パーセント計算機

The rules behind adding, subtracting, multiplying and dividing fractions

Fractions trip people up because each operation follows a different rule. This calculator applies the correct procedure for each, shows every step, and then reduces the answer to lowest terms — so it doubles as a way to learn the method, not just get a number.

Multiplication is the easy one: multiply the two numerators together and the two denominators together. 2/3 × 4/5 = 8/15. Division is multiplication in disguise — you flip the second fraction (its reciprocal) and multiply: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12, which reduces to 5/6. Addition and subtraction are the ones that need care, because you can only add numerators when the denominators match. The tool finds the least common multiple (LCM) of the two denominators, rewrites both fractions over that common denominator, and then adds or subtracts the numerators.

A worked example: 1/2 + 1/3

Follow the steps the calculator displays:

1. The denominators are 2 and 3. Their LCM is 6.
2. Rewrite each fraction over 6: 1/2 = 3/6 (multiply top and bottom by 3) and 1/3 = 2/6 (multiply by 2).
3. Add the numerators: 3 + 2 = 5, giving 5/6.
4. Check whether it reduces. The greatest common divisor of 5 and 6 is 1, so 5/6 is already in simplest form.

The result panel also shows 5/6 as the decimal 0.833333 and, when the fraction is larger than one, as a mixed number.

How simplification works

To reduce a fraction, you divide the numerator and denominator by their greatest common divisor (GCD). The tool finds the GCD with the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing it by the smaller, until the remainder is zero; the last non-zero value is the GCD. For 12/18, it computes GCD(18, 12) → remainder 6 → GCD(12, 6) → remainder 0, so the GCD is 6. Dividing both parts by 6 gives 2/3. The Simplify tab shows exactly this, including which GCD it used, so you can verify the reduction by hand.

Mixed numbers and decimals

An improper fraction (numerator bigger than denominator) can be written as a whole number plus a proper fraction. The tool divides to find the whole part and keeps the remainder over the original denominator. For example 7/4 becomes 1 3/4, because 4 goes into 7 once with 3 left over. The decimal form is simply the numerator divided by the denominator, shown to six places and trimmed of trailing zeros, which is handy when you need the value for a spreadsheet or a measurement.

Where this helps

• Cooking and baking. Halving a recipe that calls for 3/4 cup means computing 3/4 ÷ 2 = 3/8 — exactly the kind of arithmetic this handles.
• Woodworking and DIY. Imperial measurements live in fractions of an inch; adding 5/8 + 3/16 correctly avoids a misaligned cut.
• Homework and tutoring. The step-by-step working shows the method, so students can check not just the answer but each move.
• Probability and ratios. Combining fractional odds or scaling ratios needs the same operations.

Common mistakes the calculator prevents

• Adding numerators and denominators straight across. A classic error is writing 1/2 + 1/3 = 2/5. You cannot add denominators; you must find a common one first. The shown steps make the right method obvious.
• Forgetting to flip when dividing. Dividing by a fraction is multiplying by its reciprocal — skipping the flip inverts the answer.
• Leaving the answer unreduced. 10/12 is correct but not in lowest terms; teachers usually want 5/6. The tool reduces automatically.
• A zero denominator. A denominator of zero is undefined, and dividing by the fraction 0/n is impossible. The calculator catches both and warns instead of returning a meaningless result.

Notes on accuracy and privacy

The calculator works with whole-number numerators and denominators and uses exact integer arithmetic for the fraction itself, so the simplified result is precise — only the decimal preview is rounded for display. Everything runs in your browser with no data sent anywhere, so it works offline and keeps your inputs private.