Fraction Calculator: Add, Subtract, Multiply, Divide

What is 7/8 plus 5/6, and how do you get a clean answer? The Fraction Calculator adds, subtracts, multiplies, or divides two fractions and reduces the result to lowest terms.

It is made for students, parents helping with homework, and cooks scaling recipes. You type whole-number numerators and denominators and pick an operator. The answer updates as you type.

Table of Contents

• What the Calculator Does
• How to Use It, Step by Step
• The Fraction Formulas
• Worked Example
• How to Read the Results
• Tips for Working With Fractions
• Limitations and Assumptions
• FAQs About the Fraction Calculator

What the Calculator Does

The tool works with exactly two fractions at a time. One menu picks the operation, and the answer appears right away.

• Four Operations: addition, subtraction, multiplication, and division.
• Simplified Fraction: the answer in lowest terms, or a whole number when the bottom is 1.
• Mixed Number: the same answer as a whole number plus a fraction, when the result is 1 or more.
• Decimal Value: the answer rounded to four decimal places.
• Inline Messages: a red note under the boxes explains any entry the tool cannot use.

It does not show steps, keep a history, or accept mixed numbers as input.

How to Use It, Step by Step

1. Type the top number of the first fraction in the box with the Num 1 hint.
2. Type the bottom number in the box with the Den 1 hint. Never use zero here.
3. Pick +, -, ×, or ÷ from the menu between the two fractions.
4. Fill in Num 2 and Den 2 for the second fraction.
5. Watch the cards update as you type, or press Enter. The = Calculate button does the same.
6. Read the three cards: Simplified Fraction, Mixed Number, and Decimal Value.

The page loads with 3/4 + 2/5 already worked out, so you can see the layout first. Each box accepts up to 18 digits, and a minus sign is allowed.

The Fraction Formulas

Let the first fraction be a/b and the second be c/d. The tool builds a raw numerator and denominator, then divides both by their greatest common divisor.

• Add: (a × d + c × b) / (b × d).
• Subtract: (a × d - c × b) / (b × d).
• Multiply: (a × c) / (b × d).
• Divide: (a × d) / (b × c).
• Reduce: divide the top and bottom by their GCD, found with Euclid's method.
• Decimal Value: top divided by bottom, rounded to four decimals.

If the bottom comes out negative, the tool moves the minus sign to the top. The arithmetic uses exact whole numbers, so large entries do not lose digits.

Worked Example

Priya is combining two batches of trail mix. One uses 7/8 of a cup of nuts and the other uses 5/6 of a cup. She adds them.

The raw numerator is 7 × 6 + 5 × 8 = 82. The raw denominator is 8 × 6 = 48. The GCD of 82 and 48 is 2, so the answer is 41/24. That is 1 17/24 as a mixed number, or 1.7083 as a decimal.

How to Read the Results

Simplified Fraction is the main answer. It shows as top / bottom, and a whole number appears alone when the bottom is 1. For example, 1/2 + 1/2 shows 1.

Mixed Number splits an improper fraction into a whole part and a remainder. A negative result keeps its sign on the whole part, so -11/4 shows as -2 3/4. When the answer is between -1 and 1, the card reads N/A (less than 1).

Decimal Value is rounded, not cut off. The fraction 2/3 shows as 0.6667. Use the fraction card when you need an exact answer. A tiny nonzero result switches to exponent form, such as -1.0000e-5 for -1/100000.

Tips for Working With Fractions

Scaling a recipe is a common use. To double 3/4 cup, enter 3/4 × 2/1. The tool returns 3/2, which is 1 1/2 cups.

To change a decimal into a fraction, use the decimal to fraction converter. To see why a fraction reduces, check the greatest common divisor calculator.

When you add by hand, a common denominator keeps numbers small. The least common multiple calculator finds that denominator for you.

Fractions also describe ratios, such as 12 to 18. The ratio simplifier reduces those the same way. For plain arithmetic with decimals, open the standard calculator. More tools live in the math and science calculators hub.

Limitations and Assumptions

• Entries must be whole numbers. A blank box, letters, a decimal like 1.5, or an exponent like 1e5 gets a message naming the box.
• Each box holds at most 18 digits. Within that range the arithmetic is exact, even for very large products.
• A denominator of zero shows the message "Denominator cannot be zero." and hides the old result.
• Any error hides the previous answer, so the cards never show a result that no longer matches your entries.
• Only two fractions can be combined at once. Chain longer problems by using each answer as the next input.

FAQs About the Fraction Calculator

This calculator gives general estimates only and is not professional advice. Reviewed for general accuracy by Prof. Dr. Khalil Mudassar, PhD.