Negative Numbers
Negative numbers are numbers less than zero, written with a minus sign in front such as -5, -12, or -3.7. They appear to the left of zero on a number line and represent quantities that are absent, owed, or below a reference point. The concept aligns with CCSS 6.NS standards for understanding positive and negative integers.
Why it matters
Negative numbers appear throughout daily life in temperature readings below freezing, bank account overdrafts, elevator floors below ground level, and golf scores under par. Weather reports regularly use negative temperatures like -15°F during winter months. Financial contexts involve negative balances when spending exceeds available funds, such as a -$200 account balance. Sports statistics track negative yardage in football or below-par golf scores like -3. In advanced mathematics, negative numbers form the foundation for algebra, coordinate geometry, and calculus. Understanding operations with negatives prepares students for solving equations like x + 7 = 3, where x = -4, and graphing functions that extend below the x-axis.
How to solve negative numbers
Negative Numbers
- Negative numbers are less than zero, written with a minus sign (−3).
- On a number line: negatives are to the left of zero.
- Adding a negative = subtracting: 5 + (−3) = 5 − 3 = 2.
- Subtracting a negative = adding: 5 − (−3) = 5 + 3 = 8.
Example: −4 + 7 = 3. −3 − 2 = −5. −2 × −3 = 6.
Worked examples
On a number line, where is 2? (left of zero, at zero, or right of zero)
Answer: right of zero
- Picture a number line → ... -3, -2, -1, 0, 1, 2, 3 ... — A number line goes left and right. Zero is in the middle. Negative numbers go to the LEFT. Positive numbers go to the RIGHT. Like a road: left goes to colder places, right goes to warmer places.
- Find 2 on the line → 2 is to the right of zero — 2 is 2 steps to the right of zero. Moving right means getting bigger.
Which is greater: -9 or 3?
Answer: 3
- Compare a negative and a positive number → -9 < 3 — ANY positive number is always greater than ANY negative number. Think of it this way: positive means you HAVE something, negative means you OWE something. Having 3 is always better than owing 9!
- State the answer → 3 — 3 is greater than -9. On a number line, 3 is to the RIGHT of -9, and right means bigger.
The temperature was -3°C and rose by 14 degrees. What is the temperature now?
Answer: 11°C
- Start at -3°C and add 14 → -3 + 14 — The temperature starts below zero at -3°C. 'Rose by 14 degrees' means it got warmer — we ADD 14. On a thermometer, the liquid goes UP.
- Calculate → 11°C — -3 + 14 = 11°C. We crossed zero and went above freezing!
Common mistakes
- A common error is treating subtraction of a negative as regular subtraction, writing 8 - (-3) = 5 instead of 8 + 3 = 11
- Another mistake is incorrectly ordering negative numbers, claiming -8 > -3 when actually -3 > -8 since -3 is closer to zero
- A frequent error is adding negatives incorrectly, writing -4 + (-6) = 2 instead of -10 by forgetting both numbers are below zero