Add, subtract, multiply, or divide any two fractions and see the work: common denominators, GCD simplification to lowest terms, mixed numbers, and decimals.
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FORMULA USEDFraction Calculator
What a fraction calculator does
A fraction is a division that has not been carried out yet: numerator over denominator. The four operations each have their own rule — addition and subtraction need a common denominator, multiplication goes straight across, and division flips the second fraction first. This tool runs all four on two fractions (negative entries allowed) and reduces the answer to lowest terms.
The four rules
Add: a/b + c/d = (a·d + c·b) / (b·d). Subtract: a/b − c/d = (a·d − c·b) / (b·d). Multiply: (a·c) / (b·d). Divide: (a·d) / (b·c) — multiply by the reciprocal. The raw result is then divided top and bottom by the greatest common divisor (GCD), found with the Euclidean algorithm.
Improper fractions and mixed numbers
An improper fraction has a numerator at least as large as its denominator (3/2); a mixed number splits out the whole part (1 1/2) by dividing — quotient first, remainder over the original denominator. The result board shows the improper form, the mixed form, and the decimal equivalent side by side.
Worked example
A pattern calls for 7/8 yard of trim; the bolt has 5/16 yard left.
Choose Subtract, enter 7/8 and 5/16.
Cross-multiply over 16: 14/16 − 5/16 = 9/16, already in lowest terms.
The decimal row reads 0.5625 — you are 0.5625 yard short.
How to use it
Pick the operation: add, subtract, multiply, or divide.
Enter the numerator and denominator of each fraction.
Read the simplified result, its mixed-number form, and the decimal.
Follow the formula line to check the cross-multiplication by hand.
Frequently asked questions
How do you add fractions with different denominators?
Rewrite both over a common denominator, then add the numerators. The calculator uses the cross-product form (a·d + c·b)/(b·d): for 1/2 + 1/3 that gives (1×3 + 1×2)/(2×3) = 5/6. Multiplying the denominators always produces a valid common denominator, even when it is not the smallest one.
How do you multiply two fractions?
Multiply the numerators together and the denominators together — no common denominator needed: 3/4 × 1/2 = 3/8. Reduce afterward by the GCD if the parts share a factor.
Why do you flip the second fraction to divide?
Dividing by a fraction means multiplying by its reciprocal, because division undoes multiplication. So 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 1 1/2 — dividing by one-half genuinely makes the number bigger.
How does the calculator simplify to lowest terms?
It finds the greatest common divisor of the result’s numerator and denominator using the Euclidean algorithm, then divides both by it. 6/8 becomes 3/4 because GCD(6, 8) = 2.
What is the difference between proper, improper, and mixed fractions?
Proper means the numerator is smaller (3/4); improper means it is not (5/4); mixed pairs a whole number with a proper fraction (1 1/4). All three can name the same quantity, and the tool shows the improper and mixed forms together.
What happens if a denominator is zero?
The calculator refuses the entry. A zero denominator is division by zero, which has no value — and dividing by a zero-valued fraction is refused for the same reason.