Class 7 Chapter 12 – Algebraic Expressions Ex 12.1

Maths NCERT Solutions For Class 7 Chapter 12 – Algebraic Expressions Ex 12.1

Simple solutions for NCERT Solutions for Class 7 Maths Algebraic Expressions Ex 12.1  are given here in the post. This NCERT Solutions for Class 7 Maths Exercise 12.1 contains topics related to the raw data collection and its organisation. so we definitely want students of Class 7 to solve Class 7 Algebraic Expressions Ex 12.1 to empower their basics and test the students capability of understanding the concepts. It also helps the students of CBSE Class 7 Maths students

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

(i) Subtraction of z from y.

Solution:-

= y – z

(ii) One-half of the sum of numbers x and y.

Solution:-

= ½ (x + y)

= ^{(x + y)}/₂

(iii) The number z multiplied by itself.

Solution:-

= z × z

= z²

(iv) One-fourth of the product of numbers p and q.

Solution:-

= ¼ (p × q)

= ^pq/₄

(v) Numbers x and y both squared and added.

Solution:-

= x² + y²

(vi) Number 5 added to three times the product of numbers m and n.

Solution:-

= 3mn + 5

(vii) Product of numbers y and z subtracted from 10.

Solution:-

= 10 – (y × z)

= 10 – yz

(viii) Sum of numbers a and b subtracted from their product.

Solution:-

= (a × b) – (a + b)

= ab – (a + b)

2. (i) Identify the terms and their factors in the following expressions

Show the terms and factors by tree diagrams.

(a) x – 3

Solution:-

Expression: x – 3

Terms: x, -3

Factors: x; -3

(b) 1 + x + x²

Solution:-

Expression: 1 + x + x²

Terms: 1, x, x²

Factors: 1; x; x,x

(c) y – y³

Solution:-

Expression: y – y³

Terms: y, -y³

Factors: y; -y, -y, -y

(d) 5xy² + 7x²y

Solution:-

Expression: 5xy² + 7x²y

Terms: 5xy², 7x²y

Factors: 5, x, y, y; 7, x, x, y

(e) – ab + 2b² – 3a²

Solution:-

Expression: -ab + 2b² – 3a²

Terms: -ab, 2b², -3a²

Factors: -a, b; 2, b, b; -3, a, a

(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) ¾ x + ¼

(h) 0.1 p² + 0.2 q²

Solution:-

Expressions is defined as, numbers, symbols and operators (such as +. – , × and ÷) grouped together that show the value of something.

In algebra a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or – signs or sometimes by division.

Factors is defined as, numbers we can multiply together to get another number.

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

Solution:-

4. (a) Identify terms which contain 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

Solution:-

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

(i) 8 – xy² (ii) 5y² + 7x (iii) 2x²y – 15xy² + 7y²

Solution:-

5. Classify into monomials, binomials and trinomials.

(i) 4y – 7z

Solution:-

Binomial.

(ii) y²

Solution:-

Monomial.

(iii) x + y – xy

Solution:-

Trinomial.

(iv) 100

Solution:-

Monomial.

(v) ab – a – b

Solution:-

Trinomial.

(vi) 5 – 3t

Solution:-

Binomial.

(vii) 4p²q – 4pq²

Solution:-

Binomial.

(viii) 7mn

Solution:-

Monomial.

(ix) z² – 3z + 8

Solution:-

Trinomial.

(x) a² + b²

Solution:-

Binomial.

(xi) z² + z

Solution:-

Binomial.

(xii) 1 + x + x²

Solution:-

Trinomial.

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

(i) 1, 100

Solution:-

Like term. 

(ii) –7x, (5/2)x

Solution:-

Like term.

(iii) – 29x, – 29y

Solution:-

Unlike terms.

(iv) 14xy, 42yx

Solution:-

Like term.

(v) 4m²p, 4mp²

Solution:-

Unlike terms.

(vi) 12xz, 12x²z²

Solution:-

Unlike terms.

7. Identify like terms in the following:

(a) – xy², – 4yx2, 8x², 2xy², 7y, – 11x², – 100x, – 11yx, 20x²y, – 6x², y, 2xy, 3x

Solution:-

When term have the same algebraic factors, they are like terms.

They are,

• – xy², 2xy²
• – 4yx², 20x²y
• 8x², – 11x², – 6x²
• 7y, y
• – 100x, 3x
• – 11yx, 2xy

(b) 10pq, 7p, 8q, – p²q², – 7qp, – 100q, – 23, 12q²p², – 5p²2, 41, 2405p, 78qp, 13p²q, qp², 701p²

Solution:-

When term have the same algebraic factors, they are like terms.

They are,

• 10pq, – 7qp, 78qp
• 7p, 2405p
• 8q, – 100q
• – p²q², 12q²p²
• - 23, 41
• – 5p², 701p²
• 13p²q, qp²