# How to Simplify Fractions

Reducing fractions, converting improper fractions to mixed numbers and vice versa, and changing fractions to decimals and percents are all useful operations in arithmetic. Putting a fraction in its lowest terms or decimal form can help you simplify math problems on homework assignments, and prove useful in real-life applications too.

You can apply the instructions below to simplify fractions, or use the convenient fraction calculator on the left. To use the calculator, enter the fraction as either a simple fraction (numerator over denominator), or as a mixed number. The calculator will reduce the fraction if necessary, convert between improper and mixed number form if applicable, and convert the fraction to a decimal and percent.

**How to Reduce Fractions**

To reduce a simple fraction, first look for the greatest common divisor of both the numerator and denominator. Then divide both the numerator and denominator by this factor to obtain the reduced fraction.

Example: Reduce 600/540. Since 60 is the largest number that divides into both 600 and 540, 60 is the GCD. And since 600÷60 = 10 and 540÷60 = 9, the fraction reduces to 10/9.

**How to Convert an Improper Fraction to a Mixed Number**

An improper fraction is a simple fraction in which the numerator is larger than the denominator. To convert an improper fraction to a mixed number, first divide the numerator by the denominator to obtain a whole number. Then place the remainder over the denominator to obtain the fraction part. The whole number plus the fraction part is the mixed number.

Example: Convert 500/43 to a mixed number. First we have 500÷43 = 11 with remainder 27. So the mixed number is 11 ^{27}/_{43}.

**How to Convert a Mixed Number to an Improper Fraction**

To convert a mixed number into an improper fraction, first multiply the whole number part by the denominator. Then, add this number to the numerator of the fractional part. This final number is your new numerator.

Example: Convert 7 ^{16}/_{81} to an improper fraction. First we compute 7x81 = 567. Then 567+16 = 583. So the improper fraction is 583/81.

**How to Convert a Fraction to a Decimal and Percent**

To convert a fraction to a decimal, simply divide the numerator by the denominator on your calculator. To obtain the percent, move the decimal point two units to the right.

Example: Convert 14/99 to a decimal and percent. Since 14÷99 = 0.14, this is the decimal form. The percent form is 14.14%.

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