# One Number, Not Two

> **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.

- 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.
- 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: “2/5 goes between the 2 and the 5 on the number line.”
- Family: [Fractions Have Size](https://slices.org/explore/fraction-size) (slice 10 of 20)
- [Try the lesson yourself](https://slices.org/slices/one-number-not-two): about 3 minutes, free, with no sign-in.

## In plain words

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 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 ways to talk about it

| Instead of saying | Try saying |
| --- | --- |
| “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

[Try these questions one at a time](https://slices.org/set?t=Practice%3A+One+Number%2C+Not+Two&q=s10-transfer-1%2Cs10-transfer-2%2Cs10-review-1%2Cs10-review-2), with pictures you can change and a reply to every answer.

1. Place 4/5 on this number line. **Answer:** place the point at 4/5. Half of 5 is 2 and a half, so 4/5 is more than 1/2. It’s only 1/5 short of 1, which puts it between 1/2 and 1 and close to 1.
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 1/2”, “Between 1/2 and 1” and “Between 2 and 6”. **Answer:** Between 0 and 1/2. The shaded amount is 2/6 of one whole. That’s less than the 3/6 that would make half, so it belongs between 0 and 1/2.
3. Which point shows 5/6? **Answer:** A. 5/6 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.
4. Which two whole numbers is 9/4 between? The choices are “Between 2 and 3”, “Between 4 and 9” and “Between 0 and 1”. **Answer:** Between 2 and 3. Four fourths make 1, and eight fourths make 2. 9/4 is one more fourth, so it’s between 2 and 3, at 2 1/4.

## 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.

## Curriculum connections (US Common Core)

- [3.NF.A.2](https://www.thecorestandards.org/Math/Content/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](https://www.thecorestandards.org/Math/Content/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.

## Words to know

- [Fraction](https://slices.org/glossary/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](https://slices.org/glossary/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](https://slices.org/glossary/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.

## Related slices

- [Counting Spaces, Not Ticks](https://slices.org/slices/counting-spaces-not-ticks): On a number line you count the spaces between the marks, starting from 0, rather than the marks themselves.
- [More Than One Whole](https://slices.org/slices/more-than-one-whole): Six fourths is a real amount: one whole made of four fourths, and then two fourths more.
- [The Bigger Numerator Trap](https://slices.org/slices/bigger-numerator-trap): Even though 3/8 has the bigger top number, 2/3 is the bigger fraction, because thirds are much bigger pieces than eighths.
- [Compare Without Guessing](https://slices.org/slices/compare-without-guessing): When the numbers are all different, you can compare each fraction with one half instead of guessing.