Number line generator
Integers, decimals or fractions, with points, jumps and inequalities. Download it or print blank lines.
Range and ticks
Points and jumps
Inequality
How it reads what you type
- One letter (x, or any single letter) on its own, compared with numbers:
x > -2,4 ≥ x. - Signs:
<><=>=, or≤≥;=marks one point and≠(or!=) removes one. - A double inequality puts the letter in the middle with both signs pointing the same way:
-3 ≤ x < 4or4 > x ≥ -3. - Join up to 4 parts with
or(everything either part covers) or withand(only the overlap). Not both in one line. - Numbers can be whole, decimal (
-2.5), fractions (3/4) or mixed (1 1/2). - Every end must lie on the line as drawn. If an end is off the line, or anything cannot be read, the page says why and draws nothing rather than a wrong picture.
Print a sheet of 6 blank number lines
How to use it
- Type a start, an end and a step. Steps can be whole numbers, decimals (0.1, 0.25) or fractions (1/2 up to 1/12, or any denominator up to 1000). 0, 1, 1/8 gives 9 ticks: 0, 1/8, 1/4 … 1.
- Choose which ticks get a number. As many as fit skips labels when they would collide on a narrow screen; None leaves every tick blank for a worksheet.
- Turn Simplify fractions off to count in the step's own denominator (2/8, 4/8, 6/8), which is what most fraction lessons want before reducing.
- Add points such as
-2.5 A, 3/4 B, 4. Each sits exactly at its value and carries its label above it. - Add jumps such as
start at 3, add 4, subtract 6. Each jump is an arc with its size on top, and the sum is written underneath: 3 + 4 − 6 = 1. - Add an inequality such as
x < -1 or x ≥ 3. The line gets open and closed circles, the shaded rays or segments, and the interval notation (−∞, −1) ∪ [3, ∞). - Download a PNG (2400 px wide, white background) or an SVG to drop into a worksheet or slide, copy the image straight into a document, or print. The line you made stays on this device until you tap Clear.
What it cannot do
- Two variables. x + y > 3 needs a graph on a plane, not a line; the page says so instead of guessing.
- Absolute-value or quadratic inequalities. Rewrite them first: |x| < 3 is −3 < x < 3, and x² > 4 is x < −2 or x > 2. It does not solve algebra either, so type x > 2, not 2x + 1 > 5.
- More than 200 ticks. 0 to 1000 by 1 is refused; use a step of 10 or a shorter range.
- Irrational points such as √2 or π. Type a decimal like 1.414 instead; it is placed at that decimal.
- Thirds and other non-terminating fractions written as decimals are rounded to 3 places in the labels (0.333), though they are placed exactly.
- Nothing is uploaded. The line is drawn in this page, and what you type is kept only in this browser's storage.
Questions
When do you use an open circle and when a closed circle?
A closed (filled) circle means the number itself is included, which is what ≤ and ≥ say. An open (hollow) circle means it is left out, which is what < and > say. So −3 ≤ x < 4 has a closed circle at −3, an open circle at 4, and the line shaded between them. In interval notation a square bracket is the closed circle and a round bracket the open one: [−3, 4). Infinity always takes a round bracket, because no number reaches it.
How do you graph an "or" inequality such as x < −1 or x ≥ 3?
Graph each part on the same line. x < −1 is an open circle at −1 with the shading running left forever; x ≥ 3 is a closed circle at 3 with the shading running right. The answer is everything shaded by either part, written (−∞, −1) ∪ [3, ∞), where ∪ means "or". An "and" inequality keeps only the overlap: x > −2 and x ≤ 5 is the segment (−2, 5]. If two "and" parts never overlap, as in x < 1 and x > 2, nothing is shaded and the answer is the empty set ∅.
How do you put fractions on a number line?
Split each whole into as many equal parts as the denominator says and count along. For eighths from 0 to 1 there are 8 equal gaps and 9 ticks: 0, 1/8, 2/8, 3/8 … 8/8 = 1. In lowest terms 2/8 is 1/4, 4/8 is 1/2 and 6/8 is 3/4, which is why the simplify switch exists. Past 1, mixed numbers are easier to read: 0 to 3 in thirds runs 0, 1/3, 2/3, 1, 1 1/3 … 3.
How do you show addition and subtraction on a number line?
Put a dot at the starting number, then jump right to add and left to subtract, drawing an arc for each jump with its size on top. Start at 3, add 4 lands on 7; subtract 6 from there lands on 1, so 3 + 4 − 6 = 1. The same picture explains negatives: start at 2, subtract 4 crosses zero and lands on −2. Make sure the range covers every landing spot; with −5 to 5 the jump to 7 would fall off the line, and the page asks you to widen it.