Negative numbers and distance
Use a number line to distinguish a signed change from a distance.
Before you begin
- Whole-number addition
- Reading a horizontal scale
Interpret position and direction
Zero is a reference point. Positive numbers lie to its right and negative numbers to its left. A number farther right is greater: −2 is greater than −5. Adding a positive change moves right; adding a negative change moves left. The sign describes direction relative to your chosen reference, so state what positive means in the situation.
Distinguish change from distance
A signed change is final value minus initial value. A temperature can change by −7 °C, meaning a fall, whereas the size of that change is 7 °C. Absolute value is a number's distance from zero and is never negative. Similarly, the distance between two points on a number line is the absolute value of their difference.
Worked example
The temperature rises from −4 °C to 3 °C. What is the change?
Show the worked solution
- Start at −4 on a number line.
- Move four units to zero and then three more to 3.
- Calculate 3 − (−4) = 7 and check that a rise has a positive sign.
+7 °C.
Try it yourself
Which statement is true?
Common mistakes
- A larger absolute value does not always mean a larger signed number.
- Keep the negative sign inside brackets when subtracting a negative number.
What can you explain now?
A lift moves from floor 5 to floor −2. What is its signed change and how many floor intervals does it travel?
Compare with the explanation
Change −7; distance 7 floor intervals.
Final minus initial is −2 − 5 = −7, so the lift moves down. The magnitude of the movement is |−7| = 7.
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Common Core mathematics standards ↗