In plain words
Where is 2/5 on a number line?
2/5 is between 0 and 1, a little less than 1/2. To find it, split the space from 0 to 1 into 5 equal parts and count 2 parts from 0. A fraction is one number with one place on the line, even though it’s written with a 2 and a 5.
- The big idea
- A fraction is one number with its own place on the number line, so 2/5 sits two fifths of the way from 0 to 1.
- The common confusion
- A fraction is two separate whole numbers, so 2/5 belongs somewhere near 2 or 5 on the number line. It often sounds like this: “(two fifths) goes between the 2 and the 5 on the number line.”
Why it works
A fraction is written with two numbers, but it names one number. 2/5 isn’t a 2 and a 5. It’s the single amount you get from 2 of the 5 equal parts of one whole.
Because 2/5 is less than one whole, it belongs between 0 and 1 on the number line, nowhere near 2 or 5.
To find it, split the space from 0 to 1 into 5 equal parts and count 2 parts from 0. If you shade 2 of the 5 equal parts of a bar that stretches from 0 to 1, the shading ends at the same point.
Benchmarks help you check. Half of 5 is 2 and a half, so 2/5 is a little less than 1/2, and 4/5 is between 1/2 and 1, close to 1.
Every fraction has exactly one point on the number line, just as every whole number does, and that is what it means to say a fraction is a number.
A worked example
A jug has marks that split it into 5 equal parts from empty to full. Fill it to the second mark and it holds 2/5 of a jug, which is one amount and a little less than half full. It is not 2 jugs or 5 jugs, and it is less than 1 jug.
Why this confusion is so common
Until fractions come along, every number most of us know is a whole number, so when we see 2/5 it is natural to read two numbers and to look for it near 2 or 5. Many people have also met fractions mostly as shaded pictures, which show parts of shapes rather than a single amount. Placing fractions on a number line, linked to a bar, is how a fraction comes to feel like one number with a size.
Try this away from the screen
On a long strip of paper, draw a number line and mark 0 to 5 with equal gaps. Ask the learner to place sticky notes for 2/5, 4/5 and 5/5, then use a ruler to split the gap from 0 to 1 into 5 equal parts and check together.
Helpful things to say
| Instead of | Try |
|---|---|
| “The top number is 2 and the bottom number is 5.” | “If we split one whole into 5 equal parts and take 2, how much is that? More or less than one whole?” |
| “Read it as two over five.” | “Say ‘two fifths’, as one number, the way you would say ‘one half’.” |
Practice questions
These questions check the same idea with new numbers and new pictures. The best way to use them is one at a time, with pictures you can change and a reply to every answer. If you’d rather read them here, each answer stays hidden until you open it, so whoever is practicing can try first.
Try these questions one at a timeQuestion 1
Place (four fifths) on this number line.
Show the answer
To answer it, place the point at (four fifths). Half of 5 is 2 and a half, so (four fifths) is more than (one half). It’s only (one fifth) short of 1, which puts it between (one half) and 1 and close to 1.
Question 2
This bar is one whole, with 2 of its 6 equal parts shaded. Where does that amount belong on a number line?
The choices are “Between 0 and (one half)”, “Between (one half) and 1” and “Between 2 and 6”.
Show the answer
The answer is “Between 0 and (one half)”. The shaded amount is (two sixths) of one whole. That’s less than the (three sixths) that would make half, so it belongs between 0 and (one half).
Question 3
Which point shows (five sixths)?
Show the answer
The answer is “A”. (five sixths) is five of the six equal parts of one whole, so it’s less than 1 and sits just before 1. Points B and C treat the 5 and the 6 as if they were whole numbers.
Question 4
Which two whole numbers is (nine fourths) between?
The choices are “Between 2 and 3”, “Between 4 and 9” and “Between 0 and 1”.
Show the answer
The answer is “Between 2 and 3”. Four fourths make 1, and eight fourths make 2. (nine fourths) is one more fourth, so it’s between 2 and 3, at 2 (one fourth).
Questions people ask
Is 2/5 between 2 and 5 on a number line?
No. 2/5 is less than one whole, so it sits between 0 and 1. To find it, split the space from 0 to 1 into 5 equal parts and count 2 parts from 0.
Why is a fraction one number if it is written with two?
The two numbers work together to describe one amount. The denominator says what size the parts are, and the numerator says how many of them there are, so 2/5 is one amount, just as one half is.
How can you tell if a fraction is more or less than 1/2?
Compare the top number with half of the bottom number. Half of 5 is 2 and a half, so 2/5 is less than 1/2 and 3/5 is more.
What is the best way to show that fractions are numbers?
Use a number line. Shade part of a bar that stretches from 0 to 1 and mark where the shading ends, because that point is the fraction. Every fraction, including 5/5 and 7/4, has its own point.
Words to know
- Fraction
- A fraction is a number that describes equal parts of a whole, like 3/4 of a pizza. Every fraction also has its own spot on the number line.
- Number line
- A number line is a line where every point stands for a number, and fractions have their own places between the whole numbers.
- Benchmark fraction
- A benchmark fraction is a familiar fraction, like 1/2, that you can use as a landmark when you’re comparing other fractions.
Curriculum connections
We don’t assume any particular curriculum, but for teachers in the United States, here’s how this lesson lines up with the Common Core State Standards:
- 3.NF.A.2
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
- 3.NF.A.2.b
Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
Related lessons
Counting Spaces, Not Ticks
How do you find (three fourths) on a number line?
On a number line you count the spaces between the marks, starting from 0, rather than the marks themselves. · About 3 minutes
More Than One Whole
Can a fraction be bigger than 1?
Six fourths is a real amount: one whole made of four fourths, and then two fourths more. · About 3 minutes
The Bigger Numerator Trap
Which is bigger, (three eighths) or (two thirds)?
Even though 3/8 has the bigger top number, 2/3 is the bigger fraction, because thirds are much bigger pieces than eighths. · About 3 minutes
Compare Without Guessing
Which is bigger, (three eighths) or (four sevenths)?
When the numbers are all different, you can compare each fraction with one half instead of guessing. · About 4 minutes
If you’d rather read plain text, there’s a markdown version of this lesson.