The DAV Class 6 Maths Solutions and **DAV Class 6 Maths Chapter 6 Worksheet 7 **Solutions of Introduction to Algebra offer comprehensive answers to textbook questions.

## DAV Class 6 Maths Ch 6 WS 7 Solutions

Question 1.

If a = 2, b = 3 find the value of the following algebraic expressions.

(a) 3a + 2b

Solution:

Here a = 2, b = 3

3a + 2b = 3(2) + 2(3)

= 6 + 6

= 12

(b) 2a – b

Solution:

Here a = 2, b = 3

2a – 6 = 2(2) – 3

= 4 – 3

= 1

Question 2.

If x = – 1, y = 2, z = – 3 find the value of

(a) x + y + z

Solution:

Here x = – 1, y = 2, z = – 3

x + y + z = – 1 + 2 + (- 3)

= – 1 + 2 – 3

= – 2

(b) 2x – 3y + 6z

Solution:

Here x = – 1, y = 2, z = – 3

2x – 3y + 6z = 2(- 1) – 3(2) + 6 (- 3)

= – 2 – 6 – 18

= – 26

Question 3.

If p = – 3, q = 0, r = 2, find the value of

(a) p + q + r + 1

Solution:

Here p = – 3, q = 0, r = 2

p + q + r + 1 = – 3 + 0 + 2 + 1

= – 3 + 3

= 0

(b) 2pq + 3qr – 4pr

Solution:

Here p = – 3, q = 0, r = 2

2pq + 3qr – 4pr

= 2(- 3) (0) + 3(0) (2) – 4(- 3) (2)

= 0 + 0 + 24

= 24

Question 4.

If z = – 9, find the value of \(\frac{2}{3}\) z + 6

Solution:

\(\frac{2}{3}\) z + 6 = \(\frac{2}{3}\) × (- 9) + 6

= 2 × (- 3) + 6

= – 6 + 6

= 0

Question 5.

If a = 1, b = – 2, c = – 1, show that 7a + 6 + c = 2abc.

Solution:

Here a = 1, b = – 2, c = – 1

7a + b + c = 2abc

L.H.S. :

7(1) + (- 2) + (- 1)

= 7 – 2 – 1

= 4

R.H.S.:

2abc = 2 × 1 × (- 2) × (- 1)

= 2 × 2

= 4

L.H.S. = R.H.S.

Hence Proved.

### DAV Class 6 Maths Chapter 6 Value Based Questions

Question 1.

Amounts donated by Mr. Lai and Mr. Sohan to an orphanage are represented by the expressions ₹ (2a^{2} – 3b^{2} + 6ab) and < (5b^{2} – 2ab + 3a^{2}) respectively.

(а) Find the expression for total amount donated by them. Also, when a = 100, b = 150 find the total amount.

Solution:

Amount donated by Mr. Lai = ₹ (2a^{2} – 3b^{2} + 6ab)

Amount donated by Mr. Sohan = ₹ (5b^{2} – 2ab + 3a^{2})

∴ Total amount donated by them = ₹ (2a^{2} – 3b^{2} + 6ab) + ₹ (5b^{2} – 2ab + 3a^{2})

= ₹ (5a^{2} + 2b^{2} + 4ab)

On putting a = 100 and 6 = 150 in the expression, we get

₹ [5(100)^{2} + 2(150)^{2} + 4 × 100 × 150]

= ₹ ([5 × 10000 + 2 × 22500 + 60000]

= ₹ [50000 + 45000 + 60000]

= ₹ 1,55,000

(b) What value is depicted by them?

Solution:

Helpful to the deprived or cooperative with others in helping the needy, etc.

Question 2.

Number of students of Class-V and VI who participated in “SAVE ENVIRONMENT” campaign is given by the expression (2pq + 3p^{2} + 2q^{2}) and (4p^{2} + q^{2} + 3pq) respectively.

(а) If p = 2, q = 5, find how many more students of Class-V participated in the campaign.

Solution:

Given that p = 2 and q – 5

No. of students of Class-V participated in campaign = (2pq + 3p^{2} + 2q^{2})

= 2(2)(5) + 3(2)^{2} + 2(5)^{2}

= 20 + 12 + 50 = 82

No. of students of Class-VI, participated in campaign = (4p^{2} + q^{2} + 3pq)

= 4(2)^{2} + (5)^{2} + 3(2)(5)

= 16 + 25 + 30 = 71

∴ No. of more student of Class V with respect to Class VI = 82 – 71 = 11

(b) What value is possessed by participating students?

Solution:

Environment friendly, etc.