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Primary - Stage 3 (Year 5 & 6) Stage 3 (Year 5 & 6) Fractions

Fractions on a number line

20 practice questions 0 video lessons Theory + worked examples
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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 \(1\dfrac{1}{4}\).

Number line from 0 to 1 in quarters with a point at three quarters A number line from 0 to 1 split into four equal gaps. Ticks are labelled 0, one quarter, two quarters, three quarters and 1. A red dot marks three quarters. 0 14 24 34 1 34
The line from \(0\) to \(1\) has \(4\) equal gaps, so it counts in quarters. The point is \(3\) gaps along: \(\dfrac{3}{4}\).

Work out the denominator from the number of equal gaps, then count the gaps to the point.

Gaps to 1Counts in3 gaps along
\(4\)quarters\(\dfrac{3}{4}\)
\(5\)fifths\(\dfrac{3}{5}\)
\(6\)sixths\(\dfrac{3}{6}=\dfrac{1}{2}\)
Count gaps, not ticks. Four ticks make three gaps; the point sits at a gap count.

How to read a fraction on a number line

  1. Count the gaps between \(0\) and \(1\); that number is the denominator.
  2. Count how many gaps the point is along from \(0\); that is the numerator.
  3. Past one, write the whole number and the fraction as a mixed number.
Example 1 — Read a point
A line from \(0\) to \(1\) has \(4\) gaps. A point sits \(3\) gaps along.
Solution

Four gaps means quarters; three gaps along.

point\(=\)\(\dfrac{3}{4}\)
Example 2 — Count carefully
A line to \(1\) has \(5\) gaps. A point is \(3\) gaps along.
Solution

Five gaps means fifths; three gaps along.

point\(=\)\(\dfrac{3}{5}\)
Example 3 — Same point, two names
A quarters line has a point \(2\) gaps along. Name it two ways.
Solution

\(\dfrac{2}{4}\) and \(\dfrac{1}{2}\) mark the same spot.

point\(=\)\(\dfrac{2}{4}=\dfrac{1}{2}\)
Example 4 — Past one
A quarters line has a point \(1\) whole and \(1\) gap more.
Solution

One whole plus one quarter.

point\(=\)\(1\dfrac{1}{4}\)

Common pitfalls

Count gaps, not ticks. Four ticks make three gaps; the point sits at a gap count, not a tick count.
The denominator is the number of parts. It comes from how many equal gaps fill one whole.
Past one, use a mixed number. A point beyond \(1\) is a whole number plus a fraction, like \(1\dfrac{1}{4}\).

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.