## Equivalent Fractions Calculator

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# How to Calculate Equivalent Fractions

Equivalent fractions are fractions that hold the same value as another fraction, even though they have different numerators and denominators. To find equivalent fractions, follow these steps:

## Step One: Simplify

The first step in finding equivalent fractions is to simplify the original fraction to its reduced form.

Determine the greatest common factor (GCF) of the numerator and denominator, then divide both by the GCF to simplify the fraction.

For example, let's find an equivalent fraction for 6/9 by simplifying:

The GCF of 6 and 9 is 3 (3 is the largest number that divides evenly into both 6 and 9).

6 ÷ 3 = 2

9 ÷ 3 = 3

Hence, 2/3 is equivalent to 6/9.

## Step Two: Calculate Equivalent Fractions

The second step is to calculate fractions that hold the same value as the original fraction. Multiply the numerator and denominator of the simplified fraction by a multiplier to obtain an equivalent fraction.

For example, let's find some equivalent fractions for 2/6 by simplifying and then multiplying:

Start by simplifying the fraction:

2/6 = 1/3

Choose a multiplier – let's use 4 as the multiplier.

Multiply both the numerator and denominator of 1/3 by the multiplier 4:

1 × 4/3 × 4 = 4/12

Thus, 4/12 is an equivalent fraction of 1/3.

Another convenient way to find equivalent fractions is by utilizing an equivalent fractions chart.

### How to Determine if Two Fractions are Equivalent

There are three methods to determine if two fractions are equivalent to each other.

The first method is to simplify both fractions to their simplest form. If the simplified fractions are equal, then the fractions are equivalent.

For instance, let's determine if 5/10 and 6/12 are equivalent:

Simplify 5/10 by dividing both the numerator and denominator by their greatest common factor, 5.

5 ÷ 5 = 1

10 ÷ 5 = 2

1/2 is the simplest form of 5/10.

Simplify 6/12 by dividing both the numerator and denominator by their greatest common factor, 6.

6 ÷ 6 = 1

12 ÷ 6 = 2

1/2 is the simplest form of 6/12.

Since both 5/10 and 6/12, when simplified, result in 1/2, we can conclude that the fractions are equivalent.

The second method is to convert both fractions to decimals by dividing the numerator by the denominator. If the decimal values are equal, then the fractions are equivalent.

For example, let's determine if 5/10 and 6/12 are equivalent by dividing the numerators by the denominators:

5 ÷ 10 = 0.5

6 ÷ 12 = 0.5

Since the decimal values are the same (0.5), we can deduce that the fractions are equivalent.

The third method is to use a fraction comparison calculator, which automatically determines if the fractions are equivalent.

## Recommended Fraction Resources

- Least Common Denominator Calculator

- Decimal to Fraction Calculator

- Mixed Number Calculator

- Subtracting Fractions Calculator

- Adding Fractions Calculator