Place, position, and compare integers, fractions, and decimals on a number line, including scaled and negative segments and locating a value between marks.
Free, timed SHSAT practice sets on number line representation— every question includes a full worked explanation, and there's no account required.
Loading questions…
Most number line questions ask for one of two things.
The value at a tick mark. Find the size of one step first: step = (right end − left end) ÷ number of equal parts. Then start at the left end and add that many steps. If the segment from \(2\) to \(4\) has 4 equal parts, each step is \(\frac{2}{4} = \frac{1}{2}\), so the mark 3 steps right of 2 is \(2 + \frac{3}{2} = 3\frac{1}{2}\).
The distance between two points. Subtract and take the absolute value: from \(-3\) to \(5\) is \(|5 - (-3)| = 8\). A distance is never negative.
Common traps:
Each of the 5 equal parts has length \((-3 - (-7)) \div 5 = \frac{4}{5}\). The mark 1 step to the right of -7 is \((-7) + \frac{4}{5} = -6\frac{1}{5}\). Counting one tick too few gives \(-7\). Counting the steps back from -3 instead of forward from -7 gives \(-3\frac{4}{5}\). Taking each step as 1 whole unit gives \(-6\).
Each of the 3 equal parts has length \((3 - (-1)) \div 3 = 1\frac{1}{3}\). The mark 2 steps to the right of -1 is \((-1) + 2 \times 1\frac{1}{3} = 1\frac{2}{3}\). Counting one tick too few gives \(\frac{1}{3}\). Taking each step as 1 whole unit gives \(1\). Counting one tick too many gives \(3\).
Distance is the absolute value of the difference: \(|-5 - 12| = 17\). Subtracting in the wrong order and keeping the negative result gives \(-17\). Adding the two coordinates instead of subtracting them gives \(7\). Finding the point halfway between A and B instead of the distance gives \(3\frac{1}{2}\).