RBSE Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Intext Questions

Rajasthan Board RBSE Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Intext Questions Textbook Exercise Questions and Answers.

RBSE Class 7 Maths Solutions Chapter 12 Algebraic Expressions Intext Questions

(Try These - Page 230)

Question 1.
Describe how the following expressions are obtained:
7xy + 5, 3x²y, 4x² - 5x
Answer:
(i) 7xy + 5
We first multiply two variables x and y, i.e. x × y = xy. Then we .multiply product by a constant 7 to get 7xy. Next we add 5 to 7xy to obtain 7xy + 5.

(ii) x²y
First the variable x is multiplied by itself, i.e. x × x = x². Then multiply x² by y to get x²y.

(iii) 4x² - 5x
First the variable x is multiplied by itself, i.e. x × x = x². Then multiply x² by a constant 4, i.e. x² × 4 = 4x². Next, we multiply the variable x by a constant 5, i.e. x × 5 = 5x. Now, we subtract 5x from 4x² to get 4x² - 5x.

(Try These - Page 231)

Question 1.
What are the terms in the following expressions? Show how the terms are are formed ? Draw a tree diagram for each expression:
8y + 3x², 7mn - 4, 2x²y
Answer:
(i) 8y + 3x² Terms are 8y and 3x².
The term 8y is formed by multiplying the variable y by constant 8.
Then term 3x² is formed by first multiplying the variable x with itself to get x × x = x² and term multiplying x² by 3.

Tree diagram:

(ii) 7mn - 4
Terms are 7mn and - 4.
The term 7mn is formed by first multiplying variable m and n to get m × n = mn, then multiplying mn by constant 7 to get 7 × mn = 7mn. ,
The term - 4 is a constant.

Tree diagram:

(iii) 2x²y
This expression has only one term to form 2x2y. First we multiply the variable x by itself to get x × x = x², then x² is multiplied by another variable y to get x² + y = x²y, next this product x²y is multiplied by constant 2 to get 2x²y.

Tree diagram:

Question 2.
Write three expression each having 4 terms.
Answer:
Expression having 4 terms

• x² + xy - 2x + 3
• 3x² + x - 2y - 1
• - 5xy + 3x² - y² - x

(Try These - Page 231)

Question 1.
Identify the coefficients of the terms of the following expressions :
4x - 3y, a + b + 5, 2y + 5, 2xy.
Answer:
(i) 4x - 3y

• The coefficient of x in 4x is 4.
• The coefficient of y in - 3y is - 3.

(ii) a + b + 5

• The coefficient of a is then a is 1.
• The coefficient of b in term 6 is 1.
• The coefficient of 5 in term 5 is 1.

(iii) 2y + 5

• The coefficient of y in term 2y is 2.
• The coefficient of 5 in term 5 is 1.

(iv) 2xy
The coefficient of xy in 2xy is 2.

(Try These - Page 233)

Question 1.
Group the like terms together from the following:
12x, 12, - 25x, - 25, - 25y, 1, x, 12y, y
Answer:
25x, x and 12x are the like terms; - 25y, 12y and y are the like terms; 12, - 25 and 1 are like terms.

(Try These - Page 233)

Question 1.
Classify the following expressions as a monomial, a binomial or a trinomial: a, a + b, ab + a + b, ab + a + b - 5, xy, xy + 5, 5x² - x + 2, 4pq - 3q + 5p, 7, 4m - 7n + 10, 4mn + 7.
Answer:

(Try These - Page 236)

Question 1.
Think of at least two situations in each of which you need to form two algebraic expressions and add or subtract them.
Answer:

1. Ram has thrice the number of book Shaym has. Vinod has 10 books more than twice the number of books Ram and Shyam together have. Find the number of books that Vinod has.
2. Rohan’s per month salary is twice the per month salary of Abha. Kavya’s per month salary is ₹ 1000 more than the sum of Rohan’s and Abha’s per month salary. What is the per month salary of Kavya?

(Try These - Page 238)

Question 1.
Add and subtract:
(i) m - n, m + n
(ii) ran + 5 - 2, mn + 3
Answer:
(i) Addition of m - n and m + n
= m - n + m + n - m + m + n - n
= 2m + 0
= 2m

Subtraction of m + n from m - n
= (m - n) - (m + n)
= (m - n) + (- m - n)
= m - n - m - n
= m - m - n-n = 0 - 2n = -2n

(ii) Addition of mn + 5 - 2 and mn + 3
= mn + 5 - 2 + mn + 3
= mn + mn + 5 - 2 + 3
= 2 mn + 6

Subtraction of mn + 3 from mn + 5 - 2
= (mn + 5 - 2) - (mn + 3)
(mn + 5 - 2) + (- mn - 3)
= mn + 5 - 2 - mn - 3
= mn - mn + 5 - 2 - 3
= 0 + 0 = 0
Note: Subtracting a term is the same as adding its inverse. Subtracting - 10b is the same as adding + 10b.

(Try These - Page 245)

Question 1.
Make similar pattern with basic figures as shown:

(The number of segments required to make the figure is given to the right. Also, the expression for the number of segments required to make n shapes is also given.)
Go ahead and discover more such patterns,
Answer:
Some more such patterns are as follow: