RD Sharma Solutions for Class 6 Maths Chapter 8: RD Sharma Solutions for Class 6 Maths Chapter 8 β Introduction to Algebra are specially designed to help students build a strong foundation in Algebra. These solutions, created by subject experts as per the latest CBSE syllabus, cover all important topics like integers, basic algebraic language, and solving simple equations using addition, subtraction, multiplication, and division.
The step-by-step solutions are based on a concept-based approach, making it easier for students to understand and practice algebraic problems. Students can easily download the RD Sharma Class 6 Maths Chapter 8 PDF to strengthen their skills, revise quickly, and stay exam-ready with confidence.
Aspects | Details |
Class | Class 6 |
Subject | Mathematics / Maths |
Book | RD Sharma |
Chapter Number | 8 |
Name of Chapter | Introduction to Algebra |
Study Material Here | RD Sharma Class 6 Maths Chapter 8 Introduction to Algebra Solutions |
RD Sharma Solutions of All Chapters of This Class | RD Sharma Class 6 Solutions |
All RD Sharma Solutions PDF Available | Yes |
RD Sharma Solutions for Class 6 Maths Chapter 8: Introduction to Algebra help students understand the basics of Algebra in an easy and simple way. Designed by subject experts as per the latest CBSE syllabus, these solutions explain key topics like variables, expressions, and simple equations through clear, step-by-step methods.
To practice more, students can solve Class 6 Maths worksheets along with the RD Sharma Solutions for better problem-solving skills. For quick and easy revision, the Class 6 Maths PDF download is also available. By using RD Sharma Solutions for Class 6 Maths Chapter 8, students can strengthen their Algebra basics and prepare well for their exams with full confidence.
(i) The diameter of a circle is twice its radius.
(ii) The area of a rectangle is the product of its length and breadth.
(iii) The selling price equals the sum of the cost price and the profit.
(iv) The total amount equals the sum of the principal and the interest.
(v) The perimeter of a rectangle is two times the sum of its length and breadth.
(vi) The perimeter of a square is four times its side.
Solution:
(i) Consider d as the diameter and r as the radius of the circle
Hence, we get d = 2r.
(ii) Consider A as the area, l as the length and b as the breadth of a rectangle
Hence, we get A = l Γ b.
(iii) Consider S.P as the selling price, C.P as the cost price and P as the profit
Hence, we get S.P = C.P + P
(iv) Consider A as the amount, P as the principal and I as the interest
Hence, we get A = P + I
(v) Consider P as the perimeter, l as the length and b as the breadth of a rectangle
Hence, P = 2 (l + b)
(vi) Consider P as the perimeter and a as the side of a square
Hence, P = 4a
(i) The sum of 6 and x.
(ii) 3 more than a number y.
(iii) One-third of a number x.
(iv) One-half of the sum of number x and y.
(v) Number y less than a number 7.
(vi) 7 taken away from x.
(vii) 2 less than the quotient of x and y.
(viii) 4 times x taken away from one-third of y.
(ix) Quotient of x by 3 is multiplied by y.
Solution:
(i) The sum of 6 and x can be written as 6 + x.
(ii) 3 more than a number y can be written as y + 3.
(iii) One-third of a number x can be written as x/3.
(iv) One-half of the sum of number x and y can be written as (x + y)/ 2.
(v) Number y less than a number 7 can be written as 7 β y.
(vi) 7 taken away from x can be written as x β 7.
(vii) 2 less than the quotient of x and y can be written as x/y β 2.
(viii) 4 times x taken away from one-third of y can be written as y/3 β 4x.
(ix) Quotient of x by 3 is multiplied by y can be written as xy/3.
Solution:
Consider x as the number.
Multiplying the number by 5 = 5x
Again add 6 to the number = 5x + 6
By subtracting y from the above equation = 5x + 6 β y.
Hence, the result is 5x + 6 β y.
Solution:
Consider y as the number of rooms on the ground floor
We know that
The number of rooms on the first floor = x
It is given that number of rooms on the ground floor of a building is 12 less than the twice of the number of rooms on first floor
So we get
y = 2x β 12
Hence, the rooms on the ground floor is y = 2x β 12.
Solution:
Amount spent by Binny = Rs a
Amount saved by Binny = Rs b
Amount spent by Binny in one week = 7a
So the total income for one week = Amount spent by Binny in one week + Amount saved by Binny
Substituting the values
Total income for one week = 7a + b
We get Binnyβs income for 2 weeks = 2 (7a + b) = Rs 14a + 2b
Hence, the income of Binny for two weeks is Rs 14a + 2b.
Solution:
Marks scored by Rahul in English = 80
Marks scored by Rahul in Hindi = x
So the total scores in the two subjects = x + 80
Hence, the total score of Rahul in two subjects is x + 80.
Solution:
Distance covered by Rohit in one step = x cm
So the distance covered by Rohit in y steps = xy cm
Hence, Rohit covers xy cm in y steps.
Solution:
Weight of one apple = 75 g
Weight of one orange = 40 g
So the weight of x apples = 75x g
So the weight of y oranges = 40y g
We get the weight of x apples and y oranges = (75x + 40y) g
Hence, the weight of x apples and y oranges is (75x + 40y) g.
Solution:
Cost of one pencil = Rs 2
Cost of one fountain pen = Rs 15
Cost of x pencils = 2x
Cost of y fountain pens = 15y
So the cost of x pencils and y fountain pens = Rs (2x + 15y)
Hence, the cost of x pencils and y fountain pens is Rs (2x + 15y).
(i) a Γ a Γ a Γ a Γ β¦β¦.. 15 times
(ii) 8 Γ b Γ b Γ b Γ a Γ a Γ a Γ a
(iii) 5 Γ a Γ a Γ a Γ b Γ b Γ c Γ c Γ c
(iv) 7 Γ a Γ a Γ a β¦β¦.. 8 times Γ b Γ b Γ b Γ β¦β¦ 5 times
(v) 4 Γ a Γ a Γ β¦β¦ 5 times Γ b Γ b Γ β¦β¦. 12 times Γ c Γ c β¦β¦ 15 times
Solution:
(i) a Γ a Γ a Γ a Γ β¦β¦.. 15 times is written in exponential form as a15.
(ii) 8 Γ b Γ b Γ b Γ a Γ a Γ a Γ a is written in exponential form as 8a4b3.
(iii) 5 Γ a Γ a Γ a Γ b Γ b Γ c Γ c Γ c is written in exponential form as 5a3b2c3.
(iv) 7 Γ a Γ a Γ a β¦β¦.. 8 times Γ b Γ b Γ b Γ β¦β¦ 5 times is written in exponential form as 7a8b5.
(v) 4 Γ a Γ a Γ β¦β¦ 5 times Γ b Γ b Γ β¦β¦. 12 times Γ c Γ c β¦β¦ 15 times is written in exponential form as 4a5b12c15.
(i) a2 b5
(ii) 8x3
(iii) 7a3b4
(iv) 15 a9b8c6
(v) 30x4y4z5
(vi) 43p10q5r15
(vii) 17p12q20
Solution:
(i) a2 b5 is written in the product form as a Γ a Γ b Γ b Γ b Γ b Γ b.
(ii) 8x3 is written in the product form as 8 Γ x Γ x Γ x.
(iii) 7a3b4 is written in the product form as 7 Γ a Γ a Γ a Γ b Γ b Γ b Γ b.
(iv) 15 a9b8c6 is written in the product form as 15 Γ a Γ a β¦β¦ 9 times Γ b Γ b Γ β¦ 8 times Γ c Γ c Γ β¦.. 6 times.
(v) 30x4y4z5 is written in the product form as 30 Γ x Γ x Γ x Γ x Γ y Γ y Γ y Γ y Γ z Γ z Γ z Γ z Γ z.
(vi) 43p10q5r15 is written in the product form as 43 Γ p Γ p β¦. 10 times Γ q Γ q β¦. 5 times Γ r Γ r Γ β¦. 15 times.
(vii) 17p12q20 is written in the product form as 17 Γ p Γ p β¦. 12 times Γ q Γ q Γ β¦.. 20 times.
(i) 4a3 Γ 6ab2 Γ c2
(ii) 5xy Γ 3x2y Γ 7y2
(iii) a3 Γ 3ab2 Γ 2a2b2
Solution:
(i) 4a3 Γ 6ab2 Γ c2 is written in exponential form as 24a4b2c2.
(ii) 5xy Γ 3x2y Γ 7y2 is written in exponential form as 105x3y4.
(iii) a3 Γ 3ab2 Γ 2a2b2 is written in exponential form as 6a6b4.
Solution:
Number of bacteria in a culture = x
It is given that
Number of bacteria becomes square of itself in one week = x2
So the number of bacteria after two weeks = (x2)2 = x4
Hence, the number of bacteria after two weeks is x4.
Solution:
It is given that
Area of rectangle = l Γ b
Breadth = x cm
Length = (2/3) x cm
So the area of the rectangle = (2/3) x Γ x = 2/3 x2 cm2
Hence, the area of rectangle is (2/3) x2 cm2.
Solution:
Number of rows of chairs = x
Each row contains = x2 chairs
So the total number of chairs = number of rows of chairs Γ chairs in each row
We get
Total number of chairs = x Γ x2 = x3
Hence, the total number of chairs is x3.
Algebra is a branch of mathematics that uses symbols and letters to represent numbers and quantities in formulas and equations. It's important because it provides a foundation for solving complex problems, helps develop logical thinking, and creates a bridge to advanced mathematics
You can easily find the best RD Sharma Solutions for Class 6 Maths Chapter 8 online and this article as well, specially prepared by experts as per the latest CBSE syllabus, offering step-by-step explanations for easy learning.
RD Sharma Solutions for Class 6 Maths Chapter 8 help students build a strong understanding of Algebra by explaining variables, expressions, and equations in a simple and clear way.
Yes, students can easily access and download the Class 6 Maths PDF for Chapter 8 to revise important Algebra concepts quickly and strengthen their problem-solving skills.
An algebraic expression is a combination of variables, constants, and operations (like 2x + 3y) that doesn't contain an equals sign. An equation, however, contains an equals sign (=) and states that two expressions are equal (like 2x + 3y = 12). Expressions can be simplified or evaluated, while equations are solved to find specific values of the variables.