How to Add and Simplify Fractions Step by Step
Fraction Calculator
What is Fraction Calculator?
A Fraction Calculator is an accurate online tool that lets you solve, simplify, and perform arithmetic on fractions easily. Instead of working out complex calculations by hand, you simply enter your numerators and denominators, select an operation (addition, subtraction, multiplication, division, or simplification), and get instant step-by-step answers. Whether you’re a student learning fractions, prepping for exams, or just want to check your work, this calculator makes fraction problems fast and error-free.
Formula or Logic Behind Fraction Calculator
The calculator uses arithmetic rules and formulas for all fraction operations:
Addition (like denominators): (a/b) + (c/b) = (a + c)/b
Addition (unlike denominators): (a/b) + (c/d) = (ad + bc)/(bd)
Subtraction: (a/b) – (c/d) = (ad – bc)/(bd)
Multiplication: (a/b) × (c/d) = (a×c)/(b×d)
Division: (a/b) ÷ (c/d) = (a×d)/(b×c)
Simplification: Divide numerator and denominator by their Greatest Common Divisor (GCD).
The calculator also converts improper fractions to mixed numbers and always provides answers in lowest (simplest) form.
Examples of Fraction Operations
| Operation | Example | Result |
|---|---|---|
| Addition | 1/2 + 1/3 | 5/6 |
| Subtraction | 3/4 − 1/5 | 11/20 |
| Multiplication | 2/3 × 2/3 | 4/9 |
| Division | 4/5 ÷ 2/7 | 14/5 or 2 4/5 |
| Simplify | 15/25 | 3/5 |
Steps to Use the Fraction Calculator
- Enter the numerators and denominators for your fractions. Fill both if performing arithmetic, or just Fraction 1 for simplification.
- Select the operation: addition (+), subtraction (−), multiplication (×), division (÷), or simplification.
- Click the 'Calculate' button.
- View your instant answer, displayed in fraction and mixed number forms with solution steps.
Why Use Vedantu’s Fraction Calculator?
Vedantu’s Fraction Calculator is easy to use, mobile-friendly, and highly trusted by students, teachers, and parents alike. It provides stepwise explanations alongside direct answers. Instantly check your fraction homework, prep for school or competitive exams, or solve real-life fraction questions in seconds.
For further concepts, you can explore Vedantu’s resources like Addition of Fractions, Improper Fractions, and How to Simplify Fractions.
Real-life Applications of Fraction Calculator
Fractions are part of daily life—from dividing a pizza with friends, sharing inheritances, measuring ingredients in recipes, reading test scores, or understanding time (quarters, halves, thirds). This calculator helps:
- Quickly find fractional parts when sharing or splitting items
- Double or reduce recipe proportions
- Convert improper fractions (e.g. from measurement tools) to mixed numbers at a glance
- Verify step-by-step homework calculations for school or competitive entrance exams
- Apply in jobs where precision matters—like construction, finance, and labs
FAQs on Fraction Calculator – Free Online Tool
1. What is a fraction calculator?
A fraction calculator is a free online tool that simplifies fraction calculations. It helps you quickly add, subtract, multiply, divide, and simplify fractions, providing both the answer and step-by-step solutions. This is especially useful for students learning about fractions, decimal to fraction conversions, and other fraction operations.
2. How do I use a fraction calculator?
Using a fraction calculator is easy! Simply enter the numerator and denominator of each fraction. Select the desired operation (+, -, ×, ÷, simplify). Then, click 'Calculate' to get the result and see the steps involved. Many calculators also handle converting decimals to fractions.
3. What are the different types of fractions?
There are several types of fractions: proper fractions (numerator < denominator), improper fractions (numerator ≥ denominator), mixed fractions (whole number and a proper fraction), and equivalent fractions (representing the same value). Understanding these types of fractions is crucial for various fraction operations.
4. How do you add fractions with unlike denominators?
To add fractions with unlike denominators, you first need to find the least common multiple (LCM) of the denominators. Then, convert each fraction to an equivalent fraction with the LCM as the denominator. Finally, add the numerators and keep the common denominator. For example, 1/2 + 1/3 = (3+2)/6 = 5/6. This involves finding the common denominator.
5. How do you subtract fractions?
Subtracting fractions is similar to addition. If the denominators are the same, simply subtract the numerators. If they are different, find the LCM of the denominators, convert the fractions to equivalent fractions, and then subtract the numerators, keeping the same denominator. Remember the concept of unlike denominators.
6. How do you multiply fractions?
Multiplying fractions is straightforward. Multiply the numerators together and the denominators together. Simplify the resulting fraction if possible. For example, (1/2) × (2/3) = (1 × 2) / (2 × 3) = 2/6, which simplifies to 1/3. This is a basic fraction operation.
7. How do you divide fractions?
To divide fractions, you invert (flip) the second fraction and then multiply. For example, (1/2) ÷ (1/3) = (1/2) × (3/1) = 3/2 or 1 1/2. This involves understanding the concept of reciprocals in fraction operations.
8. How do I simplify fractions?
To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator. Divide both the numerator and denominator by the GCD to obtain the simplified fraction. For example, simplifying 15/25 involves finding the GCD of 15 and 25, which is 5. Thus 15/25 simplifies to 3/5. This is also known as reducing fractions.
9. What is the formula for adding fractions?
The formula for adding fractions depends on whether the denominators are the same or different. For like denominators, it's (a/b) + (c/b) = (a+c)/b. For unlike denominators, it's (a/b) + (c/d) = (ad + bc) / bd. Remember to always simplify the resulting fraction.
10. How do I convert a decimal to a fraction?
To convert a decimal to a fraction, write the decimal as the numerator and use a power of 10 (10, 100, 1000, etc.) as the denominator, depending on the number of decimal places. Then simplify the fraction. For example, 0.75 = 75/100, which simplifies to 3/4. This is a common decimal to fraction conversion.
11. What are some real-life applications of fractions?
Fractions are used everywhere! Examples include: measuring ingredients in recipes, dividing objects or amounts equally (like sharing pizza), expressing parts of a whole (e.g., 1/4 of a day), and understanding proportions and ratios in various fields. This showcases the practical applications of fraction knowledge.
