Geometry Problem Solver The positive and negative number line
A number line is a straight line with zero in the middle, positive numbers to the right and negative numbers to the left. Numbers grow as you move right, so any positive is larger than any negative, and of two negatives the one closer to zero is the larger.
Which of two numbers is larger
On a number line the rule never changes: whichever number sits further right is the larger one. That is the whole comparison, and it survives the case people get wrong.
The case people get wrong is two negatives. -2 is larger than -7, because -2 sits closer to zero and therefore further right. The digit 7 is bigger than the digit 2, but the number -7 is smaller. Owing seven is worse than owing two.
Adding and subtracting as movement
Adding a positive moves right. Subtracting a positive moves left. Start at 3, subtract 5, and you walk five steps left, landing on -2.
Adding a negative also moves left, which is why 4 + (-6) and 4 - 6 give the same answer. Subtracting a negative moves right, which is the reason two minus signs turn into a plus: -3 - (-8) starts at -3 and walks eight steps right, ending at 5.
Absolute value is distance, not direction
The absolute value of a number is how far it sits from zero, ignoring which side. |-6| and |6| are both 6, because both are six units away.
That is why absolute value is never negative: a distance cannot be. It is also why -6 has a larger absolute value than -2 while being the smaller number, which is exactly the confusion the number line clears up.
Reading the line
| Statement | True or false | Why |
|---|---|---|
| -2 > -7 | True | -2 is further right |
| |-7| > |-2| | True | 7 units from zero beats 2 |
| 0 is positive | False | Zero is neither positive nor negative |
| Any negative < any positive | True | The whole left side is below the whole right side |
Questions
Is zero positive or negative?
Neither. Zero is the dividing point of the line. It is the only number that is not on either side.
Which is bigger, -3 or -8?
-3. On the line it sits closer to zero, so further right. The larger digit belongs to the smaller number when both are negative.
Why does subtracting a negative add?
Subtracting means moving left, and the negative flips the direction, so you end up moving right. 5 - (-3) is the same walk as 5 + 3, landing on 8.
More geometry reference
Stuck on the actual problem
Photograph it and get the worked solution, step by step, with the theorem named at each one.
