MathPractice
Fractions · Grade 3

Fractions on a number line

A fraction has a position on a number line. Find the unit, count equal spaces, and mark the distance from zero.

Grade 38 questions per setNo account needed
Practice 8 questions Download worksheet

US Letter PDF · A4 version · Answer key

What we’re working onLocate and name fractions on number lines from 0 to 1 and then from 0 to 2.

First page of the Fractions on a number line worksheet, with visible questions and room to work.Open worksheet PDF · 8 questions · US Letter
See how it works

Worked examples

Example 1

Count spaces from zero

The space from 0 to 1 is divided into six equal intervals. What number is four intervals to the right of 0?

  1. The distance from 0 to 1 is one whole.
  2. Each interval has length 1/6.
  3. Starting at 0, move four intervals: 1/6, 2/6, 3/6, 4/6.

4/6, which is also 2/3

Example 2

Go beyond one

Each whole unit on a number line is split into four equal intervals. Locate 5/4.

  1. Each interval has length 1/4.
  2. Four intervals reach 4/4, which is 1.
  3. One more interval reaches 5/4. It is between 1 and 2.

The first fourth-length interval after 1.

A question from this worksheet

Place a point at 3/4. The distance from 0 to 1 is one whole.

See the explanation

3/4

A is 3 spaces of 1/4 from zero: 3/4.

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Each set has eight questions. The online practice and prepared worksheet use the same questions.

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For the grown-up beside them

Help the thinking along.

A useful question

Where are 0 and 1? What distance does one small space represent?

What to look for

The learner counts intervals from zero and keeps each whole unit the same length beyond 1.

A common sticking point

Counting the mark at zero as the first fractional step.

Help without giving the answer

Trace the first space from 0 with a finger. Label its length, then count spaces rather than marks.

Keep the words clear

Words in this skill.

number line
A line that shows numbers at positions with a consistent scale.
unit interval
The distance from 0 to 1; one whole unit.
interval
The space between two positions on the line.
equivalent fractions
Different fraction names for the same number.

What these sets cover.

  • Begin on 0 to 1; extend to 0 to 2 after the unit is clear.
  • Use denominators 2, 3, 4, 6, and 8.
  • Equivalent names are accepted unless a particular denominator is explicitly requested.

Common questions

Why do four equal spaces need five marks?

The marks show both ends of each space. Include 0 and 1: four spaces have five boundary marks.

Can a fraction be greater than 1?

Yes. Once you have counted all the fractional parts in one whole, keep going with parts of the same size.

Try next

Whole numbers as fractions

Next, see why whole numbers can also be written as fractions.

Explore this skill

Related standards: 3.NF.2. These materials focus on this skill, not every part of a grade-level curriculum. How we check materials.