Your Guide to Calculating Fractions

Fractions represent parts of a whole and are fundamental in everything from baking recipes to complex engineering. While they can seem intimidating, understanding the basic operations is straightforward. Our calculator handles the hard work for you, but learning the manual methods can deepen your mathematical understanding. For even more advanced calculations involving trigonometry or logarithms, our Scientific Calculator is the perfect tool.

How to Add and Subtract Fractions

To add or subtract fractions, they must have a "common denominator."

1. Convert Mixed Numbers: If you have mixed numbers (like 1 ¾), convert them to improper fractions first. (e.g., 1 ¾ becomes (1*4+3)/4 = 7/4).
2. Find a Common Denominator: The easiest way is to multiply the two denominators together. For 1/3 + 2/5, the common denominator is 3 × 5 = 15.
3. Adjust the Numerators: Multiply each numerator by the same value its denominator was multiplied by. For our example, 1/3 becomes 5/15 and 2/5 becomes 6/15.
4. Perform the Operation: Add or subtract the new numerators: 5 + 6 = 11. The denominator stays the same. The result is 11/15.

Our calculator performs these steps instantly, saving you time on homework or projects. Browse our other Math calculators for more tools.

How to Multiply Fractions

Multiplication is the simplest fraction operation.

1. Convert to Improper Fractions: Just like with addition, start by converting any mixed numbers.
2. Multiply Straight Across: Multiply the numerators together, and then multiply the denominators together. For 2/3 × 4/5, you get (2×4) / (3×5) = 8/15.
3. Simplify: Reduce the resulting fraction to its lowest terms if possible. Our calculator does this automatically.

How to Divide Fractions

Dividing fractions involves one extra step: "inverting" the second fraction.

1. Convert to Improper Fractions: As always, convert mixed numbers first.
2. Invert and Multiply: Flip the second fraction (this is called finding the reciprocal) and change the division sign to a multiplication sign. For 1/2 ÷ 2/5, it becomes 1/2 × 5/2.
3. Multiply Straight Across: Now, just multiply: (1×5) / (2×2) = 5/4.
4. Simplify and Convert: The result is 5/4, which can be simplified or converted to a mixed number (1 ¼).

Understanding these concepts is not just for math class; they're crucial in fields like finance. If you're working with loans or mortgages, which often involve complex ratios, our Loan & Mortgage Calculator can be a huge help.