CBSE Class 6 Mathematics Chapter 11: Algebra NCERT Solutions

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NCERT Solutions PDF Class 6 PDF

CBSE Class 6 Mathematics Chapter 11: Algebra introduces students to the foundational ideas of algebraic expressions. This chapter focuses on recognizing patterns and developing simple rules using variables. You'll learn to represent unknown quantities or general rules with letters such as 'n', 'b', 's', and 't'. The NCERT Solutions offer clear, step-by-step guidance on how to derive these rules, which is crucial for building a solid understanding of algebra. These solutions also help in translating word problems into algebraic expressions, making the use of variables and the formation of equations easier to understand. Working through these exercises will sharpen your problem-solving abilities and prepare you for more advanced algebraic topics later on, ensuring effective exam revision.

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Quick info

BoardCBSE
ClassClass 6
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 11: Algebra

Chapter summary

Chapter 11: Algebra for Class 6 Mathematics NCERT Solutions focuses on introducing the concept of variables and forming simple algebraic expressions. It covers exercises on identifying patterns in matchstick arrangements and deriving general rules using variables. The solutions explain how to represent quantities like the number of cadets, mangoes, pencils, or distances covered based on given conditions and variables. This chapter lays the groundwork for understanding algebraic notation and its application in real-world scenarios.

Learning outcomes

  • Understand the concept of a variable in algebra.
  • Identify patterns and formulate rules using variables.
  • Write algebraic expressions for given situations.
  • Solve simple problems involving algebraic rules.
  • Relate algebraic expressions to real-world scenarios.

Topics covered

Paper topics

  • Introduction to Algebra
  • Variables
  • Forming Rules
  • Algebraic Expressions
  • Matchstick Patterns
  • Representing Quantities
  • Number of Cadets
  • Number of Mangoes
  • Number of Pencils
  • Distance and Time

Important topics

  • Understanding and using variables
  • Formulating algebraic rules from patterns
  • Translating word problems into expressions
  • Applying rules to find unknown quantities

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Questions and Solutions

Question 1

Find the rule, which gives the number of matchsticks required to make the following matchsticks patterns. Use a variable to write the rule for each pattern:

(a) A pattern of letter T

(b) A pattern of letter Z

(d) A pattern of letter V

(c) A pattern of letter U

(e) A pattern of letter E

(f) A pattern of letter S

(g) A pattern of letter A

Solution:

To find the rule, we observe the number of matchsticks needed for each pattern and represent it using a variable, typically 'n', to denote the number of times the pattern is repeated.

(a) For a pattern of the letter T, 2 matchsticks are used for each T. So, the rule is 2n, where 'n' is the number of T's.

(b) For a pattern of the letter Z, 3 matchsticks are used for each Z. So, the rule is 3n, where 'n' is the number of Z's.

(c) For a pattern of the letter U, 3 matchsticks are used for each U. So, the rule is 3n, where 'n' is the number of U's.

(d) For a pattern of the letter V, 2 matchsticks are used for each V. So, the rule is 2n, where 'n' is the number of V's.

(e) For a pattern of the letter E, 5 matchsticks are used for each E. So, the rule is 5n, where 'n' is the number of E's.

(f) For a pattern of the letter S, 5 matchsticks are used for each S. So, the rule is 5n, where 'n' is the number of S's.

(g) For a pattern of the letter A, 6 matchsticks are used for each A. So, the rule is 6n, where 'n' is the number of A's.

Question 2

We already know the rule for the pattern of letter L, C and F. Some of the letters from Q.1 (given above) give us the same rule as that given by L. Which are these? Why does this happen?
Solution:

The letter 'L' requires 2 matchsticks to form. Looking at the rules derived in Question 1, the patterns for the letter 'T' and the letter 'V' also use 2 matchsticks for each instance of the letter.

Therefore, the letters 'T' and 'V' from Question 1 give the same rule (2n) as the letter 'L'. This happens because each of these letters (L, T, and V) is constructed using exactly 2 matchsticks.

Question 3

Cadets are marching in a parade. There are 5 cadets in a row. What is the rule, which gives the number of cadets, given the number of rows? (Use n for the number of rows)
Solution:

We are given that there are 5 cadets in each row. We need to find a rule for the total number of cadets based on the number of rows.

Let 'n' represent the number of rows.

Since each row has 5 cadets, the total number of cadets will be the number of rows multiplied by the number of cadets per row.

Total number of cadets = (Number of rows) × (Number of cadets in each row)

Total number of cadets = n × 5

Therefore, the rule is 5n.

Question 4

If there are 50 mangoes in a box, how will you write the total number of mangoes in terms of the number of boxes? (Use b for the number of boxes)
Solution:

We are told that each box contains 50 mangoes. We need to express the total number of mangoes using a variable for the number of boxes.

Let 'b' represent the number of boxes.

Since each box contains 50 mangoes, the total number of mangoes is the number of boxes multiplied by the number of mangoes per box.

Total number of mangoes = (Number of boxes) × (Number of mangoes in each box)

Total number of mangoes = b × 50

Therefore, the rule is 50b.

Question 5

The teacher distributes 5 pencils per student. Can you tell how many pencils are needed, given the number of students? (Use s for the number of students)
Solution:

The teacher gives 5 pencils to each student. We need to find the total number of pencils required based on the number of students.

Let 's' represent the number of students.

Since each student receives 5 pencils, the total number of pencils needed is the number of students multiplied by the number of pencils per student.

Total number of pencils = (Number of students) × (Number of pencils per student)

Total number of pencils = s × 5

Therefore, the rule is 5s.

Question 6

A bird flies 1 kilometer in one minute. Can you express the distance covered by the bird in terms of its flying time in minutes? (Use t for flying time in minutes)
Solution:

We know that the bird flies at a speed of 1 kilometer per minute. We need to find the distance covered based on the flying time.

Let 't' represent the flying time in minutes.

The formula for distance is: Distance = Speed × Time.

In this case, Speed = 1 km/minute and Time = t minutes.

Distance covered = 1 × t

Therefore, the distance covered by the bird is t kilometers.

Common mistakes

  • Confusing variables with constants.
  • Incorrectly forming algebraic expressions from word problems.
  • Not understanding the meaning of 'n times' or 'per student' in an algebraic context.
  • Errors in applying the derived rule to specific cases.

Revision tips

  • Focus on understanding how each variable represents a specific quantity.
  • Practice converting word problems into algebraic expressions step-by-step.
  • Review the matchstick patterns to see how the number of matchsticks relates to the number of letters.
  • Try to create your own simple patterns and derive their algebraic rules.

Practice MCQs

Q1. What is the rule for a pattern of the letter 'E' if each letter requires 5 matchsticks?

Q2. If there are 'n' rows with 5 cadets in each row, what is the total number of cadets?

Q3. Which letters from Question 1 use the same rule as the letter 'L' (which requires 2 matchsticks)?

Q4. If a bird flies at a speed of 1 km per minute, what is the distance covered in 't' minutes?

Q5. What does the variable 'b' represent in the context of mangoes in boxes?

Frequently asked questions

What is the main concept covered in CBSE Class 6 Maths Chapter 11: Algebra?

This chapter introduces the basic concepts of algebra, focusing on understanding variables and forming simple algebraic expressions or rules based on patterns and given conditions.

How do these NCERT Solutions help students?

These solutions provide clear, step-by-step explanations for each problem, helping students understand how to derive algebraic rules and expressions, which is crucial for building a strong foundation in mathematics.

What is a variable in the context of this chapter?

A variable is a symbol, usually a letter (like n, b, s, t), that is used to represent an unknown quantity or a quantity that can change.

Can you give an example of forming a rule from a pattern?

Yes, for a pattern of the letter 'T' using 2 matchsticks per letter, the rule is 2n, where 'n' is the number of 'T's formed.

How are these solutions useful for exam preparation?

By working through these rewritten solutions, students can reinforce their understanding of algebraic concepts and practice problem-solving techniques, making their revision more effective for exams.

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