/75
(vii) 12/60
(viii) 16/96
(ix) 12/75
(x) 12/72
(xi) 3/18
(xii) 4/25
Solution:
(i) 2/12
We know that HCF of 2 and 12 = 2
By dividing numerator and denominator by HCF of 2 and 12
2/12 ÷ 2/2 = 1/6
(ii) 3/15
We know that HCF of 3 and 15 = 3
By dividing numerator and denominator by HCF of 3 and 15
3/15 ÷ 3/3 = 1/5
(iii) 8/50
We know that HCF of 8 and 50 = 2
By dividing numerator and denominator by HCF of 8 and 50
8/50 ÷ 2/2 = 4/25
(iv) 16/100
We know that HCF of 16 and 100 = 4
By dividing numerator and denominator by HCF of 16 and 100
16/100 ÷ 4/4 = 4/25
(v) 10/60
We know that HCF of 10 and 60 = 10
By dividing numerator and denominator by HCF of 10 and 60
10/60 ÷ 10/10 = 1/6
(vi) 15/75
We know that HCF of 15 and 75 = 15
By dividing numerator and denominator by HCF of 15 and 75
15/75 ÷ 15/15 = 1/5
(vii) 12/60
We know that HCF of 2 and 12 = 12
By dividing numerator and denominator by HCF of 2 and 12
12/60 ÷ 12/12 = 1/5
(viii) 16/96
We know that HCF of 16 and 96 = 16
By dividing numerator and denominator by HCF of 16 and 96
16/96 ÷ 16/16 = 1/6
(ix) 12/75
We know that HCF of 12 and 75 = 3
By dividing numerator and denominator by HCF of 12 and 75
12/75 ÷ 3/3 = 4/25
(x) 12/72
We know that HCF of 12 and 72 = 12
By dividing numerator and denominator by HCF of 12 and 72
12/72 ÷ 12/12 = 1/6
(xi) 3/18
We know that HCF of 3 and 18 = 3
By dividing numerator and denominator by HCF of 3 and 18
3/18 ÷ 3/3 = 1/6
(xii) 4/25
We know that HCF of 4 and 25 = 1
By dividing numerator and denominator by HCF of 4 and 25
4/25 ÷ 1/1 = 4/25
Three groups of equal fractions: 2/12, 10/60, 16/96, 12/72, 3/18, 3/15, 15/75, 12/60, 8/50, 16/100, 12/75, 4/25
6. Isha read 25 pages of a book containing 100 pages. Nagma read ½ of the same book. Who read less?
Solution:
No. of pages in the book = 100
We know that
Fraction of book Isha read = (25/100) ÷ (25/25) = 1/4 by dividing both numerator and denominator by HCF of 25 and 100
So the fraction of book Nagma read = 1/2
By comparing 1/4 and 1/2 we get the LCM of 4 and 2 = 4
Now convert the fraction into equivalent fraction having denominator as 4
1/4 × 1/1 and 1/2 × 2/2
1/4 < ½
Hence, Isha read less.
7. Arrange the following fractions in the ascending order:
(i) 2/9, 7/9, 3/9, 4/9, 1/9, 6/9, 5/9
(ii) 7/8, 7/25, 7/11, 7/18, 7/10
(iii) 37/47, 37/50, 37/100, 37/1000, 37/85, 37/41
(iv) 3/5, 1/5, 4/5, 2/5
(v) 2/5, 3/4, 1/2, 3/5
(vi) 3/8, 3/12. 3/6, 3/4
(vii) 4/6, 3/8, 6/12, 5/16
Solution:
(i) 2/9, 7/9, 3/9, 4/9, 1/9, 6/9, 5/9 can be written in ascending order as
1/9, 2/9, 3/9, 4/9, 5/9, 6/9, 7/9
(ii) 7/8, 7/25, 7/11, 7/18, 7/10 can be written in ascending order as
7/25, 7/18, 7/11, 7/10, 7/8
(iii) 37/47, 37/50, 37/100, 37/1000, 37/85, 37/41 can be written in ascending order as
37/1000, 37/100, 37/85, 37/50, 37/47, 37/41
(iv) 3/5, 1/5, 4/5, 2/5 can be written in ascending order as
1/5, 2/5, 3/5, 4/5
(v) 2/5, 3/4, 1/2, 3/5 can be written in ascending order as
2/5, 1/2, 3/5, 3/4
(vi) 3/8, 3/12, 3/6, 3/4 can be written in ascending order as
3/12, 3/8, 3/6, 3/4
(vii) 4/6, 3/8, 6/12, 5/16 can be written in ascending order as
5/16, 3/8, 6/12, 4/6
8. Arrange in descending order in each of the following using the symbol >:
(i) 8/17, 8/9, 8/5, 8/13
(ii) 5/9, 3/12, 1/3, 4/15
(iii) 2/7, 11/35, 9/14, 13/28
Solutions:
(i) 8/17, 8/9, 8/5, 8/13 can be written in the descending order as
8/5 > 8/9 > 8/13 > 8/17
(ii) 5/9, 3/12, 1/3, 4/15 can be written in the descending order as
5/9 > 1/3 > 4/15> 3/12
(iii) 2/7, 11/35, 9/14, 13/28 can be written in the descending order as
9/14 > 13/28 > 11/35 > 2/7
9. Find answers to the following. Write and indicate how you solved them.
(i) Is 5/9 equal to 4/5?
(ii) Is 9/16 equal to 5/9?
(iii) Is 4/5 equal to 16/20?
(iv) Is 1/15 equal to 4/30?
Solution:
(i) No. We know that 5 × 5 ≠ 9 × 4
(ii) No. We know that 9 × 9 ≠ 16 × 5
(iii) Yes. We know that 4 × 20 = 16 × 5
(iv) No. We know that 1 × 30 ≠ 15 × 4
RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.7 PDF Download
Students can improve their skills in comparing and ordering fractions with the detailed RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.7.
This exercise focuses on arranging fractions in ascending and descending order, comparing fractions with the same or different denominators, and placing fractions correctly on a number line.
To get clear, step-by-step solutions and boost your understanding of fractions, you can download the RD Sharma Solutions for Class 6 Maths Chapter 6 Exercise 6.7 PDF from the link below.
