How to solve it
- Divide each unit on the line into as many equal parts as the denominator says.
- Start at 0 and count as many marks as the numerator says.
- If the numerator is larger than the denominator, the mark falls after 1.
- Label the mark with the fraction.
1 = 3/3
0/3, 1/3, 2/3, 3/3, 4/3, 5/3
5/3 = 1 2/3
Result: 5/3 = 1 2/3
Common mistake:Wrong: 0 < 7/4 < 1.Right: 1 < 7/4 < 2.7/4 is greater than 4/4 = 1, so the mark falls between 1 and 2, not between 0 and 1.
Enter the values in the tool, choose the scale if you want to fix it, and select “Calculate”. The line draws each point with its label, and the ordered list appears below, for example 1. -2/3; 2. 1/2; 3. 7/4. If you would rather see a fraction as part of a whole, use visual fractions, which draws bars, circles and sets.
Worked example: 7/4 on a number line from 0 to 2
You want to place seven fourths between 0 and 2 with a tick mark at every fourth. Where does it land, and how many interior tick marks do you need?
- Split each unit into fourths. The denominator is 4, so from 0 to 1 there are four equal parts, and the same from 1 to 2.
- Count seven parts from 0. The numerator is 7: four fourths reach 1, and 3 more remain.
- Convert to a mixed number. 7/4 = 1 3/4, which is three fourths past 1.
- Count the tick marks. From 0 to 2 there are 8 parts, which leave 8 − 1 = 7 interior tick marks, or 2 × 4 − 1 in the general rule.
Result. 7/4 = 1 3/4, seven parts from 0 and one part before 2, with 7 interior tick marks on the scale.
Check. Seven fourths is 1.75 units, and the point sits between 1 and 2, closer to 2 than to 1.
8 parts of one fourth between 0 and 2: 7 interior tick marks and the point at the seventh
The method works for any positive fraction. With a negative fraction you count the same way, but to the left, and a mixed number is first converted to an improper fraction with improper fraction to mixed number.
How to count for each type of fraction
The procedure is always the same; only the direction and the starting point change. The table gathers the most common cases, each with a different example from the one above.
| Case | How to count | Example |
|---|---|---|
| Positive proper fraction | From 0 to the right, stopping before 1 | 3/5, three of five parts between 0 and 1 |
| Improper fraction | From 0 to the right, past 1 | 11/6 = 1 5/6, five sixths past 1 |
| Negative fraction | From 0 to the left | −5/3, five thirds to the left, two thirds past −1 |
| Mixed number | The whole part first, then the fraction | 2 1/3, one third past 2 |
What changes between rows is the side of 0 and how many whole units you cover before counting the leftover parts. Since 2 1/3 is seven thirds, you can also count seven thirds from 0 and land on the same point.
How to order points and measure distances
The point farthest to the right is the greatest. With −4/5 and −3/10, the second is closer to 0, so it is greater: −4/5 < −3/10, even though 4/5 is greater than 3/10.
The distance between two points is the greater minus the lesser. Between 1/6 and 5/6 the distance is 5/6 − 1/6 = 2/3, four spaces if the tick marks are at the sixths. To decide between two fractions without drawing, use compare fractions; to sort a long list, order fractions. To estimate a position before drawing, the guide to benchmark fractions uses 0, 1/2 and 1 as anchor points, and the guide to negative fractions explains the sign.
Which scale to choose
With both ends empty, the scale runs from the least to the greatest of your values, so the points at the extremes sit on the edge. If you fix the start and end, the start must be less and every value must fall inside. The position of each value is the share of the scale from the start up to it: on a scale from −1 to 2, the value 1/4 sits at (1/4 + 1)/3 = 5/12 of the length.
To see the fractions of one denominator, choose the tick marks with the rule above: from 0 to 1 with eighths you need 7 tick marks, and from 0 to 3 with fourths, 3 × 4 − 1 = 11. If two points look almost together, shrink the scale around them, for example from 0 to 1/10, because their spacing on screen depends on the interval you show.
The paper construction with a ruler and compass is in divide a segment into equal parts, and for practice with printable sheets there are the number line worksheets.
Sources
OpenStax, Prealgebra 2e, 4.1 Visualize Fractions: to locate fractions on a number line, divide the segment between 0 and 1 into as many equal parts as the denominator says (accessed October 17, 2026).
Frequently asked questions
Can I plot a repeating decimal on the number line?
Yes. Put the repeating block in parentheses: 0.(3) becomes the fraction 1/3 and is drawn exactly at that point. A terminating decimal like 0.333 is a different number, slightly less than 1/3, with its own point a little to the left.
Why do I get an error if I fill in only one end of the scale?
A scale needs a start and an end. If you fill in only one, the tool asks you to complete the other or leave both empty. It also reports an error if the start is not less than the end or if a value falls outside: 7/5 does not fit on a scale from 0 to 1.
What does the line look like if I enter a single value?
With the automatic scale, the line extends half a unit on each side so it has some length. With 5/8, it runs from 1/8 to 9/8 and the point sits in the middle. To compare two separate calculations, set the same start and the same end in both.
What happens if I enter two equivalent fractions?
They share one point. With 4/6 and 2/3 the line keeps both values, one on top of the other, and labels both with the reduced fraction 2/3. The text order lists them separately, so you can tell they were equivalent.