Fraction Calculator Instructions

Use this fraction calculator to easily add, subtract, multiply, and divide fractions. Results are given as fractions in their simplest form or as reduced mixed numbers.

Input Instructions:

• Enter proper or improper fractions.
• Choose the mathematical operation you need.
• Click the “Calculate” button.
• Step-by-step solutions are provided.

For negative fractions, place a minus sign before the numerator. For example, to input -6/7, enter -6 in the numerator field and 7 in the denominator field.

In some math problems, the word “of” indicates multiplication. For instance, “What is 1/3 of 3/8?” means you should multiply 1/3 by 3/8.

Working with Unlike Denominators

There are two situations where you need to handle fractions with different denominators:

1. Adding fractions
2. Subtracting fractions

Steps to Add or Subtract Fractions:

1. Find the Least Common Denominator (LCD):
   • Use the LCD Calculator to find the least common denominator for the given fractions.
2. Adjust the Fractions:
   • For each fraction, determine the number needed to multiply the denominator to reach the LCD.
   • Multiply both the numerator and denominator by this number.
3. Combine the Numerators:
   • For addition, add the adjusted numerators.
   • For subtraction, subtract the adjusted numerators.
4. Simplify:
   • Convert improper fractions to mixed numbers.
   • Reduce the fraction to its lowest terms.

Multiplying Fractions

1. Multiply all numerators together.
2. Multiply all denominators together.
3. Reduce the result to its lowest terms.

Dividing Fractions

1. Rewrite the division as “Keep, Change, Flip”:
   • Keep the first fraction as is.
   • Change the division sign to multiplication.
   • Flip the second fraction by swapping its numerator and denominator.
2. Multiply all numerators together.
3. Multiply all denominators together.
4. Reduce the result to its lowest terms.

Fraction Formulas

You can add or subtract fractions without finding the least common denominator by using cross multiplication. Here are the formulas:

Adding Fractions

$\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$

Example Steps:

$\frac{2}{6}+\frac{1}{4}=\frac{2\times 4+6\times 1}{6\times 4}=\frac{14}{24}=\frac{7}{12}$

Subtracting Fractions

$\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd}$

Example Steps:

$\frac{2}{6}-\frac{1}{4}=\frac{2\times 4-6\times 1}{6\times 4}=\frac{2}{24}=\frac{1}{12}$

Multiplying Fractions

$\frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd}$

Example Steps:

$\frac{2}{6}\times \frac{1}{4}=\frac{2\times 1}{6\times 4}=\frac{2}{24}=\frac{1}{12}$

Dividing Fractions

$\frac{a}{b}÷\frac{c}{d}=\frac{a\times d}{b\times c}$

Example Steps:

$\frac{2}{6}÷\frac{1}{4}=\frac{2\times 4}{6\times 1}=\frac{8}{6}=\frac{4}{3}=1\frac{1}{3}$

Note-Please use this Percentage Calculator