NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1

NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1, are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1.

NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions 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 numbers m and n.
7. Product of numbers y and z subtracted from 10.
8. Sum of numbers a and b subtracted from their product.

Solution:

1. y – z
2. \(\frac { 1 }{ 2 } \) ( x + y )
3. z²
4. \(\frac { 1 }{ 4 } \) pq
5. x² + y²
6. 3mn + 5
7. 10 – yz
8. 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) 1.2 ab -2.4 b + 3.6 a
(g) \(\frac { 3 }{ 4 } \) x + \(\frac { 1 }{ 4 } \)
(h) 0.1 p² + 0.2 q²

Solution:

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

1. 5 – 3t²
2. 1 + t + t² + t³
3. x + 2xy + 3y
4. 100m + 1000n
5. -p²q² + 7pq
6. 1.2 a + 0.8 b
7. 3.14 r²
8. 2 (l + b)
9. 0.1 y + 0.01 y².

Solution:

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

1. y²x + y
2. 13y² – 8yx
3. x + y + 2
4. 5 + z + zx
5. 1 + x + xy
6. 12xy² + 25
7. 7x + xy².

(b) Identify terms which contain y² and give the coefficient of y².

1. 8 – xy²
2. 5y² + 7x
3. 2x²y – 15xy² + 7y²

Solution:

Question 5.
Classify into monomials, binomials and trinomials.

1. 4y – 7z
2. y²
3. x + y – xy
4. 100
5. ab – a – b
6. 5 – 3t
7. 4p²q – 4pq²
8. 7mn
9. z² – 3z + 8 a² + b²
10. z² + z
11. 1 + x+ x²

Solution:
(i) 4y – 7z.
This expression is a binomial because it contains two terms : 4y and – Iz.
(ii) y².
This expression is a monomial because it contains only one term : y²
(iii) x + y – xy.
This expression is a trinomial because it contains three terms : x, y and – xy.
(iv) 100.
This expression is a monomial because it contains only one term : 100
(v) ab – a – b.
This expression is a trinomial because it contains three terms : ab,-a and -b
(vi) 5 – 3t.
This expression is a binomial because it contains two terms : 5 and – 31.
(vii) 4p²q – 4pq².
This expression is a binomial because it contains two terms: 4p²q and – 4pq².
(viii) 7mn.
This expression is a monomial because it contains only one term : 7mn.
(ix) z² – 3z + 8.
This expression is a trinomial because it contains three terms : z², – 3z and 8.
(x) a² + b².
This expression is a binomial because it contains two terms : a² and b².
(xi) z² + z.
This expression is a binomial because it contains two terms : z² and z.
(xii) 1 + x + x².
This expression is a trinomial because j it contains three terms : 1, x and x².

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

1. 1,100
2. -7x, \(\frac { 5 }{ 2 } \) x
3. -29 x, -29 y
4. 14 xy, 42 yx
5. 4m²p, 4mp²
6. 12xz, 12x² z².

Solution:

1. Like
2. Like
3. Unlike
4. Like
5. Unlike
6. Unlike

Question 7.
Identify like terms in the following :

Solution:

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