7 th maths chapter 3 || 3.2

7th Standard Mathematics — Chapter 3: Algebra

Exercise 3.2 Solutions

1. Fill in the blanks

1. The addition of -7b and 2b is -5b.
2. The subtraction of 5m from -3m is -8m.
3. The additive inverse of -37xyz is 37xyz.

2. Say True or False

1. The expressions 8x + 3y and 7x + 2y can not be added.
   Answer: False
   Reason: They can be added by combining their like terms to get (8x + 7x) + (3y + 2y) = 15x + 5y.
2. If x is a natural number, then x + 1 is its predecessor.
   Answer: False
   Reason: x + 1 is its successor, while x - 1 is its predecessor.
3. Sum of a - b + c and -a + b - c is zero.
   Answer: True
   Reason: (a - a) + (-b + b) + (c - c) = 0 + 0 + 0 = 0.

3. Add

1. 8x, 3x
   8x + 3x = (8 + 3)x = 11x
2. 7mn, 5mn
   7mn + 5mn = (7 + 5)mn = 12mn
3. -9y, 11y, 2y
   -9y + 11y + 2y = (-9 + 11 + 2)y = 4y

4. Subtract

1. 4k from 12k
   12k - 4k = 8k
2. 15q from 25q
   25q - 15q = 10q
3. 7xyz from 17xyz
   17xyz - 7xyz = 10xyz

5. Find the sum of the following expressions

1. 7p + 6q, 5p - q, q + 16p
   = (7p + 5p + 16p) + (6q - q + q)
   = 28p + 6q
2. a + 5b + 7c, 2a + 10b + 9c
   = (a + 2a) + (5b + 10b) + (7c + 9c)
   = 3a + 15b + 16c
3. mn + t, 2mn - 2t, -3t + 3mn
   = (mn + 2mn + 3mn) + (t - 2t - 3t)
   = 6mn - 4t
4. u + v, u - v, 2u + 5v, 2u - 5v
   = (u + u + 2u + 2u) + (v - v + 5v - 5v)
   = 6u + 0 = 6u
5. 5xyz - 3xy, 3zxy - 5yx
   Note: xyz = zxy and xy = yx
   = (5xyz + 3xyz) + (-3xy - 5xy)
   = 8xyz - 8xy

6. Subtract

1. 13x + 12y - 5 from 27x + 5y - 43
   = (27x + 5y - 43) - (13x + 12y - 5)
   = 27x + 5y - 43 - 13x - 12y + 5
   = (27x - 13x) + (5y - 12y) + (-43 + 5)
   = 14x - 7y - 38
2. 3p + 5 from p - 2q + 7
   = (p - 2q + 7) - (3p + 5)
   = p - 2q + 7 - 3p - 5
   = (p - 3p) - 2q + (7 - 5)
   = -2p - 2q + 2
3. m + n from 3m - 7n
   = (3m - 7n) - (m + n)
   = 3m - 7n - m - n
   = (3m - m) + (-7n - n)
   = 2m - 8n
4. 2y + z from 6z - 5y
   = (6z - 5y) - (2y + z)
   = 6z - 5y - 2y - z
   = (-5y - 2y) + (6z - z)
   = -7y + 5z (or 5z - 7y)

7. Simplify

1. (x + y - z) + (3x - 5y + 7z) - (14x + 7y - 6z)
   = x + y - z + 3x - 5y + 7z - 14x - 7y + 6z
   = (x + 3x - 14x) + (y - 5y - 7y) + (-z + 7z + 6z)
   = -10x - 11y + 12z
2. p + p + 2 + p + 3 - p - 4 - p - 5 + p + 10
   = (p + p + p - p - p + p) + (2 + 3 - 4 - 5 + 10)
   = 2p + 6
3. n + (m + 1) + (n + 2) + (m + 3) + (n + 4) + (m + 5)
   = n + m + 1 + n + 2 + m + 3 + n + 4 + m + 5
   = (m + m + m) + (n + n + n) + (1 + 2 + 3 + 4 + 5)
   = 3m + 3n + 15