Comparing Negative Numbers
Comparing negative numbers uses the number line principle: the further left a number sits, the smaller it is. In Grade 6 Saxon Math Course 1, students learn that −9 < −5 because −9 is further from zero toward the left. The deeper the negative, the smaller the value — like comparing debt: owing $100 (−100) is worse than owing $10 (−10). Ordering −11, −3, 0, −15, −7 from least to greatest gives −15, −11, −7, −3, 0.
Key Concepts
Property When comparing two numbers on a number line, the number on the left is less than the number on the right. For example, $ 4$ is to the left of $ 3$, so $ 4 < 3$.
Examples To compare $ 9$ and $ 5$, notice $ 9$ is farther left, so $ 9 < 5$. Arrange from least to greatest: $ 20, 2, 8$. The correct order is $ 20, 8, 2$. Owing 100 dollars ($ 100$) is a smaller value than owing 10 dollars ($ 10$).
Explanation Things get a little weird in negative land! Think about temperature: is $ 10^\circ$ colder or warmer than $ 2^\circ$? It's way colder! The number that is 'more negative' (further to the left on the number line) is actually the smaller number. Being closer to zero means a number is bigger (or warmer!).
Common Questions
Which is greater: −8 or −3?
−3. On the number line, −3 is to the right of −8, so −3 > −8.
Order −11, −3, 0, −15, −7 from least to greatest.
−15, −11, −7, −3, 0 — ordered by distance from zero increasing leftward.
Why is −100 smaller than −10?
−100 means owing $100; −10 means owing $10. Owing more is a worse financial position, corresponding to a smaller number further left on the number line.
Is zero positive or negative?
Neither. Zero is the boundary point between positive and negative numbers.
How does comparing negatives differ from comparing positives?
With positives, larger absolute value means larger number. With negatives, larger absolute value means smaller (more negative) number.