A number line turns fractions into distances, which makes their sizes easy to compare: a fraction is simply a point between two whole numbers. This tool draws a number line divided into any denominator from 2 to 16, can add a second line with a different denominator for comparison, and marks any fraction you choose.
How to use the number line tool
- Choose how many parts to divide each whole into — halves, thirds, fourths, up to sixteenths.
- Optionally pick a second line with another denominator to compare the two sets of marks.
- Set where the line starts and ends. Negative numbers are allowed, and up to 6 whole units can be shown at once.
- Choose the labels: fractions as counted (2/4, 4/4, 6/4), simplified fractions (1/2, 1, 3/2) or decimals (0.5, 1, 1.5).
- Optionally mark a fraction such as 5/8 or 1 3/8. It is drawn as a red point across both lines, and the tape says which marks it falls on or between.
When the marks get too close together to label them all — sixteenths across six units, for example — only every few marks are labeled, so the text never overlaps.
How a fraction number line is built
Each whole unit is split into d equal steps of size 1/d. The mark after k steps from 0 is k/d. After d steps you reach 1, after 2d steps you reach 2, and so on. Steps to the left of 0 are negative fractions.
Worked example: fourths and eighths from 0 to 2
- The fourths line has marks at 0, 1/4, 2/4, 3/4, 4/4 (= 1), 5/4, … , 8/4 (= 2).
- The eighths line has twice as many marks: 1/8, 2/8, … , 16/8.
- Every fourths mark lines up with an eighths mark: 1/4 = 2/8, 2/4 = 4/8, 3/4 = 6/8. Since GCF(4, 8) = 4, the marks coincide every 1/4 of a whole.
- Mark 1 3/8: on the eighths line it is the 11th mark (11/8). On the fourths line it falls between 5/4 and 6/4 — halfway, because 5/4 = 10/8 and 6/4 = 12/8.
What number lines teach
- Size of pieces: with more parts, each piece is smaller, so 1/8 < 1/4 even though 8 > 4.
- Equivalent fractions: marks that line up across two lines are equal, the visual form of equivalent fractions.
- Comparing and ordering: the fraction farther right is larger, which is how the ordering fractions calculator arranges a list.
- Benchmarks: you can see at a glance whether a fraction is near 0, 1/2 or 1 — the skill behind estimating fractions.
- Improper fractions: 5/4 is clearly past 1, which makes the link to the mixed number 1 1/4 concrete.
Lines that share marks
Two lines with denominators a and b have marks that coincide every 1/GCF(a, b) of a whole. Thirds and sixths meet every 1/3; fourths and sixths meet every 1/2; thirds and fourths meet only at whole numbers. To compare any two marks exactly, rename both over the least common denominator — 12 for thirds and fourths.
For decimal equivalents of every fraction up to 64ths, see the fraction to decimal chart.
Frequently asked questions
How do you place a fraction on a number line?
Divide each whole unit into as many equal parts as the denominator, then count that many parts given by the numerator from 0. To place 3/4, split the space from 0 to 1 into 4 equal parts and count 3 of them.
How do I show a mixed number on a number line?
Move to the whole number first, then count the fraction part within the next unit. 1 3/8 is 1 whole plus 3 of the 8 equal parts between 1 and 2, the same point as 11/8.
How does a number line show equivalent fractions?
Draw two lines with different denominators one above the other. Marks that line up name the same number: on fourths and eighths lines, 1/4 sits directly above 2/8 and 3/4 above 6/8.
What if the fraction does not land on a mark?
It falls between two marks. 1 3/8 on a line marked in fourths lies between 5/4 and 6/4. Adding a second line in eighths shows its exact position, because 1 3/8 = 11/8.