Fractions are numbers too
A fraction isn’t only part of a pizza. It’s also a number with its own place on the number line, just like 3 or 10. Placing fractions on a number line helps you compare them and see how they relate to whole numbers.
Making a fraction number line
- Draw a line and mark 0 and 1.
- Partition the space between 0 and 1 into equal intervals. The denominator tells you how many.
- Label each tick mark.
Fourths:
0 — 1/4 — 2/4 — 3/4 — 1
Each interval is 1/4 long. The point 3/4 is three intervals from 0.
Beyond 1
The pattern continues past 1:
0 — 1/3 — 2/3 — 3/3 — 4/3 — 5/3 — 6/3
Notice: 3/3 = 1 and 6/3 = 2. Points beyond 1 are improper fractions or mixed numbers: 4/3 = 1 1/3.
Equivalent fractions on the line
Draw lines for halves, quarters and eighths one above another, with 0 and 1 lined up:
| Halves | 0 | 1/2 | 1 | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Quarters | 0 | 1/4 | 2/4 | 3/4 | 1 | ||||
| Eighths | 0 | 1/8 | 2/8 | 3/8 | 4/8 | 5/8 | 6/8 | 7/8 | 1 |
1/2, 2/4 and 4/8 line up at the same point: they are equivalent fractions.
Comparing on the number line
A fraction further right is bigger. On the line above, 5/8 is right of 1/2, so 5/8 > 1/2.
Finding a fraction on an unmarked line
If a line runs from 0 to 1 with a point marked but no labels:
- Count the intervals between 0 and 1 → denominator.
- Count the intervals from 0 to the point → numerator.
Worked examples
Example 1: Where is 2/5 on a number line?
Split 0 to 1 into 5 equal intervals. Count 2 from 0.
Example 2: A line from 0 to 1 has 6 equal intervals. A point is at the 4th tick. What fraction?
4/6 (= 2/3).
Example 3: Where does 7/4 go?
Between 1 and 2: it’s 1 3/4, three quarters of the way from 1 to 2.
Common mistakes
- Counting tick marks instead of intervals. A line split into fourths has 5 tick marks (including 0 and 1) but 4 intervals.
- Unequal spacing, which makes fractions look wrong.
- Starting the count at 1 instead of at 0.
Try it yourself
- How many equal intervals are needed between 0 and 1 to show eighths?
- A point is 3 intervals from 0 on a line split into tenths. What fraction?
- Which is further right: 2/3 or 3/4?
- Between which two whole numbers is 11/4?
Answers: 1) 8 2) 3/10 3) 3/4 4) 2 and 3
Quick recap
- Fractions have places on the number line.
- The denominator sets how many equal intervals lie between 0 and 1.
- Equivalent fractions sit at the same point.