NCERT Solutions Class 7 Maths Chapter 10 Algebraic Expressions Exercise 10.1

Introduction:

In this chapter 10 algebraic expressions we will learn that algebraic expressions are formed from variables and constants. We use the operations of addition, subtraction, multiplication and division on the variables and constants to form expressions.

Expressions are made up of terms. Terms are added to make an expression. For example, the addition of the terms 5xy and 7 gives the expression 5xy + 7.

NCERT Class 7 Maths Chapter 10 Algebraic Expressions Exercise 10.1

NCERT Class 7 Maths Chapter 10 Algebraic Expressions Exercise 10.2

Class 7 Maths Exercise 10.1 (Page-165)

Q1. Get the algebraic expressions in the following cases using variables, constants and arithmetic operations:

(i) Subtraction of z from y.

(ii) One half of the sum of numbers x and y.

(iii) The number z multiplied by itself.

(iv) One-fourth of the product of numbers p and q.

(v) Numbers x and y both squared and added.

(vi) Number 5 added to three times the product of number m and n.

(vii) Product of numbers y and 2 subtracted from 10.

(viii) Sum of numbers a and b subtracted from their product.

Solution:

(i) y - z

(ii) \(\displaystyle \frac{{x + y}}{2}\)

(iii) z²

(iv) \(\displaystyle \frac{{pq}}{4}\)

(v) x² + y²

(vi) 3mn + 5

(vii) 10 - yz

(viii) ab - (a +b)

Q2. (i) Identify the terms and their factors in the following expressions show the terms and factors by tree diagrams.

(a) x - 3

(b) 1 + x + x²

(d) 5xy² + 7x²y

(e) - ab + 2b² - 3a²

(ii). Identify terms and factors in the expressions given below:

(a) - 4x + 5

(b) - 4x + 5y

(d) xy + 2x²y²

(e) pq + q

(f) 1.2 ab - 2.4b + 3.6a

(g) \(\displaystyle \frac{{3}}{4}\) x + \(\displaystyle \frac{{1}}{4}\)

(h) 0.1p² + 0.2 q²

Solution: (1)

(ii)

(a) Terms : -4x, 5

Factors: -4, x ; 5

(b) Terms : - 4x, 5y

Factors: -4, x ; 5,y

Factors: 5, y ; 3, y, y

(d) Terms : xy, 2x²y²

Factors: x, y ; 2x, x, y,y

(e) Terms : pq, q

Factors: p, q, q

(f) Terms : 1.2 ab, - 2.4b, 3.6a

Factors: 1.2,a,b ; - 2.4, b ; 3.6, a

(g) Terms : \(\displaystyle \frac{{3}}{4}\) x , \(\displaystyle \frac{{1}}{4}\)

Factors: \(\displaystyle \frac{{3}}{4}\) , x ; \(\displaystyle \frac{{1}}{4}\)

(h) Terms : 0.1p², 0.2 q²

Factors : 0.1, p,p ; 0.2,q,q

Q3. Identify the numerical coefficients of terms (other than constants) in the following expressions :

(i) 5 - 3t²

(ii) l + t + t² + t³

(iii) x + 2xy + 3y

(iv) 100m + 1000n

(v) - p²q² + 7pq

(vi) 1.2a + 0.8b

(vii) 3.14 r²

(viii) 2 (l + b)

(ix) 0.1y + 0.01y²

Solution:

Q4. (a) Identify terms which contain x and give the coefficient of x.

(i) y²x + y

(ii) 13y² - 8yx

(iii) x + y + 2

(iv) 5 + z + zx

(v) 1 + x + xy

(vi) 12xy² + 25

(vii) 7x + xy²

(b) Identify terms which contain y² and give the coefficient of y².

(i) 8 - xy²

(ii) 5y² + 7x

(iii) 2x²y - 15xy² + 7y²

Solution:

(a)

(i) Terms contain x :- y²

Coefficient of x :- y²

(ii) Terms contain x :- -8yx

Coefficient of x :- -8y

(iii) Terms contain x :- x

Coefficient of x :- 1

(iv) Terms contain x :- zx

Coefficient of x :- z

(v) Terms contain x :- x; xy

Coefficient of x :- 1 ; y

(vi) Terms contain x :- 12xy²

Coefficient of x :- 12y²

(vii) Terms contain x :- 7x ; xy²

Coefficient of x :- 7 ; y²

(b)

(i) Terms contain y² : - xy²

coefficient of y² : -x

(ii) Terms contain y² : 5y²

coefficient of y² : 5

(iii) Terms contain y² : -15y² , 7y²

coefficient of y² : -15x, 7

Q5. Classify into monomials, binomials and trinomials.

(i) 4y - 7z

(ii) y²

(iii) x + y - xy

(iv) 100

(v) ab - a - b

(vi) 5 - 3t

(vii) 4p²q - 4pq²

(viii) 7mn

(ix) z² - 3z + 8

(x) a² + b²

(xi) z² + z

(xii) 1 + x + x²

Solution:

(i) Binomial

(ii) Monomial

(iii) Trinomial

(iv) Monomial

(v) Trinomial

(vi) Binomial

(vii) Binomial

(viii) Monomial

(ix) Trinomial

(x) Binomial

(xi) Binomial

(xii) Trinomial

Q6. State whether a given pair of terms is of like or unlike terms.

(i) 1, 100

(ii) - 7x, \(\displaystyle \frac{{5}}{2}\) x

(iii) - 29x, - 29y

(iv) 14xy, 42yx

(v) 4m²p, 4mp²

(vi) 12xz, 12x²z²

Solution:

(i) Like terms

(ii) Like terms

(iii) Unlike terms

(iv) Like terms

(v) Unlike terms

(vi) Unlike terms

Q7. Identify like terms in the following:

(a) - xy², -4yx², 8x², 2xy², 7y, - 11x², - 100x, -11yx, 20x²y, -6x², y, 2xy, 3x

(b) 10pq, 7p, 8q, - p²q², -7qp, - 100q, -23, 12q²p², -5p², 41, 2405p, 78qp, 13p²q, qp², 701p²

Solution:

(a)

(i) -xy², 2xy²

(ii) -4yx², 20yx²

(iii) 8x², -11x², -6x²

(iv) 7y,y

(v) - 100x, 3x

(vi) - 11yx, 2xy

(b)

(i) 10pq, -7pq, 78pq

(ii) 7p, 2405p

(iii) 8q, -100q

(iv) -p²q², 12p²q²

(v) -12, 41

(vi) -5p², 701p²

(vii) 13p²q,qp²