Which Fraction is Equivalent to 1/3?
Fractions equivalent to 1/3 include 2/6, 3/9, 4/12, and 5/15. You make them by multiplying the top and bottom of 1/3 by the same number. This guide shows you the simple method and a full list of examples.
Equivalent fractions look different but have the same value. Knowing them helps with adding fractions, comparing sizes, and solving math problems. Here is how they work.
The Quick Answer
Here are some common fractions that equal 1/3.
| Multiply by | Equivalent Fraction |
|---|---|
| 2 | 2/6 |
| 3 | 3/9 |
| 4 | 4/12 |
| 5 | 5/15 |
| 10 | 10/30 |
Each of these fractions equals 1/3. They just use bigger numbers to show the same amount.
How to Find Fractions Equivalent to 1/3 (Step by Step)
Making an equivalent fraction takes just one simple rule. Here is how it works for 1/3.
- Pick any whole number. For example, choose 4.
- Multiply the top and bottom by that number. Multiply 1 × 4 = 4 and 3 × 4 = 12.
- Write your new fraction. You get 4/12, which equals 1/3.
So 4/12 is equivalent to 1/3. You can repeat this with any number to make endless equal fractions.
Why These Fractions Are Equal
An equivalent fraction has the same value, even though the numbers change. This works because you multiply the top and bottom by the same number, which is the same as multiplying by 1.
In the fraction 1/3, the top (1) is the numerator and the bottom (3) is the denominator. When you multiply both by 4, you scale the whole fraction evenly, so its value stays the same. For more on this, visit Khan Academy, a free and trusted math source.
Try It Yourself
Want to check equivalent fractions fast? Use our free Fraction Calculator for instant results. You can also see 1/3 as a percent or open our main Scientific Calculator.
Frequently Asked Questions
Is 2/6 equivalent to 1/3?
Yes. If you divide both the top and bottom of 2/6 by 2, you get 1/3. So 2/6 and 1/3 have the same value.
How many fractions are equivalent to 1/3?
There are endless equivalent fractions. You can multiply the top and bottom of 1/3 by any whole number to make a new one every time.
How do I know two fractions are equal?
Simplify both to their lowest form. If they reduce to the same fraction, they are equal. For example, 3/9 reduces to 1/3.
What is 1/3 as a percent?
1/3 as a percent is 33.33%. You divide 1 by 3 and multiply by 100. Read our full guide on 1/3 as a percent.
Final Answer
Fractions equivalent to 1/3 include 2/6, 3/9, 4/12, and 5/15. Just multiply the top and bottom by the same number. With this simple method, you can find endless fractions equal to 1/3.