What Is Equivalent to 13/17 Fraction?

Equivalent fractions look different but stand for exactly the same value. This page explains what fractions are equivalent to 13/17, how to find them, and how to check your answer.

Understanding the fraction 13/17

13/17 means 13 parts out of 17 equal parts. If a chocolate bar is split into 17 equal pieces and you eat 13, you have eaten 13/17 of the bar.

Breaking down 13/17

13 (Numerator): how many parts are selected.
17 (Denominator): the total number of equal parts in the whole.

What are equivalent fractions?

Two fractions are equivalent when they represent the same portion, even though their numbers are different. You make one by multiplying or dividing both the top and bottom numbers by the same whole number.

Some fractions equivalent to 13/17 include: 26/34, 39/51, 52/68.

Equivalent fractions of 13/17

Multiply both the numerator and the denominator by the same number:

Multiply by	Equivalent fraction
2	26/34
3	39/51
4	52/68
5	65/85
6	78/102
7	91/119
8	104/136
9	117/153
10	130/170

How to find equivalent fractions, step by step

Step 1: Start with 13/17.

Step 2: Pick any whole number, for example 2.

Step 3: Multiply the top and the bottom by it: 13 × 2 = 26, and 17 × 2 = 34. So one equivalent fraction is 26/34.

You can repeat this with any whole number, so there are infinitely many equivalent fractions.

Why equivalent fractions are useful

Simplifying: A larger equivalent fraction can often be divided back down to 13/17.

Comparing: Two fractions are easier to compare once they share a denominator.

Adding and subtracting: Equivalent fractions let you rewrite fractions with a common denominator before you add or subtract them. For example, 13/17 + 1/34 becomes 26/34 + 1/34 = 27/34, because 13/17 and 26/34 are the same value.

Visual representation of 13/17

Picture a chocolate bar cut into equal pieces. Cutting it into 17 pieces and eating 13 gives 13/17. Cutting it into 34 pieces and eating 26 gives the same share, and cutting it into 51 pieces and eating 39 gives the same share again. The number of pieces changes, the share eaten does not.

13/17 as a decimal and a percent

Decimal: 13 ÷ 17 = 0.764706. Percent: 0.764706 × 100 = 76.47%. Every fraction equivalent to 13/17 has the same decimal and percent.

How to check two fractions are equivalent

Cross-multiply. For example, is 39/51 equivalent to 13/17? Check 13 × 51 = 663 and 17 × 39 = 663. The two products are equal, so yes, they are equivalent.

Common mistakes

Multiplying only one part. You must multiply both the numerator and the denominator by the same number.

Using different multipliers. If the top is multiplied by 2 and the bottom by 3, the value changes.

Real-life examples

Cooking: A recipe needing 13/17 cup can also be measured as 26/34 cup or 39/51 cup.

Time: 13/17 of an hour is 60 × 13/17 = 45.88 minutes, approximately.

Academic scores: Scoring 13 out of 17 marks means 76.47% marks.

Progress: Completing 13/17 of a project means about 76.47% of it is done.

More equivalent fractions of 13/17

There are infinitely many. A few larger ones are 143/187, 325/425, 650/850 and 1300/1700. Each one is made by multiplying both numbers by the same whole number, so each one still equals 13/17.

Learn more

For a video explanation of this topic, see Khan Academy: Equivalent fractions.