Selina Concise Class 6 Math Chapter 19 Framing Algebraic Expressions Exercise 19 Solution
EXERCISE 19
(1) Write in the form of an algebraic expression:
(i) Perimeter = P and Length = l and Breadth = b
∴ P = 2(l + b)
(ii) Perimeter = P and let the side of the square = a
∴ P = 4a
(iii) Let the area of the square = A and side = a
∴ A = a2
(iv) Let the surface area = S and the edge of the square = a
∴ S = 6a2
(2) Express each of the following as an algebraic expression:
(i) (x + y) – m
(ii) (xy)/m
(iii) (3n – 5m) + 9p
(iv) 12xyz – 5mn
(v) (p + 2r – s) – (a + 3n + 4x)
(3) Construct a formula for the following:
(4) If x = 4, evaluate:
(i) 3x + 8
= (3 × 4) + 8
= 12 + 8
= 20
(ii) x2 – 2x
= (4)2 – (2 × 4)
= 16 – 8
= 8
(iii) (x)2/2
= (4)2/2
= 16/2
= 8
(5) If m = 6, evaluate:
(i) 5m – 6
= (5 × 6) – 6
= 30 – 6
= 24
(ii) 2m2 + 3m
= 2 × (6)2 + (3 × 6)
= (2 × 36) + 18
= 72 + 18
= 90
(iii) (2m)2
= 4 × (6)2
= 4 × 36
= 144
(6) If x = 4, evaluate:
(i) 12x + 7
= (12 × 4) + 7
= 48 + 7
= 55
(ii) 5x2 + 4x
= 5 × (4)2 + (4 × 4)
= (5 × 16) + 16
= 80 + 16
= 96
(iii) (x)2/8
= (4)2/8
= 16/8
= 2
(7) If m = 2, evaluate:
(i) 16m – 7
= (16 × 2) – 7
= 32 – 7
= 25
(ii) 15m2 – 10m
= 15 × (2)2 – (10 × 2)
= (15 × 4) – 20
= 60 – 20
= 40
(iii) (1/4)m3
= (1/4) × (2)3
= 8/4
= 2
(8) If x = 10, evaluate:
(i) 100x + 225
= (100 × 10) + 225
= 1000 + 225
= 1225
(ii) 6x2 – 25x
= 6 × (10)2 – (25 × 10)
= 6 × 100 – 250
= 600 – 250
= 350
(iii) (1/50)x3
= (1/50) × (10)3
= 1000/50
= 20
(9) If a = – 10, evaluate:
(i) 5a
= 5 × (- 10)
= – 50
(ii) a2
= (- 10)2
= 100
(iii) a3
= (- 10)3
= – 1000
(10) If x = – 6, evaluate:
(i) 11x
= 11 × (- 6)
= – 66
(ii) 4x2
= 4 × (- 6)2
= 4 × 36
= 144
(iii) 2x3
= 2 × (- 6)3
= 2 × (- 216)
= – 432
(11) If m = – 7, evaluate:
(i) 12m
= 12 × (- 7)
= – 84
(ii) 2m2
= 2 × (- 7)2
= 2 × 49
= 98
(iii) 2m3
= 2 × (- 7)3
= 2 × (- 343)
= – 686
(12) Find the average (A) of four quantities p, q, r and s.
∴ A = (p + q + r + s)/4
⇒ 6 = (3 + 5 + 7 + s)/4
⇒ 24 = 15 + s
⇒ s = 24 – 15
⇒ s = 9
(13) If a = 5 and b = 6, evaluate:
(i) 3ab
= 3 × (5 × 6)
= 3 × 30
= 90
(ii) 6a2b
= 6 × (5)2 × 6
= 6 × 25 × 6
= 36 × 25
= 900
(iii) 2b2
= 2 × (6)2
= 2 × 36
= 72
(14) If x = 8 and y = 2, evaluate:
(i) 9xy
= 9 × 8 × 2
= 72 × 2
= 144
(ii) 5x2y
= 5 × (8)2 × 2
= 5 × 64 × 2
= 64 × 10
= 640
(iii) (4y)2
= (4)2 × (2)2
= 16 × 4
= 64
(15) If x = 5 and y = 4, evaluate:
(i) 8xy
= 8 × 5 × 4
= 40 × 4
= 160
(ii) 3x2y
= 3 × (5)2 × 4
= 3 × 25 × 4
= 3 × 100
= 300
(iii) 3y2
= 3 × (4)2
= 3 × 16
= 48
(16) If y = 5 and z = 2, evaluate:
(i) 100yz
= 100 × 5 × 2
= 100 × 10
= 1000
(ii) 9y2z
= 9 × (5)2 × 2
= 9 × 25 × 2
= 9 × 50
= 450
(iii) 5y2
= 5 × (5)2
= 5 × 25
= 125
(iv) (5z)3
= (5)3 × (2)3
= 125 × 8
= 1000
(17) If x = 2 and y = 10, evaluate:
(i) 30xy
= 30 × 2 × 10
= 30 × 20
= 600
(ii) 50xy2
= 50 × 2 × (10)2
= 100 × 100
= 10,000
(iii) (10x)2
= (10)2 × (2)2
= 100 × 4
= 400
(iv) 5y2
= 5 × (10)2
= 5 × 100
= 500
(18) If m = 3 and n = 7, evaluate:
(i) 12mn
= 12 × 3 × 7
= 12 × 21
= 252
(ii) 5mn2
= 5 × 3 × (7)2
= 15 × 49
= 735
(iii) (10m)2
= (10)2 × (3)2
= 100 × 9
= 900
(iv) 4n2
= 4 × (7)2
= 4 × 49
= 196
(19) If a = – 10, evaluate/;
(i) 3a – 2
= [3 × (- 10)] – 2
= – 30 – 2
= – 32
(ii) a2 + 8a
= (- 10)2 + [8 × (- 10)]
= 100 – 80
= 20
(iii) (1/5) × (- 10)2
= 100/5
= 20
(20) If x = – 6, evaluate:
(i) 4x – 9
= [4 × (- 6)] – 9
= – 24 – 9
= – 33
(ii) 3x2 + 8x
= [3 × (- 6)2] + [8 × (- 6)]
= (3 × 36) – 48
= 108 – 48
= 60
(iii) (x)2/2
= (- 6)2/2
= 36/2
= 18
(21) If m = – 8, evaluate:
(i) 2m + 21
= [2 × (- 8)] + 21
= – 16 + 21
= 5
(ii) m2 + 9m
= (- 8)2 + [9 × (- 8)]
= 64 – 72
= – 8
(iii) m2/4
= (- 8)2/4
= 64/4
= 16
(22) If p = – 10, evaluate:
(i) 6p + 50
= [6 × (- 10)] + 50
= – 60 + 50
= – 10
(ii) 3p2 – 20p
= [3 × (- 10)2] – [20 × (- 10)]
= (3 × 100) + 200
= 300 + 200
= 500
(iii) (p)2/50
= (- 10)2/50
= 100/50
= 2
(23) If y = – 8, evaluate:
(i) 6y + 53
= [6 × (- 8)] + 53
= – 48 + 53
= 5
(ii) y2 + 12y
= (- 8)2 + [12 × (- 8)]
= 64 – 96
= – 32
(iii) (y)3/4
= (- 8)3/4
= – 512/4
= – 128
(24) If x = 2 and y = – 4, evaluate:
(i) 11xy
= 11 × 2 × ( – 4)
= 22 × (- 4)
= – 88
(ii) 5x2y
= 5 × (2)2 × (- 4)
= 5 × 4 × (- 4)
= 20 × (- 4)
= – 80
(iii) (5y)2
= (5)2 × (- 4)2
= 25 × 16
= 400
(iv) 8x2
= 8 × (2)2
= 8 × 4
= 32
(25) If m = 9 and n = – 2, evaluate:
(i) 4mn
= 4 × 9 × (- 2)
= 36 × (- 2)
= – 72
(ii) 2m2n
= 2 × (9)2 × (- 2)
= 2 × 81 × (- 2)
= 162 × (- 2)
= – 324
(iii) (2n)3
= (2)3 × (- 2)3
= 8 × (- 8)
= – 64
(26) If m = – 8 and n = – 2, evaluate:
(i) 12mn
= 12 × (- 8) × (- 2)
= 12 × 16
= 192
(ii) 3m2n
= 3 × (- 8)2 × (- 2)
= 3 × 64 × (- 2)
= 192 × (- 2)
= – 384
(iii) (4n)2
= (4)2 × (- 2)2
= 16 × 4
= 64
(27) If x = – 5 and y = – 8, evaluate:
(i) 4xy
= 4 × (- 5) × (- 8)
= 4 × 40
= 160
(ii) 2xy2
= 2 × (- 5) × (- 8)2
= – 10 × 64
= – 640
(iii) 4x2
= 4 × (- 5)2
= 4 × 25
= 100
(iv) 3y2
= 3 × (- 8)2
= 3 × 64
= 192
(28) T = 2a – b
⇒ T = (2 × 7) – 3
⇒ T = 14 – 3
⇒ T = 11
(29) B = 2a2 – b2
⇒ B = [2 × (3)2] – (- 1)2
⇒ B = (2 × 9) – 1
⇒ B = 18 – 1 = 17
(30) T = 40 hours
x = Rs 39.45
W = xt = Rs (40 × 39.45) = Rs 1578