How do I add 1/2 and 1/3 in this calculator?

Type "1/2" in the first box, choose "+", type "1/3" in the second, and tap Calculate. You will get 5/6 (the simplified result), the mixed-number form (still 5/6 since it is less than 1), and the decimal 0.833. The calculator handles the common-denominator math automatically: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.

Can I mix fractions, mixed numbers, and decimals in the same calculation?

Yes. The parser accepts all three formats interchangeably. For example, "3 1/4" times "0.5" works fine - the calculator converts 3 1/4 to 13/4, converts 0.5 to 1/2, multiplies to get 13/8, and shows you 1 5/8 as the mixed-number form. Use a space between the whole number and the fraction (not a hyphen).

What does it mean when my answer is already simplified?

It means the greatest common divisor (GCD) of the numerator and denominator is 1. For example, 3/7 cannot be reduced because 3 and 7 share no factors larger than 1. The calculator runs Euclid algorithm on every result, so you always see the lowest-terms form. The "Before Simplifying" row shows the raw fraction so you can verify the reduction step.

Why is dividing fractions the same as multiplying by the reciprocal?

Because (a/b) divided by (c/d) means "how many groups of c/d fit in a/b." Algebraically, dividing by c/d is the same as multiplying by its reciprocal d/c. So 1/2 divided by 1/4 = 1/2 times 4/1 = 4/2 = 2. The calculator does the flip automatically when you pick the divide button, so you do not need to invert anything by hand.

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Fraction Calculator (Add, Subtract, Multiply, Divide)

Add, subtract, multiply, and divide fractions and mixed numbers with full simplification. Results as simplified fraction, mixed number, and decimal.

MATH

Add, subtract, multiply, and divide fractions or mixed numbers and get a simplified result, mixed-number form, and decimal value back. Accepts inputs like 1/2, 3 1/4, or 0.75 - the calculator converts every form to a common representation.

The math: a/b + c/d = (ad + bc) / bd, a/b - c/d = (ad - bc) / bd, a/b × c/d = ac / bd, a/b ÷ c/d = ad / bc. After computing the raw numerator and denominator, the result is reduced using the greatest common divisor (Euclid algorithm). Decimal inputs are parsed by counting digits after the decimal point and constructing the appropriate denominator (e.g. 0.75 = 75/100, then reduced to 3/4).

Disclaimer: Division by zero is rejected. Mixed-number input format is "whole numerator/denominator" with a space (e.g. "3 1/4").

First Fraction (e.g. 1/2, 3 1/4, 0.75)

Operation

Second Fraction

Calculator information

How to use this calculator

Enter the first fraction by filling in the numerator (top) and denominator (bottom). Example: 2/3.
Choose the operation: add (+), subtract (-), multiply (x), or divide (/).
Enter the second fraction the same way. For mixed numbers, fill in the whole part and the fractional part.
Click Compute to see the result in three formats: simplified proper fraction, mixed number, and decimal.
Review the step-by-step solution shown to understand how denominators are unified or how the fraction is simplified.
Make sure denominators are not zero (to avoid division errors) and that the divisor in a division operation is not zero.

Basic Fraction Operations

Add/Subtract: a/b +/- c/d = (a*d +/- c*b) / (b*d); Multiply: a/b x c/d = (a*c) / (b*d); Divide: a/b / c/d = (a*d) / (b*c); Simplify: numerator/GCD, denominator/GCD

a, c = numerators
b, d = denominators, b != 0 and d != 0
GCD = Greatest Common Divisor

A mixed number p (q/r) is converted to an improper fraction (p*r + q)/r before performing operations.

Worked example: Adding 2/3 + 3/4

Given:

Fraction 1 = 2/3
Fraction 2 = 3/4
Operation = addition

Steps:

Find a common denominator: LCM of 3 and 4 is 12
Convert 2/3 = 8/12 (multiply by 4/4)
Convert 3/4 = 9/12 (multiply by 3/3)
Add numerators: 8/12 + 9/12 = 17/12
Simplify: GCD(17,12) = 1, result stays 17/12
Convert to a mixed number: 17 / 12 = 1 remainder 5, giving 1 5/12
Decimal: 17 / 12 = 1.4167

Result: Result = 17/12 (improper fraction) = 1 5/12 (mixed) = 1.4167 (decimal). The result is greater than 1 because both fractions are close to 1.

Frequently asked questions

What is the difference between proper, mixed, and decimal fractions?

Improper or proper fraction: numerator/denominator, e.g., 7/4. Mixed number: a whole number plus a fraction, e.g., 1 3/4 (equal to 7/4). Decimal fraction: expressed in base 10, e.g., 1.75. All three can be converted between one another. Mixed numbers are more intuitive for values greater than 1, while improper fractions are easier to use in calculations.

How do I simplify a fraction?

Find the Greatest Common Divisor (GCD) between the numerator and denominator, then divide both by it. Example 18/24: GCD(18,24) = 6, result is 18/6 over 24/6 = 3/4. The Euclidean algorithm can find the GCD: repeatedly divide and take the remainder until the remainder is zero. A fraction is in lowest terms when the GCD of numerator and denominator is 1.

How do I add fractions with different denominators?

Find the Least Common Multiple (LCM) of the two denominators. Convert both fractions to equivalent fractions with that LCM as the denominator. Add the numerators and keep the denominator. Simplify the result if needed. Example 1/4 + 1/6: LCM = 12, so 3/12 + 2/12 = 5/12.

Is dividing fractions the same as multiplying?

Yes. Dividing by a fraction is the same as multiplying by its reciprocal. a/b / c/d = a/b x d/c. Example 2/3 / 4/5 = 2/3 x 5/4 = 10/12 = 5/6. This concept is often taught as 'keep, change, flip' in elementary school. Important: neither the second fraction's denominator nor its numerator can be zero.

What are equivalent fractions?

Equivalent fractions are different fractions that represent the same value, e.g., 1/2 = 2/4 = 3/6 = 50/100. They are created by multiplying or dividing both numerator and denominator by the same nonzero number. The concept is essential when finding common denominators for addition or subtraction. The simplest form is the standard representation where GCD(numerator, denominator) = 1.

Sources & references

Common Core Mathematics Standards - Fractions — Common Core State Standards Initiative
Fractions - Khan Academy Mathematics — Khan Academy
Fraction - Encyclopaedia Britannica — Encyclopaedia Britannica

Last updated: May 11, 2026

Fraction Calculator (Add, Subtract, Multiply, Divide)

Calculator information

📋 How to use this calculator

🧮 Basic Fraction Operations

💡 Worked example: Adding 2/3 + 3/4

❓ Frequently asked questions

📚 Sources & references

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How to use this calculator

Basic Fraction Operations

Worked example: Adding 2/3 + 3/4

Frequently asked questions

Sources & references