Add, subtract, multiply and divide fractions with full step-by-step work — every result also shown as a mixed number. Simplify any fraction to lowest terms, or convert a decimal to a fraction — instantly.
Enter two fractions and choose an operation to see the result
Enter a fraction to reduce it to lowest terms
Enter a decimal number to convert it to a fraction
This free fraction calculator adds, subtracts, multiplies, and divides fractions, simplifies any fraction to its lowest terms, and converts decimals to fractions — all with the exact working shown at every step. A fraction expresses a part of a whole as two integers, a numerator over a denominator, and mastering fraction arithmetic is one of the building blocks of algebra, geometry, and everyday measurement. Whether you're checking a homework answer, scaling a recipe, adding tape-measure readings on a job site, or reducing a ratio to its simplest form, this fraction calculator with steps handles proper and improper fractions, shows the greatest common divisor (GCD) used at each simplification, and always displays the result as a mixed number too. If your numbers start as mixed numbers (like 1 1/2), use the dedicated Mixed Fraction Calculator instead.
The tool bundles three related jobs: an Add/Subtract/Multiply/Divide mode that works on two plain fractions at once; a Simplify mode that reduces a single fraction to lowest terms and shows its mixed number, decimal, percentage, and GCD; and a Decimal → Fraction mode that converts any decimal into its exact fraction equivalent. All three modes support negative values and display full step-by-step working, not just a final answer.
Students and teachers checking fraction homework, tradespeople reading fractional measurements off a tape measure, cooks and bakers scaling recipes, engineers and machinists working to fractional tolerances, and anyone preparing for a standardized test with fraction word problems can all use this tool to skip manual cross-multiplication and get a verified, step-by-step fraction answer.
Fractions represent exact values that decimals can only approximate — 1/3 is precise, while 0.333 is a rounded stand-in. Construction, sewing, cooking, and machining all rely on fractional measurement systems (inches, cups, gauge sizes) where rounding to a decimal introduces compounding error across multiple additions. Fraction skills also underpin algebraic rearrangement, ratio and proportion problems, and probability calculations.
Bakers double or halve recipes written in fractional cups and teaspoons. Carpenters and plumbers add fractional inch measurements from a tape measure or pipe gauge. Tailors and quilters combine fractional yardages of fabric. Finance professionals convert fractional stock quotations or interest-rate fractions into decimals for comparison. Students use fraction arithmetic throughout pre-algebra, algebra, and standardized test prep.
How this fraction calculator turns two fractions or a decimal into an exact answer
Using b×d as the common denominator always works, even if it isn't the least common denominator — the final GCD simplification step still reduces the answer to lowest terms.
Multiplying numerators and denominators independently is valid regardless of the starting denominators, which is why these two operations skip the cross-multiplication step entirely.
This calculator finds the GCD by repeatedly dividing and taking remainders until the remainder is zero — the fast, classical method for reducing any fraction to lowest terms.
From picking a tool to verifying the answer
Pick the Add/Subtract/Multiply/Divide tab, the Simplify Fraction tab, or the Decimal → Fraction tab.
Type the numerator and denominator of the first fraction. If you have a mixed number, convert it to an improper fraction first (or use the Mixed Fraction Calculator).
For the operations tool, choose +, −, ×, or ÷ and enter the numerator and denominator of the second fraction.
The calculator applies the matching fraction formula instantly.
Each result shows the fraction, mixed number, decimal, and percentage or GCD where relevant, along with the full step-by-step working.
Reduce the result by hand using the shown GCD, or reverse the operation, to confirm the answer is correct.
Adding 3/2 cup of flour (1½ cups) to 2/3 cup of sugar in a recipe
A recipe calls for 1 1/2 cups of flour and 2/3 cup of sugar. Since this tool takes plain fractions, enter 1 1/2 as its improper-fraction equivalent, 3/2 (or use the Mixed Fraction Calculator to convert it automatically). What is the combined amount, as a fraction, a mixed number, and a decimal?
Explanation: The combined dry ingredients equal 13/6 cups, or 2 1/6 cups. Notice the calculator's cross-multiplication used 6 (= 2×3) as the common denominator, which happened to already be the least common denominator here — that won't always be true, but the GCD step at the end guarantees the final fraction is fully reduced regardless.
What each result field actually represents
| Result Field | What It Means | Example Reading |
|---|---|---|
| Fraction (a/b) | The exact answer, always reduced to lowest terms | 13/6 is fully reduced since GCD(13,6) = 1 |
| Mixed Number | The same value as a whole number plus a proper fraction, easier to read when the value exceeds 1 | 13/6 = 2 1/6 |
| Decimal | The value converted to base-10, useful for comparing with other decimal figures | 13/6 ≈ 2.166667 |
| Percentage (Simplify tool) | The fraction's value scaled by 100, useful for grades or proportions | 3/4 = 75% |
| GCD Used (Simplify tool) | The largest number both the original numerator and denominator were divided by | GCD(8, 12) = 4 |
Reading the sign: a negative result always appears on the numerator (e.g. -13/6), regardless of which original fraction carried the negative sign — the calculator normalizes this automatically.
Typical ranges: a denominator of 1 in the final result (shown as just the numerator) means the answer simplified to a whole number, such as 6/3 reducing to 2.
Manual verification: multiply the mixed-number or decimal result back through the original operation, or divide the fraction result's numerator and denominator by the shown GCD to confirm it's fully reduced.
Where exact fraction arithmetic matters more than rounded decimals
Check fraction addition, subtraction, multiplication, and division word problems step by step.
Practice the fraction arithmetic that appears throughout SAT, GRE, GMAT, and entrance exam quantitative sections.
Double, halve, or combine recipe quantities given in fractional cups, tablespoons, or teaspoons.
Add or compare tape-measure readings given in fractions of an inch, like 3/8" + 5/16".
Combine fractional yardages of fabric or trim needed for a pattern.
Work with fractional pipe, fitting, and gauge sizes without rounding error.
Convert a fractional stock quotation or interest-rate fraction into an exact decimal for comparison.
Keep manufacturing tolerances in exact fraction form rather than a rounded decimal.
Scale a model's fractional dimensions precisely before exporting for print.
Work with fractional note values and time signatures, like adding an eighth note (1/8) and a quarter note (1/4).
Combine fractional probabilities from independent or combined events.
Convert and combine fractional scale ratios used on maps and blueprints.
Convert raw fractional proportions into decimals or percentages for reports and charts.
What this fraction calculator does well, and where manual judgment is still needed
Three ways of writing the same kind of value
| Form | Definition | Example |
|---|---|---|
| Proper Fraction | Numerator smaller than denominator (value < 1) | 3/4 |
| Improper Fraction | Numerator equal to or greater than denominator (value ≥ 1) | 9/4 |
| Mixed Number | A whole number plus a proper fraction | 2 1/4 |
Summary: This fraction calculator gives you an instant, free way to add, subtract, multiply, and divide fractions, simplify any fraction to lowest terms, and convert a decimal to its exact fraction form — all with the working shown, and every result also displayed as a mixed number. Pair it with the Mixed Fraction Calculator for direct mixed-number arithmetic, or the GCF Calculator and Ratio Calculator for a fuller picture of proportional math.
Common questions about fraction arithmetic and conversion
Trusted educational references to go deeper on fraction arithmetic
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