{"id":26839,"date":"2021-06-28T17:03:46","date_gmt":"2021-06-28T11:33:46","guid":{"rendered":"https:\/\/ncertsolutions.guru\/?p=26839"},"modified":"2021-06-28T17:03:46","modified_gmt":"2021-06-28T11:33:46","slug":"ncert-solutions-for-class-7-maths-chapter-12-ex-12-1","status":"publish","type":"post","link":"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-7-maths-chapter-12-ex-12-1\/","title":{"rendered":"NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1"},"content":{"rendered":"

These NCERT Solutions for Class 7 Maths<\/a> Chapter 12 Algebraic Expressions Ex 12.1 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Exercise 12.1<\/h2>\n

Question 1.
\nGet the algebraic expressions in the following cases using variables, constants and arithmetic operations.
\n(i) Subtraction of z from y.
\n(ii) One-half of the sum of numbers x and y.
\n(iii) The number z multiplied by itself.
\n(iv) One-fourth of the product of numbers p and q.
\n(v) Numbers x and y both squared and added.
\n(vi) Number 5 added to three times the product of number m and n.
\n(vii) Product of numbers y and z subtracted from 10.
\n(viii) Sum of numbers a and b subtracted from their product.
\nAnswer:
\n(i) y – z
\n(ii) \\(\\frac { 1 }{ 2 }\\)(x + y)
\n(iii) z2<\/sup>
\n(iv) \\(\\frac { 1 }{ 4 }\\)pq
\n(v) x2<\/sup> + y2<\/sup>
\n(vi) 5 + 3mn
\n(vii) 10 – yz
\n(viii) ab – (a + b)<\/p>\n

\"NCERT<\/p>\n

Question 2.
\n(i) Identify the terms and their factors in the following expressions. Show the terms and factors by tree diagrams.
\n(a) x – 3
\n(b) 1 + x + x2<\/sup>
\n(c) y – y3<\/sup>
\n(d) 5xy2<\/sup> + 7x2<\/sup>y
\n(e) – ab + 2b2<\/sup> – 3a2<\/sup><\/p>\n

(ii) Identify terms and factors in the expressions given below:
\n(a) – 4x + 5
\n(b) – 4x + 5y
\n(c) 5y + 3y2<\/sup>
\n(d) xy + 2x2<\/sup>y2<\/sup>
\n(e) pq + q
\n(f) 1.2ab- 2.4 b + 3.6a
\n(g) \\(\\frac { 3 }{ 4 }\\)x + \\(\\frac { 1 }{ 4 }\\)
\n(h) 0.1p2<\/sup> + 0.2p2<\/sup>
\nAnswer:
\n(i) (a) x – 3
\nTerms : x; – 3 Factors x; -3
\n1 + x + x2<\/sup>
\n\"NCERT<\/p>\n

(b) 1 + x + x2<\/sup>
\nTerms = 1; x; x2<\/sup>
\nFactors = 1; x; x, x (x2<\/sup> )
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

(c) y-y3<\/sup>
\nTerms: y; -y3<\/sup>
\nFactors y;-1,y,y,y
\n\"NCERT<\/p>\n

(d) 5xy2<\/sup> + 7x2<\/sup> y
\nTerms: 5xy2<\/sup>; 7x2<\/sup> y
\nFactors: 5, x, y, y; 7, x, x, y
\n\"NCERT<\/p>\n

(e) -ab + 2b2<\/sup> – 3a2<\/sup>
\nTerms: -ab; 2b2<\/sup>, -3a2<\/sup>
\nFactors: -1, a, b; 2; b; b; 3, a, a
\n\"NCERT<\/p>\n

(ii)<\/p>\n\n\n\n\n\n\n\n\n\n\n\n
Expression<\/td>\nTerms<\/td>\nFactors<\/td>\n<\/tr>\n
(a) -4x + 5<\/td>\n-4x
\n5<\/td>\n		-4x and z
\n5 and y<\/td>\n<\/tr>\n
(b) – 4x + 5y<\/td>\n-4x
\n5y<\/td>\n		– 4 and z
\n5 and y<\/td>\n<\/tr>\n
(c) 5y + 3y2<\/sup><\/td>\n5y
\n3y2<\/sup><\/td>\n		5 and y
\n3, y and y<\/td>\n<\/tr>\n
(d) xy + 2x2<\/sup> y2<\/sup><\/td>\nXy
\n2x2<\/sup>y2<\/sup><\/td>\n		x and y
\n2, x.x, y and y<\/td>\n<\/tr>\n
(e) pq + q<\/td>\nPq
\nq<\/td>\n		p and q
\nq<\/td>\n<\/tr>\n
(f) 1.2ab – 2.4 b + 3.6a<\/td>\n1.2ab
\n– 2.4 b
\n3.6a<\/td>\n		1.2, a and b.
\n-2.4 and b
\n3.6 and a<\/td>\n<\/tr>\n
(g) \\(\\frac{3}{4}\\)x + \\(\\frac{1}{4}\\)<\/td>\n\\(\\frac{3}{4}\\)x
\n\\(\\frac{1}{4}\\)<\/td>\n		\\(\\frac{3}{4}\\) and x
\n\\(\\frac{1}{4}\\)<\/td>\n<\/tr>\n
(h) 0.lp2<\/sup> + 0.2q2<\/sup><\/td>\n0.1p2<\/sup>
\n0.2q2<\/sup><\/td>\n		0.1, p,p
\n0.2, q and q<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Question 3.
\nIdentify the numerical coefficients of terms (other than constants) in the following expressions:
\n(i) 5 – 3t2<\/sup>
\n(ii) 1 + t + t2<\/sup> + t3<\/sup>
\n(iii) x + 2xy + 3y
\n(iv) 100m + 1000n
\n(v) -p2<\/sup>q2<\/sup> + 7pq
\n(vi) 1.2a + 0.8b
\n(vii) 3.14r2<\/sup>
\n(viii) 2(l + b)
\n(ix) 0.1y + 0.01y2<\/sup>
\nAnswer:<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n
Expression<\/td>\nTerms (other than constant)<\/td>\nNumerical coefficient<\/td>\n<\/tr>\n
(i) 5 – 3t2<\/sup><\/td>\n– 3t2<\/sup><\/td>\n-3<\/td>\n<\/tr>\n
(ii) 1 + t + t2<\/sup> + t3<\/sup><\/td>\nt
\nt2
\n<\/sup>t3<\/sup><\/td>\n		1
\n1
\n1<\/td>\n<\/tr>\n
(iii) x + 2xy + 3y<\/td>\nx
\n2xy
\n3y<\/td>\n		1
\n2
\n3<\/td>\n<\/tr>\n
(iv) 100 m + lOOOn<\/td>\n100m
\n1000n<\/td>\n		100
\n1000<\/td>\n<\/tr>\n
(v) -p2<\/sup>q2<\/sup> + 7pq<\/td>\n-p2<\/sup>q2<\/sup>
\n7pq<\/td>\n		-1
\n7<\/td>\n<\/tr>\n
(vi) 1.2a + 0.8b<\/td>\n1.2a
\n0.8b<\/td>\n		1.2
\n0.8<\/td>\n<\/tr>\n
(vii) 3.14r2<\/sup><\/td>\n3.14r2<\/sup><\/td>\n3.14<\/td>\n<\/tr>\n
(viii) 2(l + b)<\/td>\n2l
\n2b<\/td>\n		2
\n2<\/td>\n<\/tr>\n
(ix) 0.1y + 0.01y2<\/sup><\/td>\n0.1y
\n0.01y2<\/sup><\/td>\n		0.1
\n0.01<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"NCERT<\/p>\n

Question 4.
\n(a) Identify terms which contain x and give the coefficient of x.
\n(i) y2<\/sup>x + y
\n(ii) 13y2<\/sup> – 8yx
\n(iii) x + y + 2
\n(iv) 5 + z + zx
\n(iv) 1+x + xy
\n(vi) 12xy2<\/sup> + 25
\n(vii) 7x + xy2<\/sup><\/p>\n

(b) Identify terms which contain y2<\/sup> and give the coefficient of y2<\/sup>.
\n(i) 8-xy2<\/sup>
\n(ii) 5y2<\/sup> + 7x
\n(iii) 2x2<\/sup>y – 15xy2<\/sup> + 7y2<\/sup>
\nAnswer:<\/p>\n\n\n\n\n\n\n\n\n\n\n
Expression<\/td>\nTerm containing x<\/td>\nCoefficient of x<\/td>\n<\/tr>\n
(i) y2<\/sup>x + y<\/td>\ny2<\/sup>x<\/td>\ny2<\/sup><\/td>\n<\/tr>\n
(ii) x + y + 2<\/td>\n– 8yx<\/td>\n– 8y<\/td>\n<\/tr>\n
(iii) 5 + z + zx<\/td>\nx<\/td>\nl<\/td>\n<\/tr>\n
(iv) 5 + z + zx<\/td>\nzx<\/td>\nZ<\/td>\n<\/tr>\n
(v) 1 + x + xy<\/td>\nx
\nxy<\/td>\n		1
\ny<\/td>\n<\/tr>\n
(vi) 12xy2<\/sup>+ 25<\/td>\n12xy2<\/sup><\/td>\n12y2<\/sup><\/td>\n<\/tr>\n
(vii) 7x + xy2<\/sup><\/td>\n7x
\nxy2<\/sup><\/td>\n		7
\ny2<\/sup><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

(b)<\/p>\n\n\n\n\n\n\n
Expression<\/td>\nTerm containing y2<\/sup><\/td>\nCoefficient of y2<\/sup><\/td>\n<\/tr>\n
(i) 8 – xy2<\/sup><\/td>\n-xy2<\/sup><\/td>\n-X<\/td>\n<\/tr>\n
(ii) 5y2<\/sup> + 7x<\/td>\n5y2<\/sup><\/td>\n5<\/td>\n<\/tr>\n
(iii) 2x2<\/sup>y – 15xy2<\/sup> + 7y2<\/sup><\/td>\n– 15xy2 <\/sup>7f<\/td>\n– 15x 7<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Question 5.
\nClassify into monomials, binomials and trinomials.
\n(i) 4y – 7z
\n(ii) y2<\/sup>
\n(iii) x + y – xy
\n(iv) 100
\n(v) ab – a – b
\n(vi) 5 – 3t
\n(vii) 4p2<\/sup>q – 4pq2<\/sup>
\n(viii) 7mn
\n(ix) z2<\/sup> – 3z + 8
\n(x) a2<\/sup> + b2<\/sup>
\n(xi) z2<\/sup> + z
\n(xii) 1 + x + x2<\/sup>
\nAnswer:
\n(i) 4y – 7z
\nThe expression 4y – 7z is having two unlike terms (4y and – 7z)
\n\u2234 It is a binomial.<\/p>\n

\"NCERT<\/p>\n

(ii) y2<\/sup>
\nThe expression y2<\/sup> is having only one term (y2<\/sup>)
\n\u2234 It is a monomial.<\/p>\n

(iii) x + y – xy
\nThe expression x + y – xy is having three terms (x, y and – xy)
\n\u2234 It is a trinomial.<\/p>\n

(iv) 100
\nThe expression 100 is having only one term (100)
\n\u2234 It is a monomial.<\/p>\n

(v) ab – a – b.
\nThe expression ab – a – b is having three terms (ab, -a, and -b)
\n\u2234 The expression is a trinomial.<\/p>\n

(vi) 5 – 3t
\nThe expression 5 – 3t is having two terms (5 and -3t)
\n\u2234 It is a binomial expression.<\/p>\n

(vii) 4p2<\/sup>q – 4pq2<\/sup>
\nThe expression 4p2<\/sup>q – 4pq2<\/sup> is having
\ntwo unlike terms (4p2<\/sup>q and – 4pq2<\/sup>)
\n\u2234 The expression is a binomial.<\/p>\n

(viii) 7mn
\nThe expression 7mn is having only one term (ie 7mn)
\n\u2234 The expression is a monomial.<\/p>\n

(ix) z2<\/sup>– 3z + 8
\nThe expression z2<\/sup> – 3z + 8 is having three terms (ie z2<\/sup>, – 3z and 8)
\n\u2234 The expression is a trinomial.<\/p>\n

\"NCERT<\/p>\n

(x) a2<\/sup> + b2<\/sup>
\nThe expression (a2<\/sup> + b2<\/sup>) is having two unlike terms (a2<\/sup> and b2<\/sup>)
\n\u2234 It is a binomial expression.<\/p>\n

(xi) z2<\/sup> + z
\nThe expression z2<\/sup> + z is having two unlike terms (z2 and z)
\n\u2234 The expression in binomial.<\/p>\n

(xii) 1 + x + x2<\/sup>
\nThe expression 1 + x + x2<\/sup> is having three terms (1, x and x2<\/sup>)
\n\u2234 The expression is a trinomial.<\/p>\n

Question 6.
\nState whether a given pair of terms is of like or unlike terms.
\n(i) 1, 100
\n(ii) -7x, \\(\\frac { 5 }{ 2 }\\)x
\n(iii) -29x, -29y
\n(iv) 14xy, 42yx
\n(v) 4m2<\/sup>p, 4mp2<\/sup>
\n(vi) 12xz, 12x2<\/sup>z2<\/sup>
\nAnswer:
\n(i) 1, 100 is a pair of like terms.
\n(ii) \\(\\frac { 5 }{ 2 }\\)x is a pair of like terms.
\n(iii) – 29x, – 29y is a pair of unlike terms.
\n(iv) 14xy, 42<\/sup>yx is a pair of like terms.
\n(v) 4m2<\/sup>p, 4mp2<\/sup> is a pair of unlike terms.
\n(vi) 12xz; 12x2<\/sup>z2<\/sup> is a pair of unlike terms.<\/p>\n

\"NCERT<\/p>\n

Question 7.
\nIdentify like terms in the following:
\n(a) -xy2<\/sup>, – 4yx2<\/sup>, 8x2<\/sup>, 2xy2<\/sup>, 7y, -11x2<\/sup>, 100x, -11yx, 20x2<\/sup>y, – 6x2<\/sup>, y, 2xy, 3x
\n(b) 10pq, 7p, 8q, – p2<\/sup>q2<\/sup>, -7pq, -100q, -23, 12q2<\/sup>p2<\/sup>, -5p2<\/sup>, 41, 2405p, 78qp,
\n13p2<\/sup>q, qp2<\/sup>,701p2<\/sup>
\nAnswer:
\n(a) -xy2<\/sup> and 2xy2<\/sup>, – 4yx2<\/sup> and 20x2<\/sup> y, 8x2<\/sup>, -11x2<\/sup> and – 6x2<\/sup>; 7y and y; lOOx and 3x; -1 lyx and 2xy are like terms.
\n(b) 10pq, – 7pq and 78qp.
\n7p and 2405p; 8q and 100q; – p2<\/sup>q2<\/sup> and 12q2<\/sup>p2<\/sup>; – 23 and 41; – 5p2<\/sup> and 701p2<\/sup>; 13p2<\/sup>q and qp2<\/sup> are like terms.<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Exercise 12.1 Question 1. Get the algebraic expressions in the following cases using variables, constants and arithmetic operations. (i) Subtraction of …<\/p>\n

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NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Exercise 12.1 Question 1. Get the algebraic expressions in the following cases using variables, constants and arithmetic operations. 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