Fractions on a number line
Split the space from 0 to 1 into equal parts, then count the parts from 0. That count is the top number. Quiz for kids, parent help below.
🧒 Kids: find fractions on the line!
Count the jumps from 0 to the red dot. Then try the quiz!
💡 Trick: The line from 0 to 1 is cut into 4 parts. The dot is 3 parts along. That’s 3/4!
More fractions: Halves and quarters · Unit fractions · Number line · Fractions of a set · Fraction of a number · Fractions as division
This part is for grown-ups: the key idea, pictures to draw, what to say, common mistakes, questions with answers and a free worksheet.
The trick: count the parts from 0
On a number line, a fraction is a distance from 0. First look at how many equal parts the space from 0 to 1 is split into: that is the bottom number. Then count how many parts the point is from 0: that is the top number. This works past 1 too. If each whole is split into 3 parts and the point is 4 parts from 0, it is at 4/3, which is one whole and one more third.
- 4 parts, dot 1 along: 1/4
- 8 parts, dot 5 along: 5/8
- 3 parts per whole, dot 3 along: 3/3, which is 1
- 2 parts per whole, dot 5 along: 5/2, which is 2 and a half
Patterns to spot
- 0 is always 0/d and 1 is always d/d: 4/4 = 1.
- 2 is 2d/d: with thirds, 2 = 6/3.
- Fractions with the same bottom number are evenly spaced.
- 1/2 is always in the middle of 0 and 1, and 2/4, 3/6 and 4/8 sit at the same point.
- Fractions to the right are bigger: 5/8 is right of 3/8.
- A fraction with a top number bigger than the bottom is past 1.
See it: pictures to draw with your child
Draw these on paper or a whiteboard. A quick sketch makes the idea concrete before any rules.
What your child already knows
Children already know whole-number lines from counting and adding. The fraction line is the same line with the spaces between whole numbers cut into equal parts. Grade 3 is the first time fractions are treated as numbers with their own place on the line, not just pieces of a shape, and that idea makes comparing and adding fractions much easier later.
In real life: A ruler is a number line in inches or centimetres: half an inch, a quarter inch. A measuring cup has fraction marks. Distances on a walk can be split into halves and quarters: “We are 3/4 of the way to school.”
Worked examples
Example 1: Name the point
- The line from 0 to 1 is split into 5 equal parts.
- The dot is on the 2nd mark.
- So the dot is at 2/5.
Example 2: Place 3/8
- Split 0 to 1 into 8 equal parts.
- Count 3 parts from 0 and draw the dot there.
Example 3: Past 1: 7/4
- With quarters, 4/4 is at 1.
- Count 3 more quarters past 1.
- So 7/4 is between 1 and 2, three quarters of the way: 1 3/4.
Common mistakes
What to say to your child
A short script for your first session. Pause after each line and let your child answer.
- “Here is a line from 0 to 1. Let’s cut it into 4 equal jumps.”
- “Each jump is one quarter. The first mark is 1/4.”
- “What is the next mark?” (2/4.) “And the next?” (3/4.)
- “What is at the end?” (4/4, which is 1.)
- “If we keep jumping, what comes after 1?” (5/4!)
Questions to try (answers below)
Ask these out loud or write them down. The last one is a stretch.
- 0 to 1 in 4 parts; the dot is 1 part along
- 0 to 1 in 6 parts; the dot is 5 parts along
- Where is 4/4?
- Where is 0/3?
- Which is further from 0: 3/8 or 5/8?
- Which point is the same as 1/2 on an eighths line?
- Thirds; the dot is 4 parts along
- How many halves are there from 0 to 3?
- Stretch: where is 9/4?
Show the answers
- 1/4
- 5/6
- At 1
- At 0
- 5/8
- 4/8
- 4/3 (1 1/3)
- 6
- Between 2 and 3: 2 1/4
Games to play at home
Ruler fractions
Find 1/2, 1/4 and 3/4 of an inch on a ruler.
Hopscotch line
Chalk a line from 0 to 1 in quarters and hop to the fraction called out.
Walk it
On a short walk, say when you are 1/4, 1/2 and 3/4 of the way.
A 5-day plan for fractions on a number line
Ten minutes a day is enough. Short, regular practice works far better than one long session.
- Day 1: Learn it with real things: paper, snacks, counters or a ruler, like the pictures above.
- Day 2: Read the script together, then ask the first four questions.
- Day 3: Do the quiz at the top of the page and read the hints for anything missed.
- Day 4: Play one of the games above for ten minutes.
- Day 5: Ask the rest of the questions, then do a round of the matching fraction practice skill.
By grade
Grade 3 (Common Core 3.NF.A.2) understands a fraction as a number on the number line and marks fractions with the right spacing. 3.NF.A.3 uses the number line to find equivalent fractions and compare. Grade 4 extends this to fractions greater than 1. In India, number lines with fractions appear in class 4 and class 5 maths.
More for each grade: Grade 3 math and the CBSE class 3 maths guide.
What comes next
Use the line to compare fractions and find equivalent fractions. Fractions past 1 lead to improper fractions and mixed numbers, and the fraction calculator converts them step by step.
Worksheet and more practice
Print a free worksheet with an answer key, or keep practicing online with fraction practice.
Fractions on a number line
Comparing fractionsMore: fractions for kids · fraction wall · fraction calculator · fractions quiz · fraction levels · fraction games · fractions chart
Last reviewed
Questions parents ask
How do you find a fraction on a number line?
Count how many equal parts 0 to 1 is split into (the bottom number), then count how many parts the point is from 0 (the top number).
How do you show fractions bigger than 1 on a number line?
Keep the same size parts past 1. With quarters, 5/4 is one part past 1.
Why use a number line for fractions?
It shows that a fraction is a number, with a place between whole numbers, and makes comparing and equivalent fractions easy to see.
Where is 1/2 on a number line?
Exactly half-way between 0 and 1. 2/4, 3/6 and 4/8 are at the same point.
What grade learns fractions on a number line?
Grade 3 (Common Core 3.NF.A.2), with fractions greater than 1 in grades 3 and 4.