Framing Algebraic Expressions ICSE Class-6th Concise Mathematics Selina Solutions Chapter-21 (Including Evaluation). We provide step by step Solutions of Exercise / lesson-21 Framing Algebraic Expressions  (Including Evaluation) for ICSE Class-6 Concise Selina Mathematics. Our Solutions contain all type Questions to develop skill and confidence. Visit official Website for detail information about ICSE Board Class-6 .

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

### Exercise – 21

Framing Algebraic Expressions ICSE Class-6th

Concise Mathematics Selina Solutions Chapter-21 (Including Evaluation)

#### 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.

(i) Let P be the perimeter and / be the length, and b be the breadth.
P = 2 (l + b)
(ii) Let P be the perimeter and a be the side of the square.
P = 4a
(iii) Let A be the area of the square and a be the sides of the square.
A = (a)2
(iv) Let S be the surface area and a be the edges of the cube.
S = 6a2

#### 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.

i) x + y – m
(ii)  xym
(iii) 3n – 5m + 9p
(iv) 12xyz – 5mn
(v) p + 2r – s – (a + 3n + 4x)

#### 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.

Wages for t hours = ₹ B
Wages for overtime = R(T – t)
=> Total wages = Wages for t hours + wages for overtime of (T – t) hours
=> ₹ W = ₹ B + ₹ R (T – t)

#### Question- 4.

If x = 4, evaluate :
(i) 3x + 8
(ii) x2 – 2x
(iii) m

(i) 3x + 8

= (3 × 4) + 8

= 12 + 8

= 20

(ii) x2 – 2x

= (4)2 − 2(4)

= (4 × 4) − (2 × 4)

= 16 − 8

= 8

(iii) m

=

= 4 x 42

= 162

= 8

Question 5.

If m – 6, evaluate :

(i) 5m – 6
(ii) 2m2 + 3m
(iii) (2m)2

(i) 5m − 6

= (5 × 6) − 6

= 36 − 6

= 30

(ii) 2m2 + 3m

= 2 (6)2 + 3 (6)

= 2 × 6 × 6 + 3 × 6

= 72 + 18

= 90

(iii)  (2m)2

= (2 × m) × (2 × m)

= (2 × 6) × (2 × 6)

= 12 × 12

= 144

Question -6.

If x = 4, evaluate :

(i) 12x + 7
(ii) 5x2 + 4x
(iii) 8

(i) 12x + 7

= (12 × 4) + 7

= 48 + 7

= 55

(ii) 5x2 + 4x

= (5 × 4 × 4) + 4 (4)

= 80 + 16

= 96

(iii) 8

#### Question- 7.

If m = 2, evaluate :
(i) 16m – 7
(ii) 15m2 – 10m
(iii) …14..m³………

(i) 16m – 7

= (16 × 2) – 7

= 32 – 7

= 25

(ii) 15m2 – 10m

= 15 (2)2 − 10(2)

= (15 × 2 × 2) − (10 × 2)

= 60 − 20

= 40

(iii) …14..m³………

= 2

#### Question- 8.

If x = 10, evaluate :
(i) 100x + 225
(ii) 6x2 – 25x
(iii) 150..x³.

If x = 10, evaluate :
(i) 100x + 25

= (100 × 10) + 225

= 1000 + 225

= 1225

(ii) 6x2 – 25x

= 6(10)2 − 25(10)

= (6 × 10 × 10) − (25 × 10)

= 600 − 250

= 350

If a = – 10, evaluate :
(i) 5a

= 5 × (− 10)

= − 50

(ii) a2

= (− 10)2

= − 10 × (− 10)

= 100

(iii) a3

= a × a × a

= (− 10)3

= (− 10) × (− 10) × (− 10)

= − 1000

#### Question -10.

If x = – 6, evaluate :
(i) 11x
(ii) 4x2
(iii) 2x3

(i) 11x

= 11 × (− 6)

= − 66

(ii) 4x2

= 4 × (− 6) × (− 6)

= 4 × 36

= 144

#### Question -11.

If m = – 7, evaluate :
(i) 12m
(ii) 2m2
(iii) 2m3

(i) 12m

= 12 × (− 7)

= − 84

(ii) 2m2

= 2 × m × m

= 2 × (− 7) × (− 7)

= 2 × 49

= 98

#### 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.

Given, average of four quantities (A) = 6
and p = 3, q = 5, r = 7 and s = ?

⇒ 6 × 4 = 15 + s

⇒ s = 24 − 15

⇒ s = 9

#### Question -13.

If a = 5 and b = 6, evaluate :
(i) 3ab
(ii) 6a2b
(iii) 2b2

(i) 3ab

= 3 × a × b

= 3 × 5 × 6

= 90

(ii) 6a2b

= 6 × a × a × b

= 6 × 5 × 5 × 6

= 900

(iii) 2b2

= 2 × b × b

= 2 × 6 × 6

= 72

#### Question -14.

If x = 8 and y = 2, evaluate :

(i) 9xy
(ii) 5x2y
(iii) (4y)2

(i) 9xy

= 9 × x × y

= 9 × 8 × 2

= 144

(ii) 5x2y

= 5 × x × x × y

= 5 × 8 × 8 × 2

= 640

(iii) (4y)2

= 4 × y × 4 × y

= 4 × 2 × 4 × 2

= 8 × 8

= 64

#### Question- 15.

If x = 5 and y = 4, evaluate :
(i) 8xy
(ii) 3x2y
(iii) 3y2

(i) 8xy

= 8 × x × y

= 8 × 5 × 4

= 160

(ii) 3x2y

= 3 × x × x × y

= 3 × 5 × 5 × 4

= 300

(iii) 3y2

= 3 × y × y

= 3 × 4 × 4

= 48

#### Question- 16.

If y = 5 and z = 2, evaluate :
(i) 100yz
(ii) 9y2z
(iii) 5y2
(iv) (5z)3

(i) 100yz

= 100 × y × z

= 100 × 5 × 2

= 1000

(ii) 9y2z

= 9 × y × y × z

= 9 × 5 × 5 × 2

= 450

(iii) 5y2

= 5 × y × y

= 5 × 5 × 5

= 125

(iv) (5z)3

= (5 × z) × (5 × z) × (5 × z)

= 5 × 2 × 5 × 2 × 5 × 2

= 10 × 10 × 10

= 1000

#### Question -17.

If x = 2 and y = 10, evaluate :
(i) 30xy
(ii) 50xy2
(iii) (10x)2
(iv) 5y2

(i) 30xy

= 30 × x × y

= 30 × 2 × 10

= 600

(ii) 50xy2

= 50 × x × y × y

= 50 × 2 × 10 × 10

= 10000

(iii)  (10x)2

= (10 × x) × (10 × x)

= 10 × 2 × 10 × 2

= 400

(iv) 5y2

= 5 × y × y

= 5 × 10 × 10

= 500

#### Question -18.

If m = 3 and n = 7, evaluate :
(i) 12mn
(ii) 5mn2
(iii) (10m)2
(iv) 4n2

(i) 12mn

= 12 × m × n

= 12 × 3 × 7

= 252

(ii) 5mn2

= 5 × m × n × n

= 5 × 3 × 7 × 7

= 735

(iii) (10m)2

= (10 × m) × (10 × m)

= (10 × 3) × (10 × 3)

= 30 × 30

= 900

(iv) 4n2

= 4 × n × n

= 4 × 7 × 7

= 196

Question -19.

If a = -10, evaluate :
(i) 3a – 2
(ii) a2 + 8a
(iii) ….15..a².……

(i) 3a – 2

= (3 × a) − 2

= 3 × (− 10) − 2

= − 30 − 2

= − 32

(ii) a2 + 8a

= (a × a) + (8 × a)

= (− 10 × (− 10)) + (8 × (− 10))

= 100 + (− 80)

= 100 − 80

= 20

(iii)

.…..

= 20

#### Question -20.

If x = -6, evaluate :
(i) 4x – 9
(ii) 3x2 + 8x
(iii) …2..…..

(i) 4x – 9

= (4 × x) – 9

= (4 × (– 6)) – 9

= – 24 – 9

= – 33

(ii) 3x2 + 8x

= (3 × x × x) + (8 × x)

= (3 × (− 6) × (− 6)) + (8 × (− 6))

= − 108 + (− 48)

= 60

(iii)

= 18

#### Question -21.

If m = -8, evaluate :
(i) 2m + 21
(ii) m2 + 9m
(iii) 4..

(i) 2m + 21

= 2 × m + 21

= 2 × (− 8) + 21

= − 16 + 21

= 5

(ii) m2 + 9m

= (m × m) + (9 × m)

= (− 8 × − 8) + (9 × (− 8))

= 64 + (− 72)

= 64 − 72

= − 8

(iii)

= 16

#### Question- 22.

If p = -10, evaluate :
(i) 6p + 50
(ii) 3p2 – 20p
(iii) 50..

(i) 6p + 50

= (6 × p) + 50

= (6 × (− 10)) + 50

= − 60 + 50

= − 10

(ii) 3p2 – 20p

= (3 × p × p) − (20 × p)

= (3 × (− 10) × (− 10)) − (20 × (− 10))

= 300 − (− 200)

= 300 + 200

= 500

(iii)

= 2

#### Question- 23.

If y = -8, evaluate :
(i) 6y + 53
(ii) y+ 12y
(iii) 4..

(i) 6y + 53

= (6 × y) + 53

= (6 × (− 8)) + 53

= − 48 + 53

= 5

(ii) y+ 12y

= (y × y) + (12 × y)

= ((− 8) × (− 8)) + (12 × (− 8))

= 64 + (− 96)

= −32

(iii)

#### Question -24.

If x = 2 and 7 = -4, evaluate :
(i) 11xy
(ii) 5x2y
(iii) (5y)2
(iv) 8x2

(i) 11xy

= 11 × x × y

= 11 × 2 × (− 4)

= − 88

(ii) 5x2y

= 5 × x × x × y

= 5 × 2 × 2 × (− 4)

= − 80

(iii) (5y)2

= 5 × y × 5 × y

= 5 × (− 4) × 5 × (− 4)

= (− 20) × (− 20)

= 400

(iv) 8x2

= 8 × x × x

= 8 × 2 × 2

= 32

If m = 9 and n = -2, evaluate
(i) 4mn
(ii) 2m2n
(iii) (2n)3

(i) 4mn

= 4 × m × n

= 4 × 9 × (− 2)

= − 72

(ii) 2m2n

= 2 × m × m × n

= 2 × 9 × 9 × (− 2)

= 2 × 81 × (− 2)

= − 324

(iii) (2n)3

= (2 × n) × (2 × n) × (2 × n)

= (2 × (− 2)) × (2 × (− 2)) × (2 × (− 2))

= (− 4) × (− 4) × (− 4)

= − 64

#### Question- 26.

If m = -8 and n = -2, evaluate :
(i) 12mn
(ii) 3m2n
(iii) (4n)2

(i) 12mn

= 12 × m × n

= 12 × (− 8) × (− 2)

= 192

(ii) 3m2n

= 3 × m × m × n

= 3 × 64 × (− 2)

= − 384

(iii) (4n)2

= 4 × n × 4 × n

= (4 × (− 2)) × (4 × (− 2))

= (− 8) × (− 8)

= 64

#### Question -27.

If x = -5 and y = -8, evaluate :
(i) 4xy
(ii) 2xy2
(iii) 4x2
(iv) 3y2

(i) 4xy

= 4 × x × y

= 4 × (− 5) × (− 8)

= 160

(ii) 2xy2

= 2 × x × y × y

= 2 × (− 5) × (− 8) × (− 8)

= − 10 × 64

= − 640

(iii) 4x2

= 4 × x × x

= 4 × (− 5) × (− 5)

= 100

(iv) 3y2

= 3 × y × y

= 3 × (− 8) × (− 8)

= 192

#### Question -28.

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

T = 2a – b, a = 1 and b = 3
Put the value of a = 1, and b = 3 in above equation
T = (2 × 7) − 3
T = 14 – 3
T = 11

#### Question- 29.

From the formula B = 2a2 – b2, calculate the value of B when a = 3 and b = -1.

B = 2a2 – b2
Put the values of a = 3 and b = − 1 in above equation
B = 2 × (3)2 – (− 1)2
B = 18 – 1
B = 17
Value of B is = 17

#### 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.

T = 40 hours
x = ₹ 39.45
W = xt = 40 × 39.45
W = ₹ 1578

#### Question -31.

The temperature in Fahrenheit scale is represented by F and the tempera¬ture in Celsius scale is represented by C. If F = 95 x C + 32, find F when C = 40.