## Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions (Including Evaluation)

**Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions (Including Evaluation)**

### Framing Algebraic Expressions Exercise 21 – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.

Write in the form of an algebraic expression :

(i) Perimeter (P) of a rectangle is two times the sum of its length (l) and its breadth (b).

(ii) Perimeter (P) of a square is four times its side.

(iii) Area of a square is square of its side.

(iv) Surface area of a cube is six times the square of its edge.

Solution:

Question 2.

Express each of the following as an algebraic expression :

(i) The sum of x and y minus m.

(ii) The product of x and y divided by m.

(iii) The subtraction of 5m from 3n and then adding 9p to it.

(iv) The product of 12, x, y and z minus the product of 5, m and n.

(v) Sum of p and 2r – s minus sum of a and 3n + 4x.

Solution:

Question 3.

Construct a formula for the following :

Total wages (₹ W) of a man whose basic wage is (₹ B) for t hours week plus (₹ R) per hour, if he Works a total of T hours.

Solution:

Question 4.

If x = 4, evaluate :

(i) 3x + 8

(ii) x^{2} – 2x

(iii) \(\frac { { x }^{ 2 } }{ 2 }\)

Solution:

Question 5.

If m – 6, evaluate :

(i) 5m – 6

(ii) 2m^{2} + 3m

(iii) (2m)^{2}

Solution:

Question 6.

If x = 4, evaluate :

(i) 12x + 7

(ii) 5x^{2} + 4x

(iii) \(\frac { { x }^{ 2 } }{ 8 }\)

Solution:

Question 7.

If m = 2, evaluate :

(i) 16m – 7

(ii) 15m^{2} – 10m

(iii) \(\frac { 1 }{ 4 } \times { m }^{ 3 }\)

Solution:

Question 8.

If x = 10, evaluate :

(i) 100x + 225

(ii) 6x^{2} – 25x

(iii) \(\frac { 1 }{ 50 } \times { x }^{ 3 }\)

Solution:

Question 9.

If a = – 10, evaluate :

(i) 5a

(ii) a^{2}

(iii) a^{3}

Solution:

Question 10.

If x = – 6, evaluate :

(i) 11x

(ii) 4x^{2}

(iii) 2x^{3}

Solution:

Question 11.

If m = – 7, evaluate :

(i) 12m

(ii) 2m^{2}

(iii) 2m^{3}

Solution:

Question 12.

Find the average (A) of four quantities p, q, r and s. If A = 6, p = 3, q = 5 and r = 7 ; find the value of s.

Solution:

Question 13.

If a = 5 and b = 6, evaluate :

(i) 3ab

(ii) 6a^{2}b

(iii) 2b^{2}

Solution:

Question 14.

If x = 8 and y = 2, evaluate :

(i) 9xy

(ii) 5x^{2}y

(iii) (4y)^{2}

Solution:

Question 15.

If x = 5 and y = 4, evaluate :

(i) 8xy

(ii) 3x^{2}y

(iii) 3y^{2}

Solution:

Question 16.

If y = 5 and z = 2, evaluate :

(i) 100yz

(ii) 9y^{2}z

(iii) 5y^{2}

(iv) (5z)^{3}

Solution:

Question 17.

If x = 2 and y = 10, evaluate :

(i) 30xy

(ii) 50xy^{2}

(iii) (10x)^{2}

(iv) 5y^{2}

Solution:

Question 18.

If m = 3 and n = 7, evaluate :

(i) 12mn

(ii) 5mn^{2}

(iii) (10m)^{2}

(iv) 4n^{2}

Solution:

Question 19.

If a = -10, evaluate :

(i) 3a – 2

(ii) a^{2} + 8a

(iii) \(\frac { 1 }{ 5 }\) x a^{2}

Solution:

Question 20.

If x = -6, evaluate :

(i) 4x – 9

(ii) 3x^{2} + 8x

(iii) \(\frac { { x }^{ 2 } }{ 2 }\)

Solution:

Question 21.

If m = -8, evaluate :

(i) 2m + 21

(ii) m^{2} + 9m

(iii) \(\frac { { m }^{ 2 } }{ 4 }\)

Solution:

Question 22.

If p = -10, evaluate :

(i) 6p + 50

(ii) 3p^{2} – 20p

(iii) \(\frac { { p }^{ 2 } }{ 50 }\)

Solution:

Question 23.

If y = -8, evaluate :

(i) 6y + 53

(ii) y^{2 }+ 12y

(iii) \(\frac { { y }^{ 3 } }{ 4 }\)

Solution:

Question 24.

If x = 2 and 7 = -4, evaluate :

(i) 11xy

(ii) 5x^{2}y

(iii) (5y)^{2}

(iv) 8x^{2}

Solution:

Question 25.

If m = 9 and n = -2, evaluate

(i) 4mn

(ii) 2m^{2}n

(iii) (2n)^{3}

Solution:

Question 26.

If m = -8 and n = -2, evaluate :

(i) 12mn

(ii) 3m^{2}n

(iii) (4n)^{2}

Solution:

Question 27.

If x = -5 and y = -8, evaluate :

(i) 4xy

(ii) 2xy^{2}

(iii) 4x^{2}

(iv) 3y^{2}

Solution:

Question 28.

Find T, if T = 2a – b, a = 7 and b = 3.

Solution:

Question 29.

From the formula B = 2a^{2} – b^{2}, calculate the value of B when a = 3 and b = -1.

Solution:

Question 30.

The wages ₹ W of a man earning ₹ x per hour for t hours are given by the formula W = xt. Find his wages for working 40 hours at a rate of ₹ 39.45 per hour.

Solution:

Question 31.

The temperature in Fahrenheit scale is represented by F and the tempera¬ture in Celsius scale is represented by C. If F = \(\frac { 9 }{ 5 }\) x C + 32, find F when C = 40.

Solution: