Add the numbers in each picture below. Write their corresponding expressions and simplify them. Class 7

Add the numbers in each picture below. Write their corresponding expressions and simplify them. Class 7

Question 1.

Add the numbers in each picture below. Write their corresponding expressions and simplify them. Try adding the numbers in each picture in a couple different ways qnd see that you get the same thing. Class 7

Solution:

(i) For first picture, expression

= (5y - 6 + x) + (x + 2 + 5y)

= 5y - 6 + x + x + 2 + 5y

= 5y + 5y + x + x - 6 + 2

= 10y + 2x - 4.

Another way :

(x + 2 + 5y) + (5y - 6 + x)

= x + 2 + 5y + 5y-6 + x

= x+ x + 5y + 5y + 2 - 6

= 2x + 10y - 4

= 10y + 2x - 4.

(ii) For second picture,

(2p + 3q - 2 + 3) + (3q + 2p + 3 - 2) + (2p + 3q) + (3 q + 2p)

= 2p + 2p + 2p + 2p + 3q + 3q + 3q + 3q - 2 + 3 + 3 - 2

= 4 × 2p + 4 × 3q + 2 × 3 - 2 × 2

= 8p + 12q + 6 - 4

= 8p + 12q + 2.

Another way : Do it yourself.

(iii) For the third picture,

-5g + 5k + 5k - 5g + 5k + 5k + 5k + 5k + 5k + 5k + 5k + 5k - 5g + 5k + 5k - 5g

= - 5g × 4 + 5k × 12

= -20g + 60k.

Another way : Do it yourself.

Question 2.

Simplify each of the following expressions : Class 7

(a) p + p + p + p, p + p + p + q, p + q + p - q,

(b) p - q + p - q, p + q - p + q,

(c) p + q - (p + q), p - q - p - q,

(d) 2d - d - d - d, 2d - d - d - c,

(e) 2d - d - (d - c), 2d - (d - d) - c,

(f) 2d - d - c - c

Solution:

(a) p + p + p + p = 4p, p + p + p + q = 3p + q,p + q + p - q = 2p.

(b) p - q +p - q = 2p - 2q, p + q - p + q = 2q.

(c) (p + q) - (p + q) = 0, p - q - p - q = - 2q.

(d) 2d - d - d - d = 2d - 3d = -d, 2d - d - d - c = 2d - 2d - c = - c.

(e) 2d - d - (d - c) = 2d - d - d + c = c, 2d - (d - d) - c = 2d - 0 - c = 2d - c

(f) 2d - d - c - c = d - 2c.