Study guide: Locate and Compare Signed Rational Numbers
Use negatives, opposites, absolute value, order, and four-quadrant coordinates.
Ideas to explain in your own words
- Positive and negative numbers can represent directions on opposite sides of a chosen zero reference.
- Absolute value measures distance from zero and is never negative.
- Rational numbers include fractions and terminating decimals, positive or negative.
- Signed coordinates locate points on both sides of each axis.
Useful vocabulary
- opposite
- The point equally far from zero on the other side.
- absolute value
- A number’s nonnegative distance from zero.
Watch your reasoning
- A negative sign gives direction; it does not mean the amount is absent.
- Absolute value never retains a negative sign.
- For negative values, a larger absolute value can mean a smaller signed value.
- A y-axis reflection changes x, not y.
A worked review example
With sea level defined as zero, a model location 6 meters below it is −6 m. Its opposite location is +6 m above sea level. Both are six meters from the reference. Negative does not mean no distance; the sign gives direction relative to zero. State what zero represents in the model. A negative sign gives direction; it does not mean the amount is absent. Draw equally spaced points on both sides of a labeled zero.
Make a practice plan
- Represent Opposite Directions with Signed Numbers: Write the opposite of 0 and of 2.5. Expected: 0 and −2.5.
- Distinguish Distance from Zero and Numerical Order: Compare −12 and −5 in both ways. Expected: −12<−5 but 12>5 for their absolute values.
- Order Rational Numbers on a Number Line: Order −1,−0.6,0,0.4 from least to greatest. Expected: that same order.
- Use Four Quadrants and Coordinate Reflections: Points (−3,4) and (5,4) are eight units apart; reflecting (2,−6) across x gives (2,6).