What is 2/5 equivalent to as a fraction?

Two frations are equivalent when they have the same value when written in lowest terms. The fraction 4/10 is equal to 2/5 when reduced to lowest terms. To find equivalent fractions, just multiply the numerator and denominator of that reduced fraction (2/5) by any interger number, ie, multiply by 2, 3, 10, 30 ...

• 4/10 is equivalent to 2/5 because 2 x 2 = 4 and 5 x 2 = 10
• 6/15 is equivalent to 2/5 because 2 x 3 = 6 and 5 x 3 = 15
• 8/20 is equivalent to 2/5 because 2 x 3 = 8 and 5 x 3 = 20

Equivalent fractions may look different, but when you reduce then to the lowest terms you will get the same value. If any fraction is not reduced to lowest terms, you can get other equivalent fractions just dividing both numerator and denominator by the same number.

Just use this Rule:

Two fractions are equivalent if we

1) multiply the numerator of fraction 1 by the denominator of the fraction 2

and get the same value when we

2) multiply the denominator of fraction 1 by the numerator of the fraction 2.

This process is called cross-multiplication.

Here are some examples:

• 4/10 is equivalent to 2/5 because 4 x 5 = 10 x 2 = 20
• 6/15 is equivalent to 2/5 because 6 x 5 = 15 x 2 = 30
• 8/20 is equivalent to 2/5 because 8 x 5 = 20 x 2 = 40

...

Find equivalent fractions. Enter a fraction, mixed number or integer to get fractions that are equivalent to your input. Example entries:

• Fraction - like 2/3 or 15/16
• Mixed number - like 1 1/2 or 4 5/6
• Integer - like 5 or 28

What are Equivalent Fractions?

Equivalent fractions are fractions with different numbers representing the same part of a whole. They have different numerators and denominators, but their fractional values are the same.

For example, think about the fraction 1/2. It means half of something. You can also say that 6/12 is half, and that 50/100 is half. They represent the same part of the whole. These equivalent fractions contain different numbers but they mean the same thing: 1/2 = 6/12 = 50/100

How to Find Equivalent Fractions

Multiply both the numerator and denominator of a fraction by the same whole number. As long as you multiply both top and bottom of the fraction by the same number, you won't change the value of the fraction, and you'll create an equivalent fraction.

Example Equivalent Fractions

Find fractions equivalent to 3/4 by multiplying the numerator and denominator by the same whole number:

\( \dfrac{3}{4} \times \dfrac{2}{2} = \dfrac{6}{8} \)

\( \dfrac{3}{4} \times \dfrac{3}{3} = \dfrac{9}{12} \)

\( \dfrac{3}{4} \times \dfrac{4}{4} = \dfrac{12}{16} \)

\( \dfrac{3}{4} \times \dfrac{5}{5} = \dfrac{15}{20} \)

\( \dfrac{3}{4} \times \dfrac{6}{6} = \dfrac{18}{24} \)

Therefore these are all equivalent fractions:

\( \dfrac{3}{4} = \dfrac{6}{8} = \dfrac{9}{12} = \dfrac{15}{20} = \dfrac{18}{24} \)

Note that if you reduce all of these fractions to lowest terms, they equal 3/4.

For additional fraction help see our Fractions Calculator, Simplify Fractions Calculator and Mixed Numbers Calculator.

This equivalent fractions calculator is a great tool that helps you find equivalent fractions for any fraction you wish. This is the right place to learn what is an equivalent fraction of x, or how to find equivalent fractions.

Wondering whether two fractions are equivalent? You can get the answer to this question as well!

A fraction is a ratio of two numbers, the numerator, A and the denominator, B. As you already know from the ratio calculator, the ratio is equal to some specific value, x, where x = A/B.

The equivalent fraction definition tells us that any two fractions, A/B and C/D, are equivalent if they are equal to the same value. We can find whether or not two fractions are equivalent by checking one of these conditions:

• A = C and B = D;
• A × D = B × C;
• C = k × A and D = k × B, for any number k.

Converting two equivalent fractions to percentages will give us exactly the same number.

For any fraction, there are infinitely many equivalent fractions. It's convenient to present such values as a ratio of two integer numbers. That's how we divide things in everyday life, e.g., cutting a pizza into pieces (and taking a few of them).

As an example, let's check how to find equivalent fractions of 4/6. We can follow these steps:

1. Make sure both the numerator and denominator are integers. If not, start multiplying both numbers by 10 until there are no more decimal digits. In our case, both 4 and 6 are already integers.

2. Let's find the fraction in its simplest form. To do so, evaluate the greatest common factor of the numerator and the denominator. Here, the GCF of 4 and 6 is 2, so 4/6 is an equivalent fraction of 2/3, and the latter is the simplest form of this ratio. Therefore, 2/3 is our base.

🔎 For a more complex computation, feel free to use Omni's GCF calculator.

1. Multiply the base by consecutive natural numbers:

   → 2×2/2×3 = 4/6;
   → 3×2/3×3 = 6/9;
   → 4×2/4×3 = 8/12;
   → etc…

2. All of the values are equivalent fractions of 2/3 and are also equivalent to 4/6, the number we started with.

The procedure is straightforward, but what if you want to find 20 or 30 equivalent fractions? Well, it gets pretty time-consuming. However, if you use our equivalent fractions calculator, we can save you all of that hassle.

You can always convert any decimal to a fraction and then work out what are its equivalent fractions from there.

There are two different modes you can choose from. The first one helps you find as many fractions that are equivalent to your number as you want. Check the previous section for how these calculations work.

The second option helps you find if two fractions are equivalent. For instance, is 13/16 an equivalent fraction to 3/4? Let's check one of the conditions, e.g. multiply the numerator and denominator from the opposing fractions:

• 13 × 4 = 52;
• 16 × 3 = 48.

The outcomes are different, so the fractions 13/16 and 3/4 are NOT equivalent. What about 12/16 and 3/4?

• 12 × 4 = 48;
• 16 × 3 = 48.

This time, both numbers are the same, so 12/16 IS equivalent to 3/4. By using this equivalent fraction calculator, you can also see how to obtain one fraction from another!

Here is a list of a few fractions and their equivalent fractions:

• Equivalent fractions of 1/1: 2/2, 3/3, 4/4, 5/5.

• Equivalent fractions of 1/2: 2/4, 3/6, 4/8, 5/10.

• Equivalent fractions of 1/3: 2/6, 3/9, 4/12, 5/15.

• Equivalent fractions of 2/3: 4/6, 6/9, 8/12, 10/15.

• Equivalent fractions of 1/4: 2/8, 3/12, 4/16, 5/20.

• Equivalent fractions of 3/4: 6/8, 9/12, 12/16, 15/20.

• Equivalent fractions of 1/5: 2/10, 3/15, 4/20, 5/25.

• Equivalent fractions of 2/5: 4/10, 6/15, 8/20, 10/25.

• Equivalent fractions of 3/5: 6/10, 9/15, 12/20, 15/25.

• Equivalent fractions of 4/5: 8/10, 12/15, 16/20, 20/25.

• Equivalent fractions of 1/6: 2/12, 3/18, 4/24, 5/30.

• Equivalent fractions of 5/6: 10/12, 15/18, 20/24, 25/30.

Equivalent Fractions Calculator

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Here is the answer to questions like: 2/5 or What numbers are equivalent to 2/5?

This Equivalent Fractions Calculator will show you, step-by-step, equivalent fractions to any fraction you input.

See below the step-by-step solution on how to find equivalent fractions.

Two fractions are equivalent when they are both equal when written in lowest terms. The fraction 410 is equal to 25 when reduced to lowest terms. To find equivalent fractions, you just need to multiply the numerator and denominator of that reduced fraction (25) by the same natural number, ie, multiply by 2, 3, 4, 5, 6 ...

Important: 25 looks like a fraction, but it is actually an improper fraction.

• 410 is equivalent to 25 because 2 × 25 × 2 = 410
• 615 is equivalent to 25 because 2 × 35 × 3 = 615
• 820 is equivalent to 25 because 2 × 45 × 4 = 820
• 1025 is equivalent to 25 because 2 × 55 × 5 = 1025
• and so on ...

At a glance, equivalent fractions look different, but if you reduce then to the lowest terms you will get the same value showing that they are equivalent. If a given fraction is not reduced to lowest terms, you can find other equivalent fractions by dividing both numerator and denominator by the same number.

Finding equivalent fractions can be ease if you use this rule:

Equivalent fractions definition: two fractions ab and cd are equivalent only if the product (multiplication) of the numerator (a) of the first fraction and the denominator (d) of the other fraction is equal to the product of the denominator (b) of the first fraction and the numerator (c) of the other fraction.

In other words, if you cross-multiply (ab and cd) the equality will remain, i.e, a.d = b.c. So, here are some examples:

• 410 is equivalent to 25 because 4 × 5 = 10 × 2 = 20
• 615 is equivalent to 25 because 6 × 5 = 15 × 2 = 30
• 820 is equivalent to 25 because 8 × 5 = 20 × 2 = 40

This Equivalent Fractions Table/Chart contains common practical fractions. You can easily convert from fraction to decimal, as well as, from fractions of inches to millimeters.

Reference:

• [1] How to Find Equivalent Fractions

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