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

Answer:

(i) {tex}y – z{/tex}

(ii) {tex}\frac{{x + y}}{2}{/tex}

(iii) {tex}{z^2}{/tex}

(iv) {tex}\frac{{pq}}{4}{/tex}

(v) {tex}{x^2} + {y^2}{/tex}

(vi) {tex}3mn + 5{/tex}

(vii) {tex}10 – yz{/tex}

(viii) {tex}ab – \left( {a + b} \right){/tex}

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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) {tex}x – 3{/tex}

(b) {tex}1 + x + {x^2}{/tex}

(c) {tex}y – {y^3}{/tex}

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

(e) {tex} – ab + 2{b^2} – 3{a^2}{/tex}

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

(a) {tex} – 4x + 5{/tex}

(b) {tex} – 4x + 5y{/tex}

(c) {tex}5y + 3{y^2}{/tex}

(d) {tex}xy + 2{x^2}{y^2}{/tex}

(e) {tex}pq + q{/tex}

(f) {tex}1.2ab – 2.4b + 3.6a{/tex}

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

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

Answer:

(i) (a) {tex}x – 3{/tex}

Expression

Terms

Factors

(b) {tex}1 + x + {x^2}{/tex}

Expression

Terms

Factors

(c) {tex}y – {y^3}{/tex}

Expression

Terms

Factors

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

Expression

Terms

Factors

(e) {tex} – ab + 2{b^2} – 3{a^2}{/tex}

Expression

Terms

Factors –

(ii) (a) {tex} – 4x + 5{/tex}

Terms: {tex} – 4x,5{/tex}

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

(b) {tex} – 4x + 5y{/tex}

Terms: {tex} – 4x,5y{/tex}

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

(c) {tex}5y + 3{y^2}{/tex}

Terms: {tex}5y,3{y^2}{/tex}

Factors: {tex}5,y{\text{ }};{\text{ }}3,y,y{/tex}

(d) {tex}xy + 2{x^2}{y^2}{/tex}

Terms: {tex}xy,2{x^2}{y^2}{/tex}

Factors: {tex}x,y{\text{ }};{\text{ }}2x,x,y,y{/tex}

(e) {tex}pq + q{/tex}

Terms: {tex}pq,q{/tex}

Factors: {tex}p,q{\text{ }};{\text{ }}q{/tex}

(f) {tex}1.2ab – 2.4b + 3.6a{/tex}

Terms: {tex}1.2ab, – 2.4b,3.6a{/tex}

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

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

Terms: {tex}\frac{3}{4}x,\frac{1}{4}{/tex}

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

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

Terms: {tex}0.1{p^2},0.2{q^2}{/tex}

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

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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){tex}5 – 3{t^2}{/tex}

(ii){tex}1 + t + {t^2} + {t^3}{/tex}

(iii){tex}x + 2xy + 3y{/tex}

(iv) {tex}100m + 1000n{/tex}

(v){tex} – {p^2}{q^2} + 7pq{/tex}

(vi) {tex}1.2a + 0.8b{/tex}

(vii) {tex}3.14{r^2}{/tex}

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

(ix) {tex}0.1y + 0.01{y^2}{/tex}

Answer:

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

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NCERT Solutions for Class 7 Maths Exercise 12.1

Question 4.(a) Identify terms which contain {tex}x{/tex} and give the coefficient of {tex}x.{/tex}

(i) {tex}{y^2}x + y{/tex}

(ii) {tex}13{y^2} – 8yx{/tex}

(iii) {tex}x + y + 2{/tex}

(iv) {tex}5 + z + zx{/tex}

(v) {tex}1 + x + xy{/tex}

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

(vii) {tex}7x + x{y^2}{/tex}

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

(i) {tex}8 – x{y^2}{/tex}

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

(iii) {tex}2{x^2}y – 15x{y^2} + 7{y^2}{/tex}

Answer:

(a)

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

(b)

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

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NCERT Solutions for Class 7 Maths Exercise 12.1

Question 5.Classify into monomials, binomials and trinomials:

(i) {tex}4y – 7x{/tex}

(ii) {tex}{y^2}{/tex}

(iii) {tex}x + y – xy{/tex}

(iv) {tex}100{/tex}

(v) {tex}ab – a – b{/tex}

(vi) {tex}5 – 3t{/tex}

(vii) {tex}4{p^2}q – 4p{q^2}{/tex}

(viii) {tex}7mn{/tex}

(ix) {tex}{z^2} – 3z + 8{/tex}

(x) {tex}{a^2} + {b^2}{/tex}

(xi) {tex}{z^2} + z{/tex}

(xii) {tex}1 + x + {x^2}{/tex}

Answer:

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

(ii){tex} – 7x,\frac{5}{2}x{/tex}

(iii){tex} – 29x, – 29y{/tex}

(iv) {tex}14xy,42yx{/tex}

(v) {tex}4{m^2}p,4m{p^2}{/tex}

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

Answer:

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

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NCERT Solutions for Class 7 Maths Exercise 12.1

Question 7.Identify like terms in the following:

(a) {tex} – 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{/tex}

(b){tex}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}{/tex}

Answer:

(a) Like terms are:

(i) {tex} – x{y^2},2x{y^2}{/tex}

(ii) {tex} – 4y{x^2},20{x^2}y{/tex}

(iii) {tex}8{x^2}, – 11{x^2}, – 6{x^2}{/tex}

(iv) {tex}7y,y{/tex}

(v) {tex} – 100x,3x{/tex}

(vi) {tex} – 11yx,2xy{/tex}

(b) Like terms are:

(i) {tex}10pq, – 7pq,78pq{/tex}

(ii) {tex}7p,2405p{/tex}

(iii) {tex}8q, – 100q{/tex}

(iv) {tex} – {p^2}{q^2},12{p^2}{q^2}{/tex}

(v) {tex} – 12,41{/tex}

(vi) {tex} – 5{p^2},701{p^2}{/tex}

(vii) {tex}13{p^2}q,q{p^2}{/tex}

NCERT Solutions for Class 7 Maths Exercise 12.1

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