Year 9: Addition and subtraction of negative numbers

This cheat sheet covers addition and subtraction of negative numbers. Understanding this is crucial for many areas of maths and real-world applications.

Key concepts

Negative Numbers as Debt: Think of negative numbers as owing money or being in a debt.
Adding Negative Numbers: Adding two negative numbers combines their negativity. For example, $- 3 + (- 5) = - 8$
Subtracting Negative Numbers: Subtracting a negative number is the same as adding a positive number. For example, $5 - (- 2) = 5 + 2 = 7$
Subtracting Positive Numbers from Negative Numbers: This involves borrowing from the next higher place value.

Rules & examples

$- a + b = b - a$ (Adding negative numbers)
$- a - b = - (a + b)$ (Equivalent to subtracting a negative)
Example 1: $- 7 + (- 2) = - 9$
Example 2: $3 - (- 4) = 3 + 4 = 7$
Example 3: $- 6 - (- 1) = - 6 + 1 = - 5$

Tips

Visual representation: Use a number line to help visualise addition and subtraction of negative numbers.
Always simplify: Before performing calculations, simplify expressions involving negative numbers.