Fraction Calculator — Add, Subtract, Simplify, Compare Fractions with Steps

How to use the fraction calculator

This tool has four modes, each covering a different fraction task. Switch between them using the tabs at the top of the card. Everything updates as you type — there is no "Calculate" button to press.

Arithmetic mode (the default) lets you add, subtract, multiply, or divide two fractions. Each fraction has three fields: a whole number, a numerator, and a denominator. Fill in the whole number only if you're entering a mixed number like 234. Leave it at 0 for a proper or improper fraction. Enter a negative numerator (like −34) for negative fractions. Pick the operator using the four buttons below the inputs — the selected one turns purple. Use the Swap button between the two fractions to flip them quickly (useful for subtraction and division, where order matters).

Simplify mode reduces a single fraction to its lowest terms. Enter any fraction and the tool shows the greatest common factor (GCD), the division, and the simplified fraction. Improper fractions are automatically shown as mixed numbers as well.

Convert mode switches between fractions, decimals, and percents in four directions: fraction to decimal, decimal to fraction, fraction to percent, and percent to fraction. For decimals that don't terminate cleanly (like 0.333…), the converter uses a continued-fraction algorithm to find the simplest matching fraction — 13 in this case.

Compare mode sorts 2–5 fractions from least to greatest or greatest to least. Each fraction shows its decimal value alongside a proportional bar so you can see the relative size at a glance.

In every mode the result panel shows the answer in four formats at once: the simplified fraction, the mixed number (when applicable), the decimal, and the percentage. The step-by-step solution below the result walks through every stage of the calculation — the LCD, the rewritten fractions, the operation itself, and the simplification — with each fraction rendered as a proper stacked numerator over denominator.

The four fraction operations explained

Each operation has its own rule. The calculator applies the correct one automatically, but understanding the underlying math makes the results easier to trust.

Adding fractions

To add fractions with different denominators, find the least common denominator (LCD), rewrite each fraction so it shares that denominator, then add the numerators. The denominator does not change.

Worked example. Let's add 34 and 56. The LCD of 4 and 6 is 12. Rewrite each fraction to have denominator 12:

Add the numerators: 9 + 10 = 19. Result:

Subtracting fractions

Subtraction follows the same process as addition — find the LCD, rewrite, then subtract the numerators.

Worked example. 34 − 16. The LCD is 12, so 912 − 212 = 712.

Multiplying fractions

Multiplication is the simplest operation: multiply the numerators together, multiply the denominators together, then simplify.

Worked example. 23 × 34 = 2×33×4 = 612 = 12.

Dividing fractions

Dividing by a fraction is the same as multiplying by its reciprocal. Flip the second fraction and multiply — some teachers call this "keep, change, flip".

Worked example. 34 ÷ 56 = 34 × 65 = 1820 = 910.

How to simplify a fraction

A fraction is in its simplest form when the numerator and denominator share no common factors other than 1. To simplify, find the greatest common factor (GCD) of the numerator and denominator, then divide both by it.

Worked example. Simplify 1218. The factors of 12 are 1, 2, 3, 4, 6, 12. The factors of 18 are 1, 2, 3, 6, 9, 18. The greatest common factor is 6.

The calculator finds the GCD using the Euclidean algorithm — a fast, well-established method taught in every number theory course. It also handles improper fractions by converting them to mixed numbers after simplification.

💡 Why simplify? Two fractions can be equal but written differently — 68 and 34 have the same value. The simplest form makes them easier to compare, add, and picture. In cooking, construction, and almost every practical setting, the lowest-terms form is the one people expect to see.

Mixed numbers and improper fractions

A mixed number combines a whole number and a proper fraction, like 234. An improper fraction has a numerator that is greater than or equal to its denominator, like 114. They represent the same value.

Mixed to improper. Multiply the whole number by the denominator, add the numerator, and place the result over the original denominator.

Improper to mixed. Divide the numerator by the denominator. The quotient becomes the whole number, and the remainder becomes the new numerator.

⚠ Common trap: 234 does not equal 2 × 34. The whole number is added, not multiplied. This is why calculators that parse mixed numbers correctly are so useful — it is easy to lose track of whether you are adding or multiplying the whole-number part.

Finding the LCD (least common denominator)

The LCD is the smallest number that all denominators in a problem divide into evenly. It equals the least common multiple (LCM) of the denominators. To find it, factor each denominator into primes and take the highest power of each prime that appears, or use the GCD formula:

For 4 and 6: GCD(4, 6) = 2, so LCD = 4 × 62 = 12. The calculator shows the LCD as a step in every addition and subtraction problem so you can see how the fractions were aligned.

For three or more denominators, apply the formula pairwise: LCD(2, 3, 4) = LCD(LCD(2, 3), 4) = LCD(6, 4) = 12.

Converting between fractions, decimals, and percents

Fractions, decimals, and percents are three ways of writing the same quantity. Converting between them is a routine task in cooking, finance, statistics, and education.

For repeating decimals like 0.333…, the exact fraction is 13. The converter uses a continued-fraction algorithm to find the simplest fraction matching the decimal value within a small tolerance. So 0.333333… becomes 13 and 0.666666… becomes 23 automatically.

Real-world uses for fraction math

Fraction arithmetic is more common in daily life than many people realize. Here are the contexts where an accurate fraction calculator matters.

• Cooking and baking. Recipes frequently call for 34 cup, 12 teaspoon, or 112 cups. Doubling, halving, or scaling a recipe means multiplying or dividing fractions.
• Construction and woodworking. Tape-measure readings are given in fractional inches: 538", 1116", 214". Adding and subtracting these lengths requires fluent fraction arithmetic.
• Education. Fractions are a core topic from roughly 3rd grade through algebra and beyond. Seeing every step of the work makes the process transparent for students, parents helping with homework, and tutors.
• Finance and business. Interest rates, discounts, and ratios are often expressed as fractions or percentages. A 38 percentage-point change in a rate, or a 23 split of profits, is fraction arithmetic.
• Music. Note values are fractions of a whole note — a quarter note is 14, an eighth note is 18, a dotted half note is 34. Adding note durations within a measure is fraction addition.
• Sports statistics. Batting averages, completion percentages, win-loss ratios, and free-throw percentages are all fractions in disguise.
• Engineering and science. Scale drawings, gear ratios, dilutions, and molar concentrations frequently involve fractions that need to be combined or simplified.

Common fraction mistakes to avoid

Most fraction errors are not arithmetic errors — they're rule errors. These are the mistakes that trip people up most often.

• Adding denominators. 12 + 13 is not 25. Find a common denominator first: 36 + 26 = 56.
• Forgetting to simplify. 612 is a correct answer but not in lowest terms. Always reduce to 12.
• Confusing multiply and divide. When dividing fractions, remember to flip the second fraction. Flipping the first one gives the wrong answer.
• Mixing up LCD and GCD. LCD is for addition and subtraction — it aligns denominators. GCD is for simplification — it reduces a fraction. They are different tools for different jobs.
• Ignoring the sign. A negative numerator follows the same rules as a positive one, but the sign must be tracked through every step.
• Converting mixed numbers incorrectly. 234 = 114, not 54 or 64.
• Treating improper fractions as wrong. 74 is a perfectly valid fraction, equal to 134. Both forms are correct.

Tips for checking your work

• Estimate first. 34 is close to 1 and 56 is also close to 1, so their sum should be close to 2. If you get 524, you know something went wrong.
• Convert to decimals for a sanity check. 34 + 56 ≈ 0.75 + 0.833 = 1.583, and 1912 ≈ 1.583. The numbers agree.
• Look for near-1 values. When a fraction is close to 1 (like 1112), its decimal is close to 1. A result bigger than 1 when subtracting two near-1 fractions should raise an alarm.
• Check the sign. A positive fraction minus a larger positive fraction must be negative. If your result isn't negative, check the direction of the subtraction.
• Verify simplification. Multiply your simplified result back by the GCD to make sure you get the original fraction. 23 × 6 = 1218. Correct.

Limitations

• The arithmetic mode combines two fractions at a time. For expressions with three or more fractions, combine the first two, then combine the result with the third — step by step.
• Decimal-to-fraction conversion uses the continued-fraction algorithm, which finds the closest simple fraction. For a very long repeating decimal, the result is an approximation with a small denominator rather than the exact repeating fraction.
• Visual fraction bars become difficult to read when the denominator is very large (over 60 segments). The numeric result remains correct regardless, and the bars fall back to a proportional representation.
• The compare mode supports up to five fractions. For longer lists, sort them in groups or use a spreadsheet.

Frequently asked questions

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