NCERT Solutions Class 7 Math Chapter 10 Algebraic Expressions Exercise 10.1

NCERT Solutions Class 7 Math Chapter 10 Algebraic Expressions Exercise 10.1

TextbookNCERT
Class 7th
Subject Math
Chapter10th
Chapter NameAlgebraic Expressions
CategoryClass 7th Math Solutions 
Medium English
SourceLast Doubt

NCERT Solutions Class 7 Math Chapter 10 Algebraic Expressions Exercise 10.1

Chapter – 10

Algebraic Expressions

Exercise 10.1

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

(i) Subtraction of z from y.

Solution: = Y – z

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

Solution: = ½ (x + y) = (x + y)/2

(iii) The number z multiplied by itself.

Solution: = z × z = z2

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

Solution: = ¼ (p × q) = pq/4

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

Solution: = x2 + y2

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

Solution: = 3mn + 5

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

Solution: = 10 – (y × z) = 10 – yz

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

Solution: = (a × b) – (a + b) = ab – (a + b)

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

(a) x – 3

Solution:
Expression: x – 3
Terms: x, -3
Factors: x; -3

Ch 12 12.1

(b) 1 + x + x2

Solution:
Expression: 1 + x + x2
Terms: 1, x, x2
Factors: 1; x; x,x

Ch 12 12.1

(c) y – y3

Solution:
Expression: y – y3
Terms: y, -y3
Factors: y; -y, -y, -y

Ch 12 12.1

(d) 5xy2 + 7x2y

Solution:
Expression: 5xy2 + 7x2y
Terms: 5xy2, 7x2y
Factors: 5, x, y, y; 7, x, x, y

Ch 12 12.1

(e) – ab + 2b2 – 3a2

Solution:
Expression: -ab + 2b2 – 3a2
Terms: -ab, 2b2, -3a2
Factors: -a, b; 2, b, b; -3, a, a

Ch 12 12.1

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

(a) – 4x + 5 (b) – 4x + 5y (c) 5y + 3y2 (d) xy + 2x2y2
(e) pq + q (f) 1.2 ab – 2.4 b + 3.6 a (g) ¾ x + ¼
(h) 0.1 p2 + 0.2 q2

?‍♂️Solution: Expressions is defined as, numbers, symbols and operators (such as +. – , × and ÷) grouped together that show the value of something.
In algebra a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or – signs or sometimes by division.
Factors is defined as, numbers we can multiply together to get another number.

Sl.No.ExpressionTermsFactors
(a)– 4x + 5-4×5-4, x5
(b)– 4x + 5y-4x5y-4, x5, y
(c)5y + 3y25y3y25, y3, y, y
(d)xy + 2x2y2xy2x2y2x, y2, x, x, y, y
(e)pq + qpqqP, qQ
(f)1.2 ab – 2.4 b + 3.6 a1.2ab-2.4b

3.6a

1.2, a, b-2.4, b

3.6, a

(g)¾ x + ¼¾ x¼¾, x¼
(h)0.1 p2 + 0.2 q20.1p20.2q20.1, p, p0.2, q, q
4. (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

Solution:

Sl.No.ExpressionTermsCoefficient of x
(i)y2x + yy2xy2
(ii)13y2 – 8yx– 8yx-8y
(iii)x + y + 2x1
(iv)5 + z + zxxzx1z
(v)1 + x + xyxyy
(vi)12xy2 + 2512xy212y2
(vii)7x + xy27xxy27y2

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

(i) 8 – xy2 (ii) 5y2 + 7x (iii) 2x2y – 15xy2 + 7y2

Solution:

Sl.No.ExpressionTermsCoefficient of y2
(i)8 – xy2– xy2– x
(ii)5y2 + 7x5y25
(iii)2x2y – 15xy2 + 7y2– 15xy27y2– 15x7
5. Classify into monomials, binomials and trinomials.

(i) 4y – 7z

Solution: Binomial.
An expression which contains two unlike terms is called a binomial.

(ii) y2

Solution: Monomial.
An expression with only one term is called a monomial.

(iii) x + y – xy

Solution: Trinomial.
An expression which contains three terms is called a trinomial.

(iv) 100

Solution: Monomial.
An expression with only one term is called a monomial.

(v) ab – a – b

Solution: Trinomial.
An expression which contains three terms is called a trinomial.

(vi) 5 – 3t

Solution: Binomial.
An expression which contains two unlike terms is called a binomial.

(vii) 4p2q – 4pq2

Solution: Binomial.
An expression which contains two unlike terms is called a binomial.

(viii) 7mn

Solution: Monomial.
An expression with only one term is called a monomial.

(ix) z2 – 3z + 8

Solution: Trinomial.
An expression which contains three terms is called a trinomial.

(x) a2 + b2

Solution: :Binomial.
An expression which contains two unlike terms is called a binomial.

(xi) z2 + z

Solution: Binomial.
An expression which contains two unlike terms is called a binomial.

(xii) 1 + x + x2

Solution: Trinomial.
An expression which contains three terms is called a trinomial.

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

(i) 1, 100

Solution: Like term.
When term have the same algebraic factors, they are like terms.

(ii) –7x, (5/2)x

Solution: Like term.
When term have the same algebraic factors, they are like terms.

(iii) – 29x, – 29y

Solution: Unlike terms.
The terms have different algebraic factors, they are unlike terms.

(iv) 14xy, 42yx

Solution: Like term.
When term have the same algebraic factors, they are like terms.

(v) 4m2p, 4mp2

Solution: Unlike terms.
The terms have different algebraic factors, they are unlike terms.

(vi) 12xz, 12x2z2

Solution: Unlike terms.
The terms have different algebraic factors, they are unlike terms.

7. Identify like terms in the following:

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

Solution: When term have the same algebraic factors, they are like terms.They are,
– xy2, 2xy2
– 4yx2, 20x2y
8×2, – 11×2, – 6×2
7y, y
– 100x, 3x
– 11yx, 2xy

(b) 10pq, 7p, 8q, – p2q2, – 7qp, – 100q, – 23, 12q2p2, – 5p2, 41, 2405p, 78qp,

13p2q, qp2, 701p2

Solution: When term have the same algebraic factors, they are like terms.They are,
10pq, – 7qp, 78qp
7p, 2405p
8q, – 100q
– p2q2, 12q2p2
– 23, 41
– 5p2, 701p2
13p2q, qp2