NCERT Solutions: Algebra

# NCERT Solutions for Class 8 Maths Chapter 11 - Algebra

## Exercise 11.1

Q1. Find the rule which gives the number of matchsticks required to make the following matchstick patterns. Use a variable to write the rule.
(a) A pattern of letter T as
Ans:  Pattern of letter
So,
For 1T, Number for Matchsticks = 2
For 2T, Number for Matchsticks = 4
For 3T, Number for Matchsticks = 6
So, we write
Number of matchsticks = 2n
where, n = Number of T

(b) A pattern of letter Z as
Ans: Pattern of letter
So,
For 1Z, Number of matchsticks = 3
For 2Z, Number of matchsticks = 6
For 3Z, Number of matchsticks = 9
So, we write,
Number of matchsticks = 3n
where n = Number of Z

(c) A pattern of letter U as
Ans: Pattern of letter
So,
For 1U, Number of matchsticks = 3
Similarly
For 2U, Number of matchsticks = 6
For 3U, Number of matchsticks = 9
So, we write,
Number of matchsticks = 3n
where n = Number of U

(d) A pattern of letter V as
Ans: Pattern of letter
So,
For 1V, Number of matchsticks = 2
Similarly
For 2V, Number of matchsticks = 4
For 4V, Number of matchsticks = 6
So, we write,
Number of matchsticks = 2n
where n = Number of V

(e) A pattern of letter E as
Ans: Pattern of letter
So,
For one E, Number of matchsticks = 5
For 2E, Number of matchsticks = 10
For 3E, Number of matchsticks = 15
So, we write,
Number of matchsticks = 5n
where, n = Number of E

(f) A pattern of letter S as
Ans: Pattern of letter
So,
For one S, Number of matchsticks = 5
For 2S, Number of matchsticks = 10
For 3S, Number of matchsticks = 15
So, we write,
Number of matchsticks = 5n
where, n = Number of S

(g) A pattern of letter A as
Ans: Pattern of letter
So,
For 1A, Number of matchsticks = 6
For 2A, Number of matchsticks = 12
For 3A, Number of matchsticks = 18
So, we write
Number of matchsticks = 6n
where n = Number of A

Q2. We already know the rule for the pattern of letters 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?
Ans: We know that T requires only two matchsticks. So, the pattern for letter T is 2n. Among all the letters given in question 1, only T and V are the letters which require two matchsticks. Hence, (a) and (d).

Q3. 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 rows = n
Cadets in each row = 5
Total number of cadets = number of cadets in each row × number of rows = 5n

Q4. 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: Number of boxes = b
Number of mangoes in each box = 50
Therefore, total number of mangoes = number of mangoes in a box × number of boxes = 50b

Q5. 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 students = s
Number of pencils to each student = 5
The total number of pencils needed are = number of pencils to each student × number of students = 5s

Q6. A bird flies 1 kilometre 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.)
Ans: Time taken by bird = t minutes
Speed of bird = 1 km per minute
Therefore, Distance covered by bird = speed x time = 1 x t = t km

Q7. Radha is drawing a dot Rangoli (a beautiful pattern of lines joining dots) with chalk powder. She has 9 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 dots in a row = 9
Number of rows = r
Total number of dots in r rows = Number of dots in a row × number of rows = 9r
Number of dots in 8 rows = 8 × 9= 72
Number of dots in 10 rows = 10 × 9= 90

Q8. 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: Given that,
Leela is 4 years younger than Radha
So,
Leela's Age = Radha's age - 4
Let Radha's age = x years
So, Leela's age = x - 4 years

Q9. 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: Number of laddus gave away = l
Number of laddus remaining = 5
Total number of laddus = (l + 5)

Q10. 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: Number of oranges in one box = x
Number of boxes = 2
Therefore, total number of oranges in boxes = 2x
Remaining oranges = 10

Thus, number of oranges = 2x + 10

Q11: (a) Look at the following matchstick pattern of squares (Fig 11.6). The squares are not separate. Two neighboring 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)
Ans: We may observe that in the given matchstick pattern, the number of matchsticks are 4, 7, 10 and 13, which is 1 more than thrice the number of squares in the pattern

Therefore the pattern is 3x + 1, where x is the number of squares

(b) Fig 11.7 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: We may observe that in the given matchstick pattern, the number of matchsticks is 3, 5, 7 and 9 which is 1 more than twice the number of triangles in the pattern.
Therefore the pattern is 2x + 1, where x is the number of triangles.

The document NCERT Solutions for Class 8 Maths Chapter 11 - Algebra is a part of the Class 6 Course Mathematics (Maths) Class 6.
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## Mathematics (Maths) Class 6

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## FAQs on NCERT Solutions for Class 8 Maths Chapter 11 - Algebra

 1. What is the importance of studying algebra in Class 6?
Ans. Studying algebra in Class 6 is important as it lays the foundation for understanding complex mathematical concepts in higher grades. It helps in developing problem-solving skills, logical thinking, and analytical abilities.
 2. How can algebra be applied in real life?
Ans. Algebra can be applied in various real-life situations such as calculating expenses, budgeting, measuring distances, determining time and speed, predicting patterns, and solving everyday problems involving unknown quantities.
 3. What are the basic concepts of algebra covered in Class 6?
Ans. In Class 6, the basic concepts of algebra covered include understanding variables, constants, coefficients, expressions, equations, and solving simple linear equations with one variable.
 4. How can I improve my algebra skills in Class 6?
Ans. To improve algebra skills in Class 6, practice regularly by solving a variety of algebraic problems, seek help from teachers or classmates when facing difficulties, and use online resources or textbooks for additional practice and learning.
 5. Are there any online resources or websites available for practicing algebra in Class 6?
Ans. Yes, there are various online resources and websites available for practicing algebra in Class 6. Some popular ones include Khan Academy, Math Playground, IXL Math, and Math is Fun. These platforms offer interactive lessons, practice exercises, and quizzes to enhance algebraic skills.

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