These questions ask you to locate integers, reverse a value to its opposite, follow movement, or measure and count marks on a number line. You can solve each one by separating side, direction, and distance.
Use the line as a decision method
First locate zero. Positive integers are to its right and negative integers are to its left. Moving right raises the value by one at each unit step; moving left lowers it. For example, starting at -2 and moving five units right gives 3 because the path crosses zero and continues two more steps.
| Task signal | Decision method |
|---|---|
| Opposite | Keep the magnitude and reflect the point across zero. Thus the opposite of 6 is -6, and the opposite of zero remains zero. |
| Move right or left | Begin at the stated integer and count every unit step in the named direction. Check the sign again if the path crosses zero. |
| Distance between two marks | Count the gap, not the direction. On different sides of zero, add their distances from zero; from -5 to 2 the distance is 7 units. |
| Integers strictly between endpoints | Exclude both endpoints, include zero when it lies inside, and count only the remaining integer marks. |
A quick check is to ask whether the result matches the geometry. An opposite must have the same distance from zero, a rightward move cannot lower a value, and an ordinary distance cannot carry a minus sign.
Traps to reject
| Tempting route | How to reject it |
|---|---|
| Change the size while taking an opposite, or leave the original unchanged | An opposite changes only the side of zero. Doubling the magnitude or keeping the same nonzero point fails the equal-distance reflection check. |
| Use the magnitude as the direction | The digits tell how far; the sign tells the side. A negative mark belongs left of zero, and a named rightward move must increase the running value. |
| Lose the minus sign after crossing zero | Count to zero first, then count the unused steps beyond it. The side where the path ends determines the final sign. |
| Subtract magnitudes for every distance | That works only when both marks are on the same side. When they straddle zero, the two distances to zero join, and the result stays nonnegative. |
| Use the whole span between opposites as each point's distance from zero | The full span contains two equal halves. Each opposite is only one half of that span from zero. |
Try it
Enter the opposite of -12.
A learner reports the distance from -5 to 3 as 2 units, subtracting 3 from 5. What is the correct distance?
- -8 units
- 7 units
- 8 units
- 15 units
How many integers lie strictly between -3 and 2, with neither endpoint counted? Enter the count.