Add, subtract, multiply, or divide any two fractions in seconds. See steps, simplify results, and understand how to solve fractions.
A fraction calculator helps perform operations like addition, subtraction, multiplication, and division on fractions. It simplifies your work by automatically converting, simplifying, and presenting results in various forms like: improper fractions, mixed numbers, and decimals.
A fraction represents part of a whole, written as: numerator/denominator.
For example: 3/4 means you have 3 parts out of 4 total equal parts. It’s like dividing something into 4 equal pieces and taking 3 of them.
Types of fractions:
Fractions are used in cooking, construction, budgeting, academic math, and engineering. Manual operations are time-consuming. This calculator allows users to learn, solve and validate the results.
You can enter two fractions and choose an operation. The calculator shows:
Simplifying a fraction means reducing it to its lowest terms. A fraction is in its simplest form when the numerator and denominator have no common factors except 1.
Meaning:
For example, \(\frac{8}{12}\) is not simplified because both 8 and 12 can be divided by 4.
Divide both by 4:
\(\frac{8 \div 4}{12 \div 4} = \frac{2}{3}\)
Now, \(\frac{2}{3}\) is in simplest form.
Find the Greatest Common Divisor (GCD) of the numerator and denominator.
Divide both numbers by the GCD.
Example:
\(\frac{15}{25} \quad \text{→ GCD of 15 and 25 is 5} \Rightarrow \frac{15 \div 5}{25 \div 5} = \frac{3}{5}\)
Adding fractions may seem tricky at first, but it’s easy once you know whether the denominators (the bottom numbers) are the same or different. Let’s break it down step by step.
Case 1: When the Denominators Are the Same
If both fractions share the same denominator, you can add them directly. Just add the numerators and keep the denominator unchanged.
Example:
\(\frac{2}{7} + \frac{3}{7} = \frac{5}{7}\)
You’re simply adding 2 and 3 while keeping the denominator as 7.
Case 2: When the Denominators Are Different
This is where you need to take an extra step. When denominators don’t match, you must first make them the same. Here’s how:
Example:
\(\frac{1}{4} + \frac{2}{3}\)
First, find the LCD of 4 and 3, which is 12. Then:
\(\frac{1}{4} = \frac{3}{12}, \quad \frac{2}{3} = \frac{8}{12}\)
Now add:
\(\frac{3}{12} + \frac{8}{12} = \frac{11}{12}\)
Subtracting fractions follows the same basic logic as adding them. The goal is to work with like denominators so you can subtract the numerators easily.
Case 1: Fractions With the Same Denominator
If the bottom numbers (denominators) are the same, just subtract the top numbers (numerators) and keep the denominator unchanged.
Example:
\(\frac{5}{8} - \frac{3}{8} = \frac{2}{8} = \frac{1}{4}\)
In this case, subtracting 5 and 3 gives 2, and the denominator 8 stays the same. The final step is simplifying the result.
Case 2: Fractions With Different Denominators
If the denominators are different, follow these steps:
Example:
\(\frac{3}{4} - \frac{1}{6}\)
Start by finding the LCD of 4 and 6, which is 12.
Convert the fractions:
\(\frac{3}{4} = \frac{9}{12}, \quad \frac{1}{6} = \frac{2}{12}\)
Now subtract:
\(\frac{9}{12} - \frac{2}{12} = \frac{7}{12}\)
Multiplying fractions is one of the simplest fraction operations and there is no need to find a common denominator. You just multiply the numerators (top numbers) together, then multiply the denominators (bottom numbers) together. That’s it.
Formula:
\(\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}\)
Let’s walk through an example:
\(\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}\)
You’re multiplying 2 × 4 for the top and 3 × 5 for the bottom.
If the result can be simplified, reduce it to the lowest terms. In this case, 8\15 is already simplified.
Dividing fractions might seem tricky at first, but it follows a very simple rule: flip the second fraction and multiply.
This method is known as multiplying by the reciprocal. The reciprocal of a fraction means swapping its numerator and denominator.
General Formula:
\(\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}\)
You turn the division problem into a multiplication problem by inverting the second fraction.
Example:
\(\frac{3}{5} \div \frac{2}{7}\)
Step 1: Flip the second fraction 2/7 becomes 7/2
Step 2: Multiply the fractions:
\(\frac{3}{5} \times \frac{7}{2} = \frac{21}{10}\)
This is an improper fraction. You can keep it as is, simplify it (if possible), or convert it to a mixed number.
\(\frac{21}{10} = 2 \frac{1}{10}\)
Dividing fractions always comes down to three steps:
This method works for all proper, improper, and mixed fractions (as long as none of the denominators are zero).