**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 CISCE 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.

**Answer-1**

(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 = 6a^{2}

**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.

**Answer-2**

i) x + y – m

(ii) ^{xy}⁄_{m}

(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.

**Answer-3**

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) x^{2} – 2x

(iii) ^{x²}⁄_{m}

**Answer-4**

**(i) 3x + 8**

= (3 × 4) + 8

= 12 + 8

= 20

**(ii) x ^{2} – 2x**

= (4)^{2} − 2(4)

= (4 × 4) − (2 × 4)

= 16 − 8

= 8

**(iii) ^{x²}⁄_{m}**

= ^{4²}⁄_{2 }

= ^{4 x 4}⁄_{2}

= ^{16}⁄_{2}

= 8

**Question 5.**

(i) 5m – 6

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

(iii) (2m)^{2}

**Answer -5**

**(i) 5m − 6**

= (5 × 6) − 6

= 36 − 6

= 30

**(ii) 2m ^{2} + 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.**

(i) 12x + 7

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

(iii) ^{x²}⁄_{8}

**Answer-6**

**(i) 12x + 7**

= (12 × 4) + 7

= 48 + 7

= 55

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

= (5 × 4 × 4) + 4 (4)

= 80 + 16

= 96

(iii) ^{x²}⁄_{8}

**Question- 7.**

If m = 2, evaluate :

(i) 16m – 7

(ii) 15m^{2} – 10m

(iii) …** ^{1}⁄_{4}..m³…**……

**Answer-7**

**(i) 16m – 7**

= (16 × 2) – 7

= 32 – 7

= 25

**(ii) 15m ^{2} – 10m**

= 15 (2)^{2} − 10(2)

= (15 × 2 × 2) − (10 × 2)

= 60 − 20

= 40

(iii) …** ^{1}⁄_{4}..m³…**……

= 2

**Question- 8.**

If x = 10, evaluate :

(i) 100x + 225

(ii) 6x^{2} – 25x

(iii) ^{1}⁄_{50}..x³.

**Answer-8**

If x = 10, evaluate :

**(i) 100x + 25**

= (100 × 10) + 225

= 1000 + 225

= 1225

(ii) 6x^{2} – 25x

= 6(10)^{2} − 25(10)

= (6 × 10 × 10) − (25 × 10)

= 600 − 250

= 350

**Question-9**

(i) 5a

(ii) a

^{2}

(iii) a

^{3}

**Answer- 9.**

If a = – 10, evaluate :

**(i) 5a**

= 5 × (− 10)

= − 50

**(ii) a ^{2}**

= (− 10)^{2}

= − 10 × (− 10)

= 100

**(iii) a ^{3}**

= a × a × a

= (− 10)^{3}

= (− 10) × (− 10) × (− 10)

= − 1000

**Question -10.**

If x = – 6, evaluate :

(i) 11x

(ii) 4x^{2}

(iii) 2x^{3}

**Answer-10**

**(i) 11x**

= 11 × (− 6)

= − 66

**(ii) 4x ^{2}**

= 4 × (− 6) × (− 6)

= 4 × 36

= 144

**(iii) 2x**= 2 × (− 6)

^{2}^{3}

= 2 × (− 6) × (− 6) × (− 6)

= 2 × (− 216)

= − 432

**Question -11.**

If m = – 7, evaluate :

(i) 12m

(ii) 2m^{2}

(iii) 2m^{3}

**Answer-11**

**(i) 12m**

= 12 × (− 7)

= − 84

**(ii) 2m ^{2}**

= 2 × m × m

= 2 × (− 7) × (− 7)

= 2 × 49

= 98

**(iii) 2m**= 2 × m × m × m

^{3}= 2 × (− 7) × (− 7) × (− 7)

= 2 × (− 343)

= − 686

**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.

**Answer-12**

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) 6a^{2}b

(iii) 2b^{2}

**Answer-13**

**(i) 3ab**

= 3 × a × b

= 3 × 5 × 6

= 90

**(ii) 6a ^{2}b**

= 6 × a × a × b

= 6 × 5 × 5 × 6

= 900

**(iii) 2b ^{2}**

= 2 × b × b

= 2 × 6 × 6

= 72

**Question -14.**

If x = 8 and y = 2, evaluate :

(i) 9xy

(ii) 5x^{2}y

(iii) (4y)^{2}

**Answer-14**:

**(i) 9xy**

= 9 × x × y

= 9 × 8 × 2

= 144

**(ii) 5x ^{2}y**

= 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) 3x^{2}y

(iii) 3y^{2}

**Answer-15**:

**(i) 8xy**

= 8 × x × y

= 8 × 5 × 4

= 160

**(ii) 3x ^{2}y**

= 3 × x × x × y

= 3 × 5 × 5 × 4

= 300

**(iii) 3y ^{2}**

= 3 × y × y

= 3 × 4 × 4

= 48

**Question- 16.**

If y = 5 and z = 2, evaluate :

(i) 100yz

(ii) 9y^{2}z

(iii) 5y^{2}

(iv) (5z)^{3}

**Answer-16**:

**(i) 100yz**

= 100 × y × z

= 100 × 5 × 2

= 1000

**(ii) 9y ^{2}z**

= 9 × y × y × z

= 9 × 5 × 5 × 2

= 450

**(iii) 5y ^{2}**

= 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) 50xy^{2}

(iii) (10x)^{2}

(iv) 5y^{2}

**Answer-17**:

**(i) 30xy**

= 30 × x × y

= 30 × 2 × 10

= 600

**(ii) 50xy ^{2}**

= 50 × x × y × y

= 50 × 2 × 10 × 10

= 10000

**(iii) (10x) ^{2}**

= (10 × x) × (10 × x)

= 10 × 2 × 10 × 2

= 400

**(iv) 5y ^{2}**

= 5 × y × y

= 5 × 10 × 10

= 500

**Question -18.**

If m = 3 and n = 7, evaluate :

(i) 12mn

(ii) 5mn^{2}

(iii) (10m)^{2}

(iv) 4n^{2}

**Answer-18**

**(i) 12mn**

= 12 × m × n

= 12 × 3 × 7

= 252

**(ii) 5mn ^{2}**

= 5 × m × n × n

= 5 × 3 × 7 × 7

= 735

**(iii) (10m) ^{2}**

= (10 × m) × (10 × m)

= (10 × 3) × (10 × 3)

= 30 × 30

= 900

**(iv) 4n ^{2}**

= 4 × n × n

= 4 × 7 × 7

= 196

**Question -19.**

If a = -10, evaluate :

(i) 3a – 2

(ii) a^{2} + 8a

(iii) ….** ^{1}⁄_{5}..a².**……

**Answer-19**:

**(i) 3a – 2**

= (3 × a) − 2

= 3 × (− 10) − 2

= − 30 − 2

= − 32

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

(iii) …** ^{x²}⁄_{2}..**…..

**Answer-20**:

**(i) 4x – 9**

= (4 × x) – 9

= (4 × (– 6)) – 9

= – 24 – 9

= – 33

**(ii) 3x ^{2} + 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) m^{2} + 9m

(iii) ^{m²}⁄_{4}..

**Answer-21**:

**(i) 2m + 21**

= 2 × m + 21

= 2 × (− 8) + 21

= − 16 + 21

= 5

**(ii) m ^{2} + 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) 3p^{2} – 20p

(iii) ^{p²}⁄_{50}..

**Answer-22**:

**(i) 6p + 50**

= (6 × p) + 50

= (6 × (− 10)) + 50

= − 60 + 50

= − 10

**(ii) 3p ^{2} – 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^{2 }+ 12y

(iii) ^{y³}⁄_{4}..

**Answer23**:

**(i) 6y + 53**

= (6 × y) + 53

= (6 × (− 8)) + 53

= − 48 + 53

= 5

**(ii) y ^{2 }+ 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) 5x^{2}y

(iii) (5y)^{2}

(iv) 8x^{2}

**Answer-24**:

**(i) 11xy**

= 11 × x × y

= 11 × 2 × (− 4)

= − 88

**(ii) 5x ^{2}y**

= 5 × x × x × y

= 5 × 2 × 2 × (− 4)

= − 80

**(iii) (5y) ^{2}**

= 5 × y × 5 × y

= 5 × (− 4) × 5 × (− 4)

= (− 20) × (− 20)

= 400

**(iv) 8x ^{2}**

= 8 × x × x

= 8 × 2 × 2

= 32

**Question -25.**

If m = 9 and n = -2, evaluate

(i) 4mn

(ii) 2m^{2}n

(iii) (2n)^{3}

**Answer-25**:

**(i) 4mn**

= 4 × m × n

= 4 × 9 × (− 2)

= − 72

**(ii) 2m ^{2}n**

= 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) 3m^{2}n

(iii) (4n)^{2}

**Answer-26**:

**(i) 12mn**

= 12 × m × n

= 12 × (− 8) × (− 2)

= 192

**(ii) 3m ^{2}n**

= 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) 2xy^{2}

(iii) 4x^{2}

(iv) 3y^{2}

**Answer-27**:

**(i) 4xy**

= 4 × x × y

= 4 × (− 5) × (− 8)

= 160

**(ii) 2xy ^{2}**

= 2 × x × y × y

= 2 × (− 5) × (− 8) × (− 8)

= − 10 × 64

= − 640

**(iii) 4x ^{2}**

= 4 × x × x

= 4 × (− 5) × (− 5)

= 100

**(iv) 3y ^{2}**

= 3 × y × y

= 3 × (− 8) × (− 8)

= 192

**Question -28.**

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

**Answer-28**:

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

**Answer-29**:

B = 2a^{2} – b^{2}

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.

**Answer-30**:

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 = ** ^{9}⁄_{5}** x C + 32, find F when C = 40.

**Answer-31**:

= 9 × 8 + 32

F = 104°

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