This topic summary covers Knowledge Organiser: Negative Numbers within Negative Numbers for GCSE Mathematics. Revise Negative Numbers in Number for GCSE Mathematics with 12 exam-style questions and 22 flashcards. Use this page as part of a wider topic revision path rather than treating it as an isolated fact. It is section 14 of 14 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Knowledge Organiser: Negative Numbers
Key Terms
- Negative number: Any number less than zero, shown with a minus sign
- Number line: A line where numbers increase to the right and decrease to the left
- Double negative: Two minus signs next to each other that make a positive
- Integer: Any whole number including negatives and zero
- Absolute value: The distance of a number from zero (always positive)
Must-Know Facts
- Same signs × or ÷ = positive result; different signs = negative result
- Adding a negative = subtracting: 5 + (−3) = 5 − 3 = 2
- Subtracting a negative = adding: 5 − (−3) = 5 + 3 = 8
- On a number line: left is smaller, right is larger (even for negatives)
- −8 < −3 (−8 is further left, so smaller)
- (−3)² = 9 but −3² = −9 (brackets make all the difference)
Key Rules
- + × + = positive
- − × − = positive
- + × − = negative
- − − becomes + (subtracting a negative)
- Real-world uses: temperature, debt, altitude below sea level
Common Mistakes
- Subtracting a negative: 5 − (−3) = 8, not 2 — two negatives make a positive when subtracting
- Ordering negatives on a number line: −8 is less than −3, not greater — the further left, the smaller the value
- Brackets with powers: (−3)² = 9 but −3² = −9 — without brackets, the square applies only to 3, then the negative is applied
- Multiplying/dividing signs: Only different signs give a negative — same signs always give a positive result
Practice questions for Negative Numbers
Which of these statements is true?
Aisha's bank account shows a balance of -45 pounds. She deposits 70 pounds. Explain what her new balance is and what the negative sign meant originally.
Quick recall flashcards
Double Negative Rule
Subtracting a negative = Adding. Two minuses make a plus: 5 − (−3) = 5 + 3 = 8
Using a number line
Draw a horizontal line with 0 in the middle. Negative numbers go LEFT, positive RIGHT. Moving right = adding, moving left = subtracting.