Fractions on a number line
Theory
On a number line, the space from \(0\) to \(1\) is split into equal gaps. The number of gaps is the denominator, and how many gaps the point is along is the numerator. Past \(1\), name the point with a mixed number.
The space from \(0\) to \(1\) is split into equal gaps. The number of gaps is the denominator.
Count how many gaps the point is along from \(0\); that count is the numerator.
Past \(1\), name the point with a mixed number: the whole number plus the fraction into the next gap, like \(1\dfrac{1}{4}\).
Work out the denominator from the number of equal gaps, then count the gaps to the point.
| Gaps to 1 | Counts in | 3 gaps along |
|---|---|---|
| \(4\) | quarters | \(\dfrac{3}{4}\) |
| \(5\) | fifths | \(\dfrac{3}{5}\) |
| \(6\) | sixths | \(\dfrac{3}{6}=\dfrac{1}{2}\) |
How to read a fraction on a number line
- Count the gaps between \(0\) and \(1\); that number is the denominator.
- Count how many gaps the point is along from \(0\); that is the numerator.
- Past one, write the whole number and the fraction as a mixed number.
Four gaps means quarters; three gaps along.
| point | \(=\) | \(\dfrac{3}{4}\) |
Five gaps means fifths; three gaps along.
| point | \(=\) | \(\dfrac{3}{5}\) |
\(\dfrac{2}{4}\) and \(\dfrac{1}{2}\) mark the same spot.
| point | \(=\) | \(\dfrac{2}{4}=\dfrac{1}{2}\) |
One whole plus one quarter.
| point | \(=\) | \(1\dfrac{1}{4}\) |
Common pitfalls
Frequently asked questions
How do you read a fraction on a number line?
Count the equal gaps between \(0\) and \(1\) for the denominator, then count how many gaps the point is along for the numerator.
Do you count ticks or gaps?
Count the gaps between ticks. Four ticks make three gaps, so a point can be \(\dfrac{3}{4}\) even with four marks.
How do you show a point past one?
Use a mixed number: the whole number reached, plus the fraction of the way into the next gap, such as \(1\dfrac{1}{4}\).
Can one point have two names?
Yes. \(\dfrac{2}{4}\) and \(\dfrac{1}{2}\) are the same point, because they are equivalent fractions.