Fraction Calculator with Steps Shown
Use this free fraction calculator to add, subtract, multiply, and divide any fraction or mixed number in seconds. Whether you need an instant answer or complete step-by-step workings to check your math homework, this tool delivers exact reduced fractions and decimal equivalents.
Understanding Fractions and Simplification
A fraction calculator solves arithmetic between ratios of numbers, where each expression consists of a top numerator and a bottom denominator. It calculates sums, differences, products, or quotients, and automatically reduces the final result to lowest terms using the greatest common factor (GCF).
Understanding the difference between an improper fraction vs. mixed number makes manual math simple. An improper fraction has a numerator larger than or equal to its denominator (like 7/4). A mixed number pairs a whole integer with a proper fraction (like 1 3/4). Our simplify fraction calculator with whole numbers lets you toggle between both formats effortlessly.
Formulas: How to Add, Subtract, Multiply, and Divide
Every operation follows standard arithmetic rules. If you are wondering how to add fractions with different denominators calculator algorithms compute results using these core formulas:
(a / b) + (c / d) = ((a · d) + (b · c)) / (b · d)(a / b) - (c / d) = ((a · d) - (b · c)) / (b · d)Multiply: (a / b) · (c / d) = (a · c) / (b · d) | Divide: (a / b) ÷ (c / d) = (a / b) · (d / c)Simplified = (Numerator / GCF) / (Denominator / GCF)Step-by-Step Fraction Arithmetic with Worked Examples
1. Convert Mixed Numbers: When using a mixed number to improper fraction calculator approach, first multiply the whole number by the denominator and add the numerator. For example, 2 1/3 becomes ((2 × 3) + 1) / 3 = 7/3.
2. Find the Least Common Denominator (LCD): When adding 1/4 and 2/3, find the lowest common multiple of 4 and 3, which is 12. Adjust both fractions: (1 × 3)/(4 × 3) = 3/12 and (2 × 4)/(3 × 4) = 8/12.
3. Execute the Operation: Add the numerators together over the common denominator: 3/12 + 8/12 = 11/12. For division, take the second term, flip it to its reciprocal, and multiply straight across.
4. Simplify / Reduce to Lowest Terms: Find the greatest common factor (GCF) between your numerator and denominator. Divide both numbers by that value. If the numerator exceeds the denominator, divide to express it as a clean mixed number.
Frequently Asked Questions
How do you add fractions with different denominators?
To add fractions with unlike denominators, find the Least Common Denominator (LCD). Rewrite each fraction with this shared base, add the numerators directly across while keeping the denominator unchanged, and simplify the final sum to lowest terms using the greatest common factor.
How do you convert a mixed number to a fraction?
Multiply the whole number integer by the fraction's denominator, add the numerator to that product, and write the final sum over the original denominator. For instance, to convert 3 2/5: multiply 3 by 5 (15), add 2 (17), giving the improper fraction 17/5.
How do you divide fractions step by step?
Follow the "keep, change, flip" rule: keep the first fraction as written, change the division operator to multiplication, and flip the second fraction into its reciprocal. Multiply the numerators and denominators straight across, then reduce to lowest terms.
What is 3/4 simplified to its lowest terms?
3/4 is already in its simplest form. The numerator (3) and denominator (4) share no common divisor greater than 1. Because their greatest common factor (GCF) is 1, the fraction cannot be reduced further.
Fraction Calculator
1. Find the Least Common Denominator (LCD): LCD(2, 4) = 4
2. Convert to common denominator: (1 × 2) / 4 + (1 × 1) / 4 = 2/4 + 1/4
3. Add numerators: (2 + 1) / 4 = 3/4
4. Fraction is already in its simplest form (GCD = 1)
* Fraction arithmetic solves addition and subtraction by finding the Least Common Denominator (LCD). Multiplication and division multiply across and apply the reciprocal, followed by Greatest Common Divisor (GCD) reduction.
Check out 4 similar collection of math calculators