NCERT Solutions for Class 6 Maths Chapter 11
Algebra in 6th grade math introduces students to basic algebraic concepts that will be essential for understanding more complex math in later years. Here’s a breakdown of the key areas covered:
1. Variables:
- Letters are used to represent unknown numbers (variables).
- Examples: x, y, a, b
- Variables allow us to write general rules and relationships between numbers.
2. Expressions:
- Expressions are combinations of numbers, variables, and operations (addition, subtraction, multiplication, division).
- Examples: 2x + 3, 5y – 1, a + b × 2
3. Evaluating Expressions:
- Substituting numerical values for variables to find the result of an expression.
- Example: If x = 4, then the value of 2x + 3 becomes 2(4) + 3 = 11
4. Simplifying Expressions:
- Combining like terms (terms with the same variable raised to the same power).
- Using the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right)
5. Equations:
- Statements that show equality between two expressions.
- The equal sign (=) indicates a balance between the left and right sides of the equation.
- Examples: x + 5 = 10, 2y – 1 = 7
6. Solving Equations:
- Finding the value of the variable that makes the equation true.
- Often involves isolating the variable using basic operations.
- Example: Solve x + 3 = 7. Subtract 3 from both sides to get x = 4.
7. Word Problems:
- Applying algebraic concepts to solve real-world problems.
- Translating word problems into mathematical equations and solving for the unknown.
NCERT Solutions for Class 6 Maths Chapter 11
Exercise 11.1
1. Find the rule which gives the number of matchsticks required to make the following matchsticks patterns. Use a variable to write the rule.
(a) A pattern of letter T as T
(b) A pattern of letter Z as Z
(c) A pattern of letter U as U
(d) A pattern of letter V as V
(e) A pattern of letter E as E
(f) A pattern of letter S as S
(g) A pattern of letter A as A
Ans :
(a) Pattern T:
- Two sticks are used to form a single T.
- Rule: Number of matchsticks = 2 (for the T)
(b) Pattern Z:
- Three sticks are used to form a single Z.
- Rule: Number of matchsticks = 3 (for the Z)
(c) Pattern U:
- Four sticks are used to form a single U.
- Rule: Number of matchsticks = 4 (for the U)
(d) Pattern V:
- Two sticks are used to form a single V (similar to T).
- Rule: Number of matchsticks = 2 (for the V)
(e) Pattern E:
- Five sticks are used to form a single E.
- Rule: Number of matchsticks = 5 (for the E)
(f) Pattern S:
- Five sticks are used to form a single S (similar to E).
- Rule: Number of matchsticks = 5 (for the S)
(g) Pattern A:
- Six sticks are used to form a single A.
- Rule: Number of matchsticks = 6 (for the A)
2. We already know the rule for the pattern of letters L, C and F. Some of the letters from Ql. (given above) give us the same rule as that given by L. Which are these? Why does this happen?
Ans :
Rules for the following letters:
- For L, the rule is 2n
- For C, the rule is 2n
- For V, the rule is 2n
- For F, the rule is 3n
- For T, the rule is 3n
- For U, the rule is 3n
We observe that the rule is the same for L, C, and V, as they each require only 2 matchsticks. The letters F, T, and U share the same rule, which is 3n, as they each require 3 matchsticks.
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.)
Ans :
Number of cadets = Number of cadets in a row × Number of rows
We can express this rule mathematically using the variable n for the number of rows:
Number of cadets = 5 × n
5 represents the number of cadets in a single row (given in the problem).
n represents the variable for the number of rows in the parade.
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.)
Ans : The total number of mangoes in terms of the number of boxes can be written as:
50b
Here’s the explanation:
- 50: This represents the number of mangoes in a single box (given in the problem).
- b: This variable represents the number of boxes.
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.)
Ans :
Number of pencils = Pencils per student × Number of students
We can express this mathematically using the variable s for the number of students:
Number of pencils = 5s
Explanation:
- 5 represents the number of pencils the teacher distributes to each student (given in the problem).
- s represents the variable for the total number of students.
6. A bird flies 1 kilometre in one minute. Can you express the distance covered by the bird in terms of is flying time in minutes? (Use t for flying time in minutes.)
Ans :
Distance covered in 1 minute = 1 km. The flying time = t minutes.
Distance covered:
- For t = 1 is 1 x 1 km
- For t = 2 is 1 x 2 km
- For t = 3 is 1 x 3 km
∴ The rule is 1 x t km, where t represents the flying time in minutes.
7. Radha is drawing a dot Rangoli (a beautiful pattern of lines joining dots with chalk powder. She has a dots in a row. How many dots will her rangoli have for r rows? How many dots are there if there are 8 rows? If there are 10 rows?
Ans :
Number of rows = r Number of dots in a row drawn by Radha = 8
Therefore, the number of dots required:
- For r = 1 is 8 x 1
- For r = 2 is 8 x 2
- For r = 3 is 8 x 3
∴ The rule is 8r, where r represents the number of rows.
- For r = 8, the number of dots is 8 x 8 = 64
- For r = 10, the number of dots is 8 x 10 = 80
8. Leela is Radha’s younger sister. Leela is 4 years younger than Radha. Can you write Leela’s age in terms of Radha’s age? Take Radha’s age to be x years.
Ans : Since Leela is 4 years younger than Radha, and Radha’s age is represented by the variable x, we can express Leela’s age as:
Leela’s age = Radha’s age – 4 years
Substituting Radha’s age with the variable x:
Leela’s age = x years – 4 years
Therefore, Leela’s age can be written as (x – 4) years.
9. Mother has made laddus. She gives some laddus to guests and family members, still 5 laddus remain. If the number of laddus mother gave away is l, how many laddus did she make?
Ans :
Given that the number of laddus given away is l,
and the number of laddus left is 5,
∴ The total number of laddus made by mother is l + 5.
10. Oranges are to be transferred from larger boxes into smaller boxes. When a large box is emptied, the oranges from it fill two smaller boxes and still 10 oranges remain outside. If the number of oranges in a small box are taken to be x, What is the number of oranges in the larger box?
Ans :
x: Number of oranges in a small box (given).
10: Number of oranges remaining outside after emptying a large box (given).
Total oranges = Oranges in small boxes + Remaining oranges
Total oranges = 2x oranges + 10 oranges
Therefore, the large box contains 2x + 10 oranges.
11. (a) Look at the following matchstick pattern of square. The squares are not separate. Two neighbouring squares have a common matchstick. Observe the patterns and find the rule that gives the number of matchsticks in terms of the number of squares.
(Hint: If you remove the vertical stick at the end, you will get a pattern of Cs)
(b) Following figure gives a matchstick pattern of triangles. As in Exercise 11(a) above, find the general rule that gives the number of matchsticks in terms of the number of triangles.
Ans :
(a) Let n be the number of squares.
∴ The number of matchsticks required:
- For n = 1: 3n + 1 = 3 x 1 + 1 = 4
- For n = 2: 3n + 1 = 3 x 2 + 1 = 7
- For n = 3: 3n + 1 = 3 x 3 + 1 = 10
- For n = 4: 3n + 1 = 3 x 4 + 1 = 13
∴ The rule is 3n + 1, where n represents the number of squares.
(b) Let n be the number of triangles.
∴ The number of matchsticks required:
- For n = 1: 2n + 1 = 2 x 1 + 1 = 3
- For n = 2: 2n + 1 = 2 x 2 + 1 = 5
- For n = 3: 2n + 1 = 2 x 3 + 1 = 7
- For n = 4: 2n + 1 = 2 x 4 + 1 = 9
∴ The rule is 2n + 1, where n represents the number of triangles.
NCERT Solutions for Class 6 Maths Chapter 11
FAQ’s
What is NCERT Solutions for Class 6 Maths Chapter 11 a variable in algebra?
A variable is a letter or symbol (like x, y, or a) used to represent an unknown number. It helps in writing general rules and equations in algebra.
How do NCERT Solutions for Class 6 Maths Chapter 11we express the number of cadets in a parade if there are 5 cadets in each row?
If there are 5 cadets in each row and n represents the number of rows, then the total number of cadets can be written as 5n.
How can NCERT Solutions for Class 6 Maths Chapter 11 we find the total number of mangoes if one box contains 50 mangoes?
If one box contains 50 mangoes and b represents the number of boxes, then the total number of mangoes is 50b.
What is the NCERT Solutions for Class 6 Maths Chapter 11 rule for the number of matchsticks needed to form a pattern of squares?
If n represents the number of squares, the total number of matchsticks needed is 3n + 1.
How can NCERT Solutions for Class 6 Maths Chapter 11 we express Leela’s age if she is 4 years younger than Radha?
If Radha’s age is x years, then Leela’s age can be written as (x – 4) years.
