Equivalent fractions of 13/17 are 26/34, 39/51, 52/68, 65/85 and 78/102. Multiply the top and bottom of 13/17 by the same number to get any of them. 13/17 is already in simplest form, so no smaller equivalent fraction exists. This page lists the equivalent fractions of 13/17, 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 13/17? Quick Answer
| Item | Answer |
|---|---|
| Fraction | 13/17 (thirteen seventeenths) |
| Equivalent fractions | 26/34, 39/51, 52/68, 65/85, 78/102, and so on |
| Simplest form | 13/17 (already simplest) |
| Decimal value | 0.76470588235294117… (about 0.7647) |
| Percent value | 76 8/17% (about 76.47%) |
| How many are there? | Infinitely many: one for every whole number multiplier |
How to Find Equivalent Fractions of 13/17
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 13/17 by 2/2, which equals 1.
- Pick a whole number to multiply by, such as 2.
- Multiply the numerator: 13 × 2 = 26.
- Multiply the denominator: 17 × 2 = 34.
- Write the new fraction: 26/34, which is equivalent to 13/17.
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 13/17, multiply 13 and 17 by the same number, for example 13/17 = 26/34.
List of Equivalent Fractions of 13/17
This table shows 13/17 multiplied by every whole number from 2 to 10. Each row is equivalent to 13/17 and has the same decimal value, 0.76470588235294117….
| Multiplier | Working | Equivalent fraction |
|---|---|---|
| × 2 | (13 × 2) / (17 × 2) | 26/34 |
| × 3 | (13 × 3) / (17 × 3) | 39/51 |
| × 4 | (13 × 4) / (17 × 4) | 52/68 |
| × 5 | (13 × 5) / (17 × 5) | 65/85 |
| × 6 | (13 × 6) / (17 × 6) | 78/102 |
| × 7 | (13 × 7) / (17 × 7) | 91/119 |
| × 8 | (13 × 8) / (17 × 8) | 104/136 |
| × 9 | (13 × 9) / (17 × 9) | 117/153 |
| × 10 | (13 × 10) / (17 × 10) | 130/170 |
Diagram: 13/17 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 13/17 in Simplest Form?
Yes. A fraction is in simplest form when the numerator and denominator share no common factor except 1. The factors of 13 are 1, 13. The factors of 17 are 1, 17. The only common factor is 1, so the greatest common factor (GCF) of 13 and 17 is 1 and 13/17 cannot be simplified.
That means 13/17 is the smallest member of its family. Every other equivalent fraction, such as 26/34 or 52/68, is a bigger version of 13/17. Dividing the top and bottom of 52/68 by 4 takes you straight back to 13/17.
How to Check if a Fraction Is Equivalent to 13/17
Use cross-multiplication. Two fractions a/b and c/e are equivalent when a × e = b × c.
Example: Is 39/51 equivalent to 13/17? Multiply across: 13 × 51 = 663 and 17 × 39 = 663. Both products are 663, so yes.
Example: Is 14/18 equivalent to 13/17? Multiply across: 13 × 18 = 234 and 17 × 14 = 238. 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 13 gives the same whole number as the denominator divided by 17, 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 13/17 = ?/68. Work out what the denominator was multiplied by: 68 ÷ 17 = 4. Do the same to the numerator: 13 × 4 = 52. So 13/17 = 52/68.
Or, going the other way: 13/17 = 65/? has the numerator multiplied by 65 ÷ 13 = 5, so the missing denominator is 17 × 5 = 85.
13/17 and Its Equivalent Fractions as a Decimal and Percent
Every equivalent fraction of 13/17 has the same decimal and percent value: 13/17 = 26/34 = 0.76470588235294117… = 76 8/17% (about 76.47%). To get the decimal, divide 13 by 17.
Examples With 13/17
Example: A class has 51 students and 13/17 of them walk to school. The equivalent fraction 39/51 tells you the answer directly: 39 students.
Example: Express 13/17 with a denominator of 170. Multiply by 10: 13 × 10 = 130, 17 × 10 = 170. So 13/17 = 130/170.
Example: Write 65/85 in simplest form. Divide the top and bottom by the GCF, 5: 13/17.
Equivalent fractions are what let you add and compare fractions with different denominators. To add 13/17 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 13/17
- Adding instead of multiplying. Adding 2 to both numbers gives 15/19, which is not equal to 13/17. Equivalent fractions come from multiplication or division only.
- Multiplying only one number. Doubling the top but not the bottom turns 13/17 into 26/17, which is a different value.
- Using different multipliers. 13 × 2 and 17 × 3 give 26/51, which is not equivalent to 13/17.
- Thinking 13/17 can be simplified. The GCF of 13 and 17 is 1, so 13/17 is already in simplest form.
Equivalent Fractions of 13/17: Practice Problems (With Answers)
1. Write three equivalent fractions of 13/17.
26/34, 39/51, 52/68. Multiply the top and bottom by 2, 3 and 4.
2. Fill in the blank: 13/17 = ?/102.
78. 102 ÷ 17 = 6, and 13 × 6 = 78.
3. Is 91/119 equivalent to 13/17?
Yes. Both numbers were multiplied by 7. Check: 13 × 119 = 17 × 91 = 1547.
4. Is 16/20 equivalent to 13/17?
No. 13 × 20 = 260 but 17 × 16 = 272. The products are different.
5. Simplify 117/153.
13/17. Divide the top and bottom by 9.
Equivalent Fractions of 13/17: FAQ
What is equivalent to 13/17?
Any fraction made by multiplying the top and bottom of 13/17 by the same number is equivalent to it. Examples are 26/34, 39/51 and 52/68.
What is the simplest form of 13/17?
13/17 is already in simplest form, because 13 and 17 have no common factor other than 1.
How many equivalent fractions does 13/17 have?
Infinitely many. You can multiply the numerator and denominator by 2, 3, 4 and so on without end, and every result equals 13/17.
How do you check that two fractions are equivalent to 13/17?
Cross-multiply. For example, 26/34 is equivalent to 13/17 because 13 × 34 = 442 and 17 × 26 = 442.
What is 13/17 as a decimal?
13/17 as a decimal is 0.76470588235294117… (about 0.7647). 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 11/17. 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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