Learn – Algebra foundations – Addition and Subtraction

1 Exercises

1.1 Problem set

Simplify each of the following.

  1. a - (-b)
  2. -p + (-q)
  3. x + (-y)
  4. a -(-b)
  5. -p -(-q)
  6. -x -(+y)

1.2 Problem set

For each of the following, give, with a reason, whether the given equation is true or false.

  1. a + (-b) = a - b
  2. p - (-q) = p - q
  3. -x + (-y) = -x - y
  4. -a - (-b) = -a - b
  5. -p - (-q) = -p + q

1.3 Problem set

For each of the following, give, with a reason, whether the given equation is true or false.

  1. a + b + c = a + c + b
  2. p + q + r + s + t + u = t + q + r + s + p + u
  3. x + (-y) = -y + x
  4. a+(-b)+(-c)+d = -b + d + c + (-a)
  5. -p+(-q)+r+(-s)+t = -s + r + (-p) + t +(-q)

1.4 Problem set

For each of the following, give, with a reason, whether the given equation is true or false.

  1. b - c = c - b
  2. b - c = -c + b
  3. a - b - c = -b - c +a
  4. a + b - c = a - c + b
  5. a - c + b - e = a - b + c - e
  6. a - b + c - d + e - f + g - h = a + c +e + g - b - d - f - h
  7. -x - y -z + a + b + c = a - x + b - y + c - z
  8. x + y + z - a - b - c = c - x + a - y + b - z

1.5 Problem set

For each of the following, give, with a reason, whether the given equation is true or false.

  1. a - (b+c) = a - b + c
  2. a - (b+c) = a - b - c
  3. -(a-b)-c = -a - b - c
  4. (x-y)-z = x - (y-z)
  5. (x-y)-z = x - (y+z)

1.6 Problem set

For each of the following, give, with a reason, whether the given equation is true or false.

  1. (a-b) - (c-d) = a-b-c-d
  2. (a+b) - (c-d) = (a-c)+(b-d)
  3. (a-b) + (c-d) + (e-f) = (a-d)+(c-f)+(e-b)
  4. -(a-b) - (c-d) - (e-f) = (b-a)+(d-c)+(f-e)
  5. (x-y-z) - (-u+v-w) = (u - v - w) + (x - y -z)