3/4 × 2/2 = 6/8
The numerator and denominator both double, so the fraction keeps the same value.
Common fraction reference
Equivalent Fractions Chart
Use this equivalent fractions chart to find common equivalent fractions quickly. Each row names the same amount in a different way, and the fraction bars show why the value stays unchanged.
Quick lookup
Common equivalent fractions at a glance
| Fraction | Equivalent fractions |
|---|---|
| 1/4 | 2/8 · 3/12 · 4/16 |
| 1/6 | 2/12 · 3/18 · 4/24 |
| 3/8 | 6/16 · 9/24 · 12/32 |
| 3/4 | 6/8 · 9/12 · 12/16 |
| 4/6 | 2/3 · 6/9 · 8/12 |
Read the dot-separated forms as alternate names for the fraction in the first column. The examples below add the visual proof.
The rule behind the table
How to read an equivalent fractions chart
Move from left to right and look for the same multiplier on top and bottom. For example, 3/4 becomes 6/8 when both numbers are multiplied by 2. The number of pieces changes, but the shaded amount does not.
4/6 ÷ 2/2 = 2/3
Dividing both numbers by the same factor reveals a simpler name for the same amount.
Visual reference
Five equivalent fraction families
Each family below has the same shaded endpoint. More pieces do not automatically mean more of the whole; each piece simply becomes smaller.
Quarter family
1/4 = 2/8 = 3/12 = 4/16
Each fourth is split into smaller equal pieces. The shaded part still covers one quarter of the whole.
1/4
2/8
3/12
Simplest form: 1/4. Every bar above reaches the same endpoint.
Learn what is equivalent to 1/4 →Sixth family
1/6 = 2/12 = 3/18 = 4/24
The whole is divided into more equal shares, so the numerator grows with the denominator to keep the same value.
1/6
2/12
3/18
Simplest form: 1/6. Every bar above reaches the same endpoint.
Three-eighths family
3/8 = 6/16 = 9/24 = 12/32
Three eighths can be renamed with six sixteenths, nine twenty-fourths, or twelve thirty-seconds.
3/8
6/16
9/24
Simplest form: 3/8. Every bar above reaches the same endpoint.
Three-fourths family
3/4 = 6/8 = 9/12 = 12/16
All four names reach the same three-quarter point, even though each bar has a different number of pieces.
3/4
6/8
9/12
Simplest form: 3/4. Every bar above reaches the same endpoint.
See two equivalent fractions for 3/4 →Four-sixths family
4/6 = 2/3 = 6/9 = 8/12
Dividing 4/6 by 2/2 reveals the simplest name, 2/3. Multiplying 2/3 by 3/3 or 4/4 creates the other forms.
4/6
2/3
6/9
Simplest form: 2/3. Every bar above reaches the same endpoint.
Learn why 4/6 = 2/3 →Jump to a group
Quick lookup by fraction family
A useful non-example
Not every larger denominator makes an equivalent fraction
Changing only the denominator changes the size of each part without counting more shaded parts.
1/2 and 1/4 are not equivalent
1/2
1/4
The second bar stops earlier, so the two fractions name different amounts.
Common questions
Equivalent Fractions Chart FAQ
Find your fraction in the first column, then read across the row to see other names for the same value. The fraction bars below the chart show why the shaded amount stays the same.