Fractions on a number line
Theory
A number line from \(0\) to \(1\) can be split into equal intervals. The number of intervals is the denominator; the number of intervals counted from \(0\) to a point is the numerator. This Year 5 maths page shows how to read and mark fractions this way, how the same point can have equivalent names, and how to read mixed numerals past \(1\).
An interval is the space between two tick marks next to each other. Count the intervals (the jumps), not the tick marks.
If \(0\) to \(1\) is cut into \(5\) equal intervals, each interval is \(\dfrac{1}{5}\). The point \(3\) intervals from \(0\) is \(\dfrac{3}{5}\).
One point can have several names. On a line cut into tenths, the point \(\dfrac{6}{10}\) is the same point as \(\dfrac{3}{5}\). The name with the smallest numbers is the simplest form.
Past \(1\), the intervals carry on. On a line cut into thirds, the point one third past \(2\) is the mixed numeral \(2\dfrac{1}{3}\), which is also the improper fraction \(\dfrac{7}{3}\).
Reading a point on a number line:
Denominator = the number of equal intervals from \(0\) to \(1\).
Numerator = the number of intervals counted from \(0\) to the point.
How to read a point
- Count the intervals between \(0\) and \(1\): this is the denominator.
- Count the intervals from \(0\) to the point: this is the numerator.
- Past 1? Write the whole number, then the extra intervals as a fraction.
- Simplify if the question asks for simplest form.
How to mark a fraction
- Split \(0\) to \(1\) into the number of intervals in the denominator.
- Count the numerator in intervals from \(0\) and mark the point.
| \(1 \div 7\) | \(=\) | \(\dfrac{1}{7}\) |
Each interval is \(\dfrac{1}{7}\).
| \(\text{intervals from } 0\) | \(=\) | \(3\) |
P is at \(\dfrac{3}{5}\).
| \(B\) | \(=\) | \(1\dfrac{1}{3} = \dfrac{4}{3}\) |
| \(C\) | \(=\) | \(2\dfrac{2}{3} = \dfrac{8}{3}\) |
B is \(1\dfrac{1}{3}\) or \(\dfrac{4}{3}\); C is \(2\dfrac{2}{3}\) or \(\dfrac{8}{3}\).
| \(\dfrac{6}{10}\) | \(=\) | \(\dfrac{3}{5}\) |
\(\dfrac{6}{10}\), which is \(\dfrac{3}{5}\) in simplest form.
| \(\dfrac{2}{5}\) | \(=\) | \(\dfrac{4}{10}\) |
\(\dfrac{2}{5} = \dfrac{4}{10}\), so it is \(4\) intervals from \(0\).
(i) Name it in tenths.
(ii) Name it in fifths.
| \(\dfrac{8}{10}\) | \(=\) | \(\dfrac{4}{5}\) |
(i) \(\dfrac{8}{10}\)
(ii) \(\dfrac{4}{5}\)
| \(\text{intervals}\) | \(=\) | \(3 - 1 = 2\) |
He counted the tick at \(0\). There are only \(2\) jumps, so the point is \(\dfrac{2}{5}\).
Common pitfalls
Frequently asked questions
How do you find the denominator on a number line?
Count the equal intervals between \(0\) and \(1\). Five intervals means fifths.
How do you find the numerator?
Count the intervals from 0 to the point.
Can two fractions be at the same point?
Yes. Equivalent fractions such as \(\dfrac{2}{5}\) and \(\dfrac{4}{10}\) are at the same point.
How do you read a point past 1?
Write the whole number you have passed, then the extra intervals as a fraction: \(2\dfrac{2}{3}\).
Why count intervals and not ticks?
A fraction measures distance from 0. Each interval is one equal part; the tick at 0 is the start, not a part.