Apply addition, subtraction, multiplication and division rules

Key notes

Addition Rules

Commutative Property: a + b = b + a (Order doesn’t change the sum)

Associative Property: (a+b) + c = a + (b+c) (Grouping doesn’t affect the sum)

Identity Property: a + 0 = a (Adding zero doesn’t change a number)

Adding Positive and Negative Numbers:

  • Same sign → Add values and keep the sign.
  • Different signs → Subtract smaller from larger and keep the sign of the larger number.

Subtraction Rules

Subtraction as Addition of the Opposite: a − b = a + (−b)

Sign Change Rule:

  • Positive – Negative → a −(−b) = a + b
  • Negative – Positive → −a −b = −(a+b)

Order Matters: a−b ≠ b − a

Multiplication Rules

Commutative Property: a × b = b × a

Associative Property: (a×b) × c = a × (b×c)

Distributive Property: a × (b + c) = a × b + a × c

Multiplying Positive and Negative Numbers:

  • Positive × Positive = Positive
  • Negative × Negative = Positive
  • Positive × Negative = Negative

Division Rules

Dividing by 1: a ÷ 1 = a

Dividing by Itself: a ÷ a = 1 (except when a = 0)

Dividing by Zero is Undefined

Sign Rules:

  • Positive ÷ Positive = Positive
  • Negative ÷ Negative = Positive
  • Positive ÷ Negative = Negative

Order of Operations (PEMDAS/BODMAS)

  • P: Parentheses (Brackets)
  • E: Exponents (Orders)
  • MD: Multiplication and Division (Left to Right)
  • AS: Addition and Subtraction (Left to Right)

Learn with an example

The number line shows an unknown number, b.

Is 3b positive or negative?

Determine if b is positive or negative.

The unknown number b is to the left of 0. So, b is negative.

Determine if 3b is positive or negative.

In the expression 3b, 3 is positive and b is negative. The product of a positive number and a negative number is negative. So, 3b is negative.

The number line shows an unknown number, v.

Is 5v positive or negative?

Determine if v is positive or negative.

The unknown number v is to the right of 0. So, v is positive.

Determine if 5v is positive or negative.

In the expression 5v, 5 is positive and v is positive. The product of two positive numbers is positive. So, 5v is positive.

The number line shows an unknown number, u.

Is 3u positive or negative?

  • positive
  • negative

Determine if u is positive or negative.

The unknown number u is to the left of 0. So, u is negative.

Determine if 3u is positive or negative.

In the expression 3u, 3 is positive and u is negative. The product of a positive number and a negative number is negative. So, 3u is negative.

Let’s practice!🖊️