NCERT Solutions for Class 7 Maths Exercise 12.1

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NCERT solutions for Maths Algebraic Expressions Download as PDF

NCERT Solutions for Class 7 Maths Algebraic Expressions

Class –VII Mathematics (Ex. 12.1)

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

1. Subtraction of $z$ from $y.$
2. One-half of the sum of numbers $x$ and $y.$
3. The number $z$ multiplied by itself.
4. One-fourth of the product of numbers $p$ and $q.$
5. Numbers $x$ and $y$ both squared and added.
6. Number 5 added to three times the product of $m$ and $n.$
7. Product of numbers $y$ and $z$ subtracted from 10.
8. Sum of numbers $a$ and $b$ subtracted from their product.

Answer:

(i) $y – z$

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

(iii) ${z^2}$

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

(v) ${x^2} + {y^2}$

(vi) $3mn + 5$

(vii) $10 – yz$

(viii) $ab – \left( {a + b} \right)$

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NCERT Solutions for Class 7 Maths Exercise 12.1

Question 2.(i) Identify the terms and their factors in the following expressions, show the terms and factors by tree diagram:

(a) $x – 3$

(b) $1 + x + {x^2}$

(c) $y – {y^3}$

(d) $5x{y^2} + 7{x^2}y$

(e) $– ab + 2{b^2} – 3{a^2}$

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

(a) $– 4x + 5$

(b) $– 4x + 5y$

(c) $5y + 3{y^2}$

(d) $xy + 2{x^2}{y^2}$

(e) $pq + q$

(f) $1.2ab – 2.4b + 3.6a$

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

(h) $0.1{p^2} + 0.2{q^2}$

Answer:

(i) (a) $x – 3$

Expression

Terms

Factors

(b) $1 + x + {x^2}$

Expression

Terms

Factors

(c) $y – {y^3}$

Expression

Terms

Factors

(d) $5x{y^2} + 7{x^2}y$

Expression

Terms

Factors

(e) $– ab + 2{b^2} – 3{a^2}$

Expression

Terms

Factors –

(ii) (a) $– 4x + 5$

Terms: $– 4x,5$

Factors: $– 4,x{\text{ }};{\text{ }}5$

(b) $– 4x + 5y$

Terms: $– 4x,5y$

Factors: $– 4,x{\text{ }};{\text{ }}5,y$

(c) $5y + 3{y^2}$

Terms: $5y,3{y^2}$

Factors: $5,y{\text{ }};{\text{ }}3,y,y$

(d) $xy + 2{x^2}{y^2}$

Terms: $xy,2{x^2}{y^2}$

Factors: $x,y{\text{ }};{\text{ }}2x,x,y,y$

(e) $pq + q$

Terms: $pq,q$

Factors: $p,q{\text{ }};{\text{ }}q$

(f) $1.2ab – 2.4b + 3.6a$

Terms: $1.2ab, – 2.4b,3.6a$

Factors: $1.2,a,b{\text{ }};{\text{ }} – 2.4,b{\text{ }};{\text{ }}3.6,a$

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

Terms: $\frac{3}{4}x,\frac{1}{4}$

Factors: $\frac{3}{4},x{\text{ }};{\text{ }}\frac{1}{4}$

(h) $0.1{p^2} + 0.2{q^2}$

Terms: $0.1{p^2},0.2{q^2}$

Factors: $0.1,p,p{\text{ }};{\text{ }}0.2,q,q$

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NCERT Solutions for Class 7 Maths Exercise 12.1

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

(i)$5 – 3{t^2}$

(ii)$1 + t + {t^2} + {t^3}$

(iii)$x + 2xy + 3y$

(iv) $100m + 1000n$

(v)$– {p^2}{q^2} + 7pq$

(vi) $1.2a + 0.8b$

(vii) $3.14{r^2}$

(viii) $2\left( {l + b} \right)$

(ix) $0.1y + 0.01{y^2}$

Answer:

S.No.	Expression	Terms	Numerical Coefficient
(i)	$5 – 3{t^2}$	$– 3{t^2}$	$– 3$
(ii)	$1 + t + {t^2} + {t^3}$	$t$	1
		${t^2}$	1
		${t^3}$	1
(iii)	$x + 2xy + 3y$	$x$	1
		$2xy$	2
		$3y$	3
(iv)	$100m + 1000n$	$100m$	100
		$1000n$	1000
(v)	$– {p^2}{q^2} + 7pq$	$– {p^2}{q^2}$	$– 1$
		$7pq$	7
(vi)	$1.2a + 0.8b$	$1.2a$	1.2
		$0.8b$	0.8
(vii)	$3.14{r^2}$	$3.14{r^2}$	3.14
(viii)	$2\left( {l + b} \right) = 2l + 2b$	$2l$	2
		$2b$	2
(ix)	$0.1y + 0.01{y^2}$	$0.1y$	0.1
		$0.01{y^2}$	0.01

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NCERT Solutions for Class 7 Maths Exercise 12.1

Question 4.(a) Identify terms which contain $x$ and give the coefficient of $x.$

(i) ${y^2}x + y$

(ii) $13{y^2} – 8yx$

(iii) $x + y + 2$

(iv) $5 + z + zx$

(v) $1 + x + xy$

(vi) $12x{y^2} + 25$

(vii) $7x + x{y^2}$

(b) Identify terms which contain ${y^2}$ and give the coefficient of ${y^2}.$

(i) $8 – x{y^2}$

(ii) $5{y^2} + 7x$

(iii) $2{x^2}y – 15x{y^2} + 7{y^2}$

Answer:

(a)

S.No.	Expression	Term with factor $x$	Coefficient of $x$
(i)	${y^2}x + y$	${y^2}x$	${y^2}$
(ii)	$13{y^2} – 8yx$	$– 8yx$	$– 8y$
(iii)	$x + y + 2$	$x$	1
(iv)	$5 + z + zx$	$zx$	$z$
(v)	$1 + x + xy$	$x$	1
		$xy$	$y$
(vi)	$12x{y^2} + 25$	$12x{y^2}$	$12{y^2}$
(vii)	$7x + x{y^2}$	$x{y^2}$	${y^2}$
		$7x$	7

(b)

S.No.	Expression	Term contains ${y^2}$	Coefficient of ${y^2}$
(i)	$8 – x{y^2}$	$– x{y^2}$	$– x$
(ii)	$5{y^2} + 7x$	$5{y^2}$	5
(iii)	$2{x^2}y – 15x{y^2} + 7{y^2}$	$– 15x{y^2}$	$– 15x$
		$7{y^2}$	7

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NCERT Solutions for Class 7 Maths Exercise 12.1

Question 5.Classify into monomials, binomials and trinomials:

(i) $4y – 7x$

(ii) ${y^2}$

(iii) $x + y – xy$

(iv) $100$

(v) $ab – a – b$

(vi) $5 – 3t$

(vii) $4{p^2}q – 4p{q^2}$

(viii) $7mn$

(ix) ${z^2} – 3z + 8$

(x) ${a^2} + {b^2}$

(xi) ${z^2} + z$

(xii) $1 + x + {x^2}$

Answer:

S.No.	Expression	Type of Polynomial
(i)	$4y – 7z$	Binomial
(ii)	${y^2}$	Monomial
(iii)	$x + y – xy$	Trinomial
(iv)	100	Monomial
(v)	$ab – a – b$	Trinomial
(vi)	$5 – 3t$	Binomial
(vii)	$4{p^2}q – 4p{q^2}$	Binomial
(viii)	$7mn$	Monomial
(ix)	${z^2} – 3z + 8$	Trinomial
(x)	${a^2} + {b^2}$	Binomial
(xi)	${z^2} + z$	Binomial
(xii)	$1 + x + {x^2}$	Trinomial

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NCERT Solutions for Class 7 Maths Exercise 12.1

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

(i)$1,{\text{ }}100$

(ii)$– 7x,\frac{5}{2}x$

(iii)$– 29x, – 29y$

(iv) $14xy,42yx$

(v) $4{m^2}p,4m{p^2}$

(vi) $12xz,12{x^2}{z^2}$

Answer:

S.No.	Pair of terms	Like / Unlike terms
(i)	1, 100	Like terms
(ii)	$– 7x,\frac{5}{2}x$	Like terms
(iii)	$– 29x, – 29y$	Unlike terms
(iv)	$14xy,42yx$	Like terms
(v)	$4{m^2}p,4m{p^2}$	Unlike terms
(vi)	$12xz,12{x^2}{z^2}$	Unlike terms

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NCERT Solutions for Class 7 Maths Exercise 12.1

Question 7.Identify like terms in the following:

(a) $– x{y^2}, – 4y{x^2},8{x^2},2x{y^2},7y, – 11{x^2} – 100x, – 11yx,20{x^2}y, – 6{x^2},y,2xy,3x$

(b)$10pq,7p,8q, – {p^2}{q^2}, – 7qp, – 100q, – 23,12{q^2}{p^2}, – 5{p^2},41,2405p,78qp,13{p^2}q,q{p^2},701{p^2}$

Answer:

(a) Like terms are:

(i) $– x{y^2},2x{y^2}$

(ii) $– 4y{x^2},20{x^2}y$

(iii) $8{x^2}, – 11{x^2}, – 6{x^2}$

(iv) $7y,y$

(v) $– 100x,3x$

(vi) $– 11yx,2xy$

(b) Like terms are:

(i) $10pq, – 7pq,78pq$

(ii) $7p,2405p$

(iii) $8q, – 100q$

(iv) $– {p^2}{q^2},12{p^2}{q^2}$

(v) $– 12,41$

(vi) $– 5{p^2},701{p^2}$

(vii) $13{p^2}q,q{p^2}$

NCERT Solutions for Class 7 Maths Exercise 12.1

NCERT Solutions Class 7 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 7 Maths includes text book solutions from Class 7 Maths Book . NCERT Solutions for CBSE Class 7 Maths have total 15 chapters. 7 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 7 solutions PDF and Maths ncert class 7 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.

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