MP Board Class 7th Maths Solutions Chapter 12 Algebraic Expressions Ex 12.1

MP Board Class 7th Maths Solutions Chapter 12 Algebraic Expressions Ex 12.1

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

Question 2.
(i) Identify the terms and their factors in the following expressions. Show the terms and factors by tree diagrams.
(a) x – 3
(b) 1 + x + x²
(c) y – y³
(d) 5xy² + 7x²y
(e) -ab + 2b² – 3a²

(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) 1.2ab – 2.4b + 3.6a
(g) \(\frac{3}{4}\)x + \(\frac{1}{4}\)
(h) 0.1p² + 0.2q²
Solution:
(i)

Question 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) 1.2a + 0.8b
(vii) 3.14 r²
(viii) 2(l + b)
(ix) 0.1y + 0.01y²
Solution:

Question 4.
(a) Identify terms which contains 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
(b) identify terms which contains y² and give the coefficient of y².
(i) 8 – xy²
(ii) 5y² + 7x
(iii) 2x²y – 15xy² + 7y²
Solution:
(a)

Question 5.
Classify into trinomials.
(i) 4y – 7z
(ii) y²
(iii) x + y – xy
(iv) 100
(v) ab – a – b
(vi) 5 – 3t
(vii) 4p²q – 4pq²
(viii) 7mn
(ix) z² – 3z + 8
(x) a² + b²
(xi) z² + z
(xii) 1 + x + x²
Solution:
The monomials, binomials and trinomials have 1, 2 and 3 unlike terms in it respectively.
(i) 4y – 7z Binomial
(ii) y² Monomial
(iii) x + y – xy Trinomial
(iv) 100 Monomial
(v) ab – a – b Trinomial
(vi) 5 – 3t Binomial
(vii) 4p²q – 4pq² Binomial
(viii) 7mn Monomial
(ix) z² – 3z + 8 Trinomial
(x) a² + b² Binomial
(xi) z² + z Binomial
(xii) 1 + x + x² Trinomial

Question 6.
State whether a given pair of terms is of like or unlike terms.
(i) 1,100
(ii) -7x, \(\frac{5}{2}\)x
(iii) -29x, -29y
(iv) 14xy, 42yx
(v) 4m²p, 4mp²
(vi) 12xz, 12x²z²
Solution:
The terms which have same algebraic factors are called like terms. However, when terms have different algebraic factors, these are called unlike terms.
(i) 1,100 Like
(ii) -7x, \(\frac{5}{2}\)x Like
(iii) -29x, -29y Unlike
(iv) 14xy, 42yx Like
(v) 4m²p, 4mp² Unlike
(vi) 12xz, 12x²z² Unlike

Question 7.
Identify like terms in the following:
(a) -xy², -4yx², 8x², 2xy², 7y, -11x², -100x, -11yx, 20x²y, -6x², y, 2xy, 3x
(b) 10pg, 7p, 8q, -p²q², -7qp, – 100q, -23, 12q²p², – 5p², 41, 2405p, 78qp, 13p²g, qp²,701p²
Solution:
(a) -xy² and 2xy²; -4yx² and 20x²y; 8x², -11x² and -6x²; 7y and y, -100x and 3x; -11yx and 2xy

(b) 10pq, -7qp and 78qp; 7p and 2405p; 8q and -100y; -p²q² and 12q²p², -23 and 41; -5p² and 701 p²; 13p2²q and qp²

MP Board Class 7th Maths Solutions