Equivalent Fractions of 2/3 (List and Method)
Updated · By the SolverCalc team
Quick answer
2/3 = 4/6 = 6/9 = 8/12 = 10/15 = 12/18 = 14/21 = 16/24 …
Equivalent fractions name the same amount using different numbers. Two thirds of a pizza is the same as four sixths or six ninths—the slices are just cut differently. This page lists the equivalent fractions of 2/3 and shows how to find as many as you need.
The rule: multiply the top and bottom by the same number
- Pick any whole number greater than 1, for example 4.
- Multiply the numerator: 2 × 4 = 8.
- Multiply the denominator: 3 × 4 = 12.
- The new fraction 8/12 is equivalent to 2/3.
This works because multiplying by 4/4 is the same as multiplying by 1, and multiplying by 1 never changes a value.
List of fractions equivalent to 2/3
| Multiply by | Equivalent fraction |
|---|---|
| 2 | 4/6 |
| 3 | 6/9 |
| 4 | 8/12 |
| 5 | 10/15 |
| 6 | 12/18 |
| 7 | 14/21 |
| 8 | 16/24 |
| 9 | 18/27 |
| 10 | 20/30 |
How to check if a fraction equals 2/3
Use cross-multiplication. To test 14/21, multiply 2 × 21 = 42 and 3 × 14 = 42. The products match, so the fractions are equivalent. To test 10/16, multiply 2 × 16 = 32 and 3 × 10 = 30. The products differ, so 10/16 is not equal to 2/3.
You can also divide: every fraction equal to 2/3 gives 0.6666… on a calculator, or about 66.67%.
Finding a missing number
Problems often ask you to fill a blank, such as 2/3 = ?/27. Since 3 × 9 = 27, multiply the top by 9 as well: 2 × 9 = 18. The answer is 18/27. For 2/3 = 20/?, notice 2 × 10 = 20, so the denominator is 3 × 10 = 30.
2/3 as a decimal and percentage
Dividing 2 by 3 gives 0.6666…, a repeating decimal written 0.6̅. Multiplying by 100 gives about 66.67%. Every fraction in the list above produces exactly the same decimal, which is another quick way to confirm that they are equivalent.