Ncert Solutions For Class 7 Maths Ex 12.1

NCERT Solutions For Class 7 Maths Ex 12.1 PDF Free Download

NCERT Solutions for Class 7 Maths Exercise 12.1 Chapter 12 Algebraic Expressions in simple PDF are available here. In this exercise of NCERT Solutions for Class 7 Chapter 12 contains the topics related to how expressions are formed, terms of an expressions, like and unlike terms, monomials, binomials, trinomials and polynomials. These NCERT Solutions for Class 7 Maths are prepared in such a way that students who are in 7th standard can grasp the concepts quickly and prepare themselves very well for exams to score high marks.

Download the PDF of NCERT Solutions For Class 7 Maths Chapter 12 Perimeter and Area – Exercise 12.1

 

ncert sol class 7 math ch 12 ex 1
ncert sol class 7 math ch 12 ex 1
ncert sol class 7 math ch 12 ex 1
ncert sol class 7 math ch 12 ex 1
ncert sol class 7 math ch 12 ex 1
ncert sol class 7 math ch 12 ex 1
ncert sol class 7 math ch 12 ex 1
ncert sol class 7 math ch 12 ex 1
ncert sol class 7 math ch 12 ex 1

 

Access other exercises of NCERT Solutions For Class 7 Chapter 12 – Algebraic Expressions

Exercise 12.2 Solutions

Exercise 12.3 Solutions

Exercise 12.4 Solutions

Access answers to Maths NCERT Solutions for Class 7 Chapter 12 – Algebraic Expressions Exercise 12.1

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

NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Image 1

(b) 1 + x + x2

Solution:-

Expression: 1 + x + x2

Terms: 1, x, x2

Factors: 1; x; x,x

NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Image 2

(c) y – y3

Solution:-

Expression: y – y3

Terms: y, -y3

Factors: y; -y, -y, -y

NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Image 3

(d) 5xy2 + 7x2y

Solution:-

Expression: 5xy2 + 7x2y

Terms: 5xy2, 7x2y

Factors: 5, x, y, y; 7, x, x, y

NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Image 4

(e) – ab + 2b2 – 3a2

Solution:-

Expression: -ab + 2b2 – 3a2

Terms: -ab, 2b2, -3a2

Factors: -a, b; 2, b, b; -3, a, a

NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Image 5

(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.

Expression

Terms

Factors

(a)

– 4x + 5

-4x

5

-4, x

5

(b)

– 4x + 5y

-4x

5y

-4, x

5, y

(c)

5y + 3y2

5y

3y2

5, y

3, y, y

(d)

xy + 2x2y2

xy

2x2y2

x, y

2, x, x, y, y

(e)

pq + q

pq

q

P, q

Q

(f)

1.2 ab – 2.4 b + 3.6 a

1.2ab

-2.4b

3.6a

1.2, a, b

-2.4, b

3.6, a

(g)

¾ x + ¼

¾ x

¼

¾, x

¼

(h)

0.1 p2 + 0.2 q2

0.1p2

0.2q2

0.1, p, p

0.2, q, q

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

(i) 5 – 3t2 (ii) 1 + t + t2 + t3 (iii) x + 2xy + 3y (iv) 100m + 1000n (v) – p2q2 + 7pq (vi) 1.2 a + 0.8 b (vii) 3.14 r2 (viii) 2 (l + b)

(ix) 0.1 y + 0.01 y2

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.

A coefficient is a number used to multiply a variable (2x means 2 times x, so 2 is a coefficient) Variables on their own (without a number next to them) actually have a coefficient of 1 (x is really 1x)

Sl.No.

Expression

Terms

Coefficients

(i)

5 – 3t2

– 3t2

-3

(ii)

1 + t + t2 + t3

t

t2

t3

1

1

1

(iii)

x + 2xy + 3y

x

2xy

3y

1

2

3

(iv)

100m + 1000n

100m

1000n

100

1000

(v)

– p2q2 + 7pq

-p2q2

7pq

-1

7

(vi)

1.2 a + 0.8 b

1.2a

0.8b

1.2

0.8

(vii)

3.14 r2

3.142

3.14

(viii)

2 (l + b)

2l

2b

2

2

(ix)

0.1 y + 0.01 y2

0.1y

0.01y2

0.1

0.01

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.

Expression

Terms

Coefficient of x

(i)

y2x + y

y2x

y2

(ii)

13y2 – 8yx

– 8yx

-8y

(iii)

x + y + 2

x

1

(iv)

5 + z + zx

x

zx

1

z

(v)

1 + x + xy

xy

y

(vi)

12xy2 + 25

12xy2

12y2

(vii)

7x + xy2

7x

xy2

7

y2

(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.

Expression

Terms

Coefficient of x

(i)

8 – xy2

– xy2

– x

(ii)

5y2 + 7x

5y2

5

(iii)

2x2y – 15xy2 + 7y2

– 15xy2

7y2

– 15x

7

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

8x2, – 11x2, – 6x2

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


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