Comparing Negative Numbers
For any two positive numbers a and b, if a > b then -a < -b: the inequality reverses for negative numbers. Since 2.5 > 2.1, it follows that -2.5 < -2.1. Since 8 > 4, -8 < -4. On a number line, the greater number is always to the right — and -2.1 is to the right of -2.5, making -2.1 the larger value. This rule from enVision Mathematics, Grade 8, Chapter 1 is foundational for comparing real numbers, ordering sets, and solving inequalities in 8th grade math.
Key Concepts
For any two positive numbers $a$ and $b$, if $a b$, then $ a < b$.
Common Questions
How do I compare two negative numbers?
The negative number with the smaller absolute value (closer to zero) is the greater number. On a number line, it is further to the right.
Which is greater: -7 or -3?
-3 is greater than -7 because -3 is closer to zero and further to the right on the number line.
Compare -2.5 and -2.1.
Since 2.5 > 2.1, we have -2.5 < -2.1. The number -2.1 is greater because it is closer to zero.
Compare -sqrt(15) and -3.5.
sqrt(15) is approximately 3.87. Since 3.87 > 3.5, we have -sqrt(15) < -3.5. So -3.5 is the greater value.
Why does the inequality reverse for negative numbers?
As numbers increase positively (1, 2, 3...), their negatives decrease (-1, -2, -3...). Moving further from zero in the negative direction means smaller values.
When do 8th graders learn to compare negative numbers?
Chapter 1 of enVision Mathematics, Grade 8 covers this in the Real Numbers unit.