Algebra Chapter 1 Concept Of Algebraic Variables Or Quantities Or Symbols
Question 1. Write in words the following quantities:
1. 10a
Solution:
10a means that the variable a is multiplied by 10.
2. a + c
Solution:
a + c means that a is added to c or the addition of a and c.
3. x – y
Solution:
x – y means that the value of y is subtracted from the value of x.
Class 6 Math Solutions WBBSE English Medium
4. 9x + 2
Solution:
9x + 2 means that 2 is added to the value of 9 times of x.
WBBSE Class 6 Algebraic Variables Notes
5. 3x – 7
Solution:
3x – 7 means that 7 is subtracted from the value of 3 times of x.
Read And Learn More WBBSE Solutions For Class 6 Maths
6. (p/3) – 4
Solution:
(p/3) – 4 means that 4 is subtracted from the quotient p/3
i.e., 4 is subtracted from the value of p divided by 3.
7. x > y
Solution:
x > 6 means that x is greater than 6.
8. p >≠ 9.
Solution :
p >≠ 9 means that p is not greater than 9.
Understanding Algebraic Symbols
Question 2. Express the following statements in algebraical quantities by sign and symbols :
1. The addition of x and 7.
Solution:
x + 7.
2. Subtraction of 9 from y
Solution:
y – 9.
3. Multiplication of a by 3.
Solution:
3a.
4. x is greater than 13.
Solution:
x > 13.
5. Division of x by 8.
Solution:
x/8.
6. y is not equal to 5.
Solution:
y ≠ 5.
7. The addition of 7 to 10 times p.
Solution:
10p + 7.
8. Subtraction of 1 from the multiplication of x by 3.
Solution:
3x – 1.
Short Questions on Algebraic Variables
9. x is less than y.
Solution:
x < y.
10. b is not less than 8.
Solution:
b <≠ 8.
Question 3.
1. The present age of Suvadra is x years, after 4 years her age will be years.
Solution:
Given:
The present age of Suvadra is x years, after 4 years her age will be years
x + 4
2. The present age of Avisekh is y years, 7 years before his age was years.
Solution:
Given:
The present age of Avisekh is y years, 7 years before his age was years.
y – 7
3. There are x rose flower plants in the garden of Kamala. There are rose flower plants in the garden of Kamalini 1/4 the that in the garden of Kamala. So the number of rose flower plants in the garden of Kamalini is.
Common Questions About Algebraic Expressions
Solution:
Given:
There are x rose flower plants in the garden of Kamala. There are rose flower plants in the garden of Kamalini 1/4 the that in the garden of Kamala. So the number of rose flower plants in the garden of Kamalini is.
x/4
4. Shibu has given a subscription of Rs x for Durgapuja at Muktipara of Bamangachi. Manish has given a subscription of Rs 10 more than twice what Shibu has given. So Manish has given Rs. as a subscription for Durgapuja.
Solution:
Given:
Shibu has given a subscription of Rs x for Durgapuja at Muktipara of Bamangachi. Manish has given a subscription of Rs 10 more than twice what Shibu has given. So Manish has given Rs. as a subscription for Durgapuja.
2x + 10
5. The height of Himangshu is 3 less than that of Hindal. If the height of Hindal is x cm, then the height of Himangshu is cm.
Solution:
Given:
The height of Himangshu is 3 less than that of Hindal. If the height of Hindal is x cm, then the height of Himangshu is cm.
x – 3.
Practice Problems on Algebraic Quantities
Question 4. Express the following statements algebraically using symbols and operation signs:
1. The height of Kankana is y The height of Kumudini is 21 cm less than that of Kankana. What is the height of Kumudini?
Solution:
Given:
The height of Kankana is y The height of Kumudini is 21 cm less than that of Kankana.
The height of Kumudini = (y – 21) cm.
2. The present age of the father is 5 times that of his son. The present age of the son is x What is the present age of the father?
Solution:
Given:
The present age of the father is 5 times that of his son. The present age of the son is x
The present age of the father = 5x years
Conceptual Questions on Properties of Algebraic Operations
3. Anindita has pnote books. Sunanda has notebooks 1/4th that of Anindita. How many notebooks have Sunanda?
Solution:
Given:
Anindita has pnote books. Sunanda has notebooks 1/4th that of Anindita.
Sunanda has p/4 notebooks.
4. Mihir takes x hours to go from his house to school. Mitali takes 5 hours less than 3 times that Mihir takes to go from house to school. How many hours does Mitali take to go from her house to school?
Solution:
Given:
Mihir takes x hours to go from his house to school. Mitali takes 5 hours less than 3 times that Mihir takes to go from house to school.
Mitali takes (3x – 5) hours to go from her house to school.
Real-Life Scenarios Involving Problem Solving with Variables
Question 5.
1. Your present age is 4 years less than that of your elder brother. If the present age of your elder brother is x years, then what is your present age?
Solution:
Given:
Your present age is 4 years less than that of your elder brother. If the present age of your elder brother is x years,
Your present age is (x – 4) years.
2. Thirtha has caught x Partha has caught 5 fishes more than that Thirtha. How many fishes have been caught by Partha?
Solution :
Given:
Thirtha has caught x Partha has caught 5 fishes more than that Thirtha.
Partha has caught (x+ 5) fish.
Question 6.
1. My father has brought x packets of sweets today. Each packet contains 5 sweets. How many sweets have been brought my father?
Solution:
Given:
My father has brought x packets of sweets today. Each packet contains 5 sweets.
Father has brought x packets of sweets. Each packet contains 5 sweets.
So x packets of sweets contain 5x sweets.
My father brought today 5x sweets.
2. Today Pradip has worked out sums 2 less than 4 times that Prabir has worked out. Prabir has worked out x sums today. How many sums Pradip has worked out today?
Solution :
Given:
Today Pradip has worked out sums 2 less than 4 times that Prabir has worked out. Prabir has worked out x sums today.
Prabir has worked out sums today = x.
Pradip has worked out today = (4x – 2) sums.
Question 7.
1. The length of each side of a square is “a” meter, then what is the perimeter of the square?
Solution:
Given:
The length of each side of a square is “a” meter,
We know that the length of each side of the square is the same and the number of sides of the square = 4.
The length of each side = meters (given)
The perimeter of the square = 4 x a meters
= 4a meters.
2. The length and breadth of a rectangle are x cm, and y cm respectively. What is the perimeter of the rectangle?
Solution :
Given:
The length and breadth of a rectangle are x cm, and y cm respectively.
The length of the given rectangle = x cm
and the breadth of the rectangle = y cm
∴ The perimeter of the rectangle = 2 (length + Breadth)
= 2 (x + y) cm.
Examples of Real-Life Applications of Algebraic Variables
Question 8. Moumita and Madhumita have purchased some birds of different designs and different colors from a fair in their locality. Moumita has purchased n birds and Madhumita has purchased birds 8 more than 1/4th part that Moumita has purchased. How many birds have been purchased by Madhumita ?
Solution:
Given:
Moumita and Madhumita have purchased some birds of different designs and different colors from a fair in their locality. Moumita has purchased n birds and Madhumita has purchased birds 8 more than 1/4th part that Moumita has purchased.
Moumita has purchased = n birds
Madhumita has purchased = 8 birds more than 1/4th part that Moumita has
purchased = \(\left(8+\frac{1}{4} \times n\right)\) birds.
= \(\left(8+\frac{n}{4}\right)\) birds.