Equivalent fractions of 2/9 are 4/18, 6/27, 8/36, 10/45 and 12/54. Multiply the top and bottom of 2/9 by the same number to get any of them. 2/9 is already in simplest form, so no smaller equivalent fraction exists. This page lists the equivalent fractions of 2/9, shows how to find and check them, and includes a diagram, examples, practice problems with answers and an FAQ.
In this guide
What Is Equivalent to 2/9? Quick Answer
| Item | Answer |
|---|---|
| Fraction | 2/9 (two ninths) |
| Equivalent fractions | 4/18, 6/27, 8/36, 10/45, 12/54, and so on |
| Simplest form | 2/9 (already simplest) |
| Decimal value | 0.222222… (about 0.2222) |
| Percent value | 22 2/9% (about 22.22%) |
| How many are there? | Infinitely many: one for every whole number multiplier |
How to Find Equivalent Fractions of 2/9
Two fractions are equivalent when they name the same amount. The rule is simple: multiply the numerator and the denominator by the same non-zero number. This keeps the value the same, because multiplying the top and bottom by 2, for example, is just multiplying 2/9 by 2/2, which equals 1.
- Pick a whole number to multiply by, such as 2.
- Multiply the numerator: 2 × 2 = 4.
- Multiply the denominator: 9 × 2 = 18.
- Write the new fraction: 4/18, which is equivalent to 2/9.
Repeat with 3, 4, 5 and so on to get more. Notice that the multiplication happens on both numbers. Changing only one of them changes the value.
In short: To find an equivalent fraction of 2/9, multiply 2 and 9 by the same number, for example 2/9 = 4/18.
List of Equivalent Fractions of 2/9
This table shows 2/9 multiplied by every whole number from 2 to 10. Each row is equivalent to 2/9 and has the same decimal value, 0.222222….
| Multiplier | Working | Equivalent fraction |
|---|---|---|
| × 2 | (2 × 2) / (9 × 2) | 4/18 |
| × 3 | (2 × 3) / (9 × 3) | 6/27 |
| × 4 | (2 × 4) / (9 × 4) | 8/36 |
| × 5 | (2 × 5) / (9 × 5) | 10/45 |
| × 6 | (2 × 6) / (9 × 6) | 12/54 |
| × 7 | (2 × 7) / (9 × 7) | 14/63 |
| × 8 | (2 × 8) / (9 × 8) | 16/72 |
| × 9 | (2 × 9) / (9 × 9) | 18/81 |
| × 10 | (2 × 10) / (9 × 10) | 20/90 |
Diagram: 2/9 and Its Equivalent Fractions
A picture shows why the fractions are equal. Each bar below has the same length. Cutting it into more, smaller pieces changes how many pieces are shaded, but never how much of the bar is shaded.
In short: Equivalent fractions shade the same amount of the same bar, even though the number of pieces changes.
Is 2/9 in Simplest Form?
Yes. A fraction is in simplest form when the numerator and denominator share no common factor except 1. The factors of 2 are 1, 2. The factors of 9 are 1, 3, 9. The only common factor is 1, so the greatest common factor (GCF) of 2 and 9 is 1 and 2/9 cannot be simplified.
That means 2/9 is the smallest member of its family. Every other equivalent fraction, such as 4/18 or 8/36, is a bigger version of 2/9. Dividing the top and bottom of 8/36 by 4 takes you straight back to 2/9.
How to Check if a Fraction Is Equivalent to 2/9
Use cross-multiplication. Two fractions a/b and c/e are equivalent when a × e = b × c.
Example: Is 6/27 equivalent to 2/9? Multiply across: 2 × 27 = 54 and 9 × 6 = 54. Both products are 54, so yes.
Example: Is 3/10 equivalent to 2/9? Multiply across: 2 × 10 = 20 and 9 × 3 = 27. The products differ, so no. Adding 1 to both numbers does not keep the value.
You can also divide: if the numerator of the new fraction divided by 2 gives the same whole number as the denominator divided by 9, the fractions are equivalent.
In short: a/b and c/e are equivalent when a × e = b × c.
Find the Missing Number in an Equivalent Fraction
A common homework question is 2/9 = ?/36. Work out what the denominator was multiplied by: 36 ÷ 9 = 4. Do the same to the numerator: 2 × 4 = 8. So 2/9 = 8/36.
Or, going the other way: 2/9 = 10/? has the numerator multiplied by 10 ÷ 2 = 5, so the missing denominator is 9 × 5 = 45.
2/9 and Its Equivalent Fractions as a Decimal and Percent
Every equivalent fraction of 2/9 has the same decimal and percent value: 2/9 = 4/18 = 0.222222… = 22 2/9% (about 22.22%). To get the decimal, divide 2 by 9.
Examples With 2/9
Example: A class has 27 students and 2/9 of them walk to school. The equivalent fraction 6/27 tells you the answer directly: 6 students.
Example: Express 2/9 with a denominator of 90. Multiply by 10: 2 × 10 = 20, 9 × 10 = 90. So 2/9 = 20/90.
Example: Write 10/45 in simplest form. Divide the top and bottom by the GCF, 5: 2/9.
Equivalent fractions are what let you add and compare fractions with different denominators. To add 2/9 to another fraction, you rewrite it with a common denominator, which means finding an equivalent fraction. For percentages, see how to calculate a percentage.
Common Mistakes With Equivalent Fractions of 2/9
- Adding instead of multiplying. Adding 2 to both numbers gives 4/11, which is not equal to 2/9. Equivalent fractions come from multiplication or division only.
- Multiplying only one number. Doubling the top but not the bottom turns 2/9 into 4/9, which is a different value.
- Using different multipliers. 2 × 2 and 9 × 3 give 4/27, which is not equivalent to 2/9.
- Thinking 2/9 can be simplified. The GCF of 2 and 9 is 1, so 2/9 is already in simplest form.
Equivalent Fractions of 2/9: Practice Problems (With Answers)
1. Write three equivalent fractions of 2/9.
4/18, 6/27, 8/36. Multiply the top and bottom by 2, 3 and 4.
2. Fill in the blank: 2/9 = ?/54.
12. 54 ÷ 9 = 6, and 2 × 6 = 12.
3. Is 14/63 equivalent to 2/9?
Yes. Both numbers were multiplied by 7. Check: 2 × 63 = 9 × 14 = 126.
4. Is 5/12 equivalent to 2/9?
No. 2 × 12 = 24 but 9 × 5 = 45. The products are different.
5. Simplify 18/81.
2/9. Divide the top and bottom by 9.
Equivalent Fractions of 2/9: FAQ
What is equivalent to 2/9?
Any fraction made by multiplying the top and bottom of 2/9 by the same number is equivalent to it. Examples are 4/18, 6/27 and 8/36.
What is the simplest form of 2/9?
2/9 is already in simplest form, because 2 and 9 have no common factor other than 1.
How many equivalent fractions does 2/9 have?
Infinitely many. You can multiply the numerator and denominator by 2, 3, 4 and so on without end, and every result equals 2/9.
How do you check that two fractions are equivalent to 2/9?
Cross-multiply. For example, 4/18 is equivalent to 2/9 because 2 × 18 = 36 and 9 × 4 = 36.
What is 2/9 as a decimal?
2/9 as a decimal is 0.222222… (about 0.2222). Every equivalent fraction has the same decimal.
Sources and Further Reading
- Math is Fun, Equivalent Fractions.
- Math is Fun, Simplifying Fractions.
- OpenStax, Prealgebra 2e, Section 4.2: Multiply and Divide Fractions (the Equivalent Fractions Property and simplifying), Rice University.
Related: equivalent fractions of 8/9, equivalent fractions of 7/9, equivalent fractions of 2/3. Read the full guide to equivalent fractions, try the equivalent fractions calculator and browse all equivalent fraction guides. Every value on this page was checked by exact arithmetic.
Related: turn any fraction into a percent with the percentage calculator, or read the percentages and decimals guides.
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