NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions InText Questions

These NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions InText Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions InText Questions

NCERT In-text Question Page No. 230

Question 1.
Describe how the following expressions are obtained:
(i) 7xy + 5
(ii) x²
(ii) 4x² – 5x
Answer:
(i) 7xy + 5
To obtain this expression, we first multiply two variables x and y, i.e. x × y = xy. Then we multiply their product by 7 to get 7xy. Next, we add 5 to 7xy to obtain 7xy + 5.

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

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

NCERT In-text Question Page No. 231

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

Terms of 7mn – 4 are 7 mn and -4. The term 7 mn formed by first multiplying variables m and n to get m × n = mn
Then multiplying mn by constant 7 to get 7 × mn = 7 mn. The term -4 is a constant.
Tree diagram:

(iii) 2x²y
This expression has only one term, i.e. 2x²y. To form this term first we multiply the variable x by itself to get x × x = x². Then the variable y is multiplied by x² to get
y × x² = x²y
Next, the product x²y is multiplied by 2 to ‘ get
2 × x²y = 2x²y
Tree diagram:

Question 11.
Write three expressions each having 4
terms.
Answer:
(i) 2x³ – 4x² + 9xy + 8
(ii) 6x³ + 9y² – 3xy² – 12
(iii) 9x² – 3x + 12xy – 1

NCERT In-text Question Page No. 231

Question 1.
Identify the coefficients of the terms of following expressions:
Answer:
(i) 4x – 3y
(ii) a + b + 5
(iii) 2y + 5
(iv) 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 1.
The coefficient of b is 1.
The coefficient of 5 is 1.

(iii) 2y + 5
The coefficient of y in 2y is 2.
The coefficient of 5 is 1.

(iii) 2xy
The coefficient of xy in 2xy is 2.
The coefficient of y in 2xy is 2x.
The coefficient of x in 2xy is 2y.

NCERT In-text Question Page No. 233

Question 1.
Group the like terms together from the following:
12x, 12, -25x, -25, -25y, 1, x, 12y, y
Answer:
We have:
(i) 12x, -25x and x are like terms.
(ii) -25y, 12y and y are like terms.
(iii) 12, -25 and 1 are like terms.

NCERT In-text Question Page No. 233

Question 1.
Classify the following expressions as a monomial, a binomial or a trianomial: 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:
(i) a is containing 1 term. It is a monomial.
(ii) a + b is containing 2 terms. It is a binomial.
(iii) ab + a + b is containing 3 terms, it is a trinomial.
(iv) ab + a + b – 5 is containing 4 terms. It is a polynomial.
(v) xy is containing only 1 term. It is a monomial.
(vi) xy + 5 is containing 2 terms. It is a binomial.
(vii) 5x² – x + 2 is containing 3 terms. It is a trinomial.
(viii) 4pq – 3q + 5p is containing 3 terms. It is a trinomial.
(ix) 7 is containing only 1 term. It is a monomial.
(x) 4 m – 7n + 10 is containing 3 terms. It is a trinomial.
(xi) 4mn + 7 is containing 2 terms. It is a binomial.

NCERT In-text Question Page No. 236

Question 1.
Think of at least two situations in which you need to form two algebraic expressions and add or subtract them.
Answer:
Situation-I
Rohan’s per month earning is twice the per month earning of Bibha. Kavita’s per month earnings is RS. 400 more than the sum of Rohan’s and Vibha’s per month earnings. What is the montly earning of Kavita?
Situation-II
Mahesh has twice the number of toys Kanta has: Lata has 5 toys more than twice the number of toys Mahesh and Kanta together have. What is the number of toys that Kanta has?

NCERT In-text Question Page No. 238

Question 1.
Add and subtract:
(i) m – n, m + n
(ii) mn + 5-2, mn + 3
Answer:
(i) Adding (m – n) and (m + n), we have:
(m-n) + (m + n) = m- n + m + n
Collecting like terms, we have:
(m + m) + (-n + n)
= (1 + 1)m + (-1 + 1)n
= 2m + (0)n
= 2m
Now subtracting (m – n) from (m + n), we have:
(m + n)-(m-n) = m + n- m + n
= (m – m) + (n + n)
= (1 – 1)m + (1 + 1)n
= 0m + 2n
= 2n

(ii) Adding mn + 5-2 and mn + 3, we have:
(mn + 5 – 2) + (mn + 3)
= mn + 5 – 2 + mn + 3
= (mn + mn) + (5 – 2 + 3)
= (1 + 1)mn + (6)
= 2 mn + 6
Now, subtracting (mn + 3) from (mn + 5 – 2), we have:
(mn + 5 – 2) – (mn + 3)
= mn + 5 – 2 – mn – 3
= (mn – mn) + (5 – 2 – 3)
= (0)mn + 0 = 0 + 0 = 0

NCERT In-text Question Page No. 245

Question 1.
Make similar pattern with basic figure 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.)
Answer:
Discover more such patterns as follow.