Fraction Calculator

Five inputs, in plain English:

1. First numerator — the top number of the first fraction.
2. First denominator — the bottom number of the first fraction. Cannot be 0 (dividing by zero breaks math).
3. Operation — pick add, subtract, multiply, or divide.
4. Second numerator — the top number of the second fraction. (If you’re dividing, this also cannot be 0.)
5. Second denominator — the bottom number of the second fraction. Same no-zero rule.

Hit calculate and you’ll get six results. The raw result numerator and denominator show what you get directly from the formula before simplification — useful for checking homework where the teacher wants to see the work. The simplified numerator and denominator are the same value reduced to lowest terms by dividing both by their greatest common divisor. The decimal result is the fraction as a decimal, rounded to four places. The percent result is that decimal times 100.

A quick example to anchor it: enter 1, 2, add, 1, 3 to compute 1/2 + 1/3. The calculator returns raw 5/6, simplified 5/6 (already in lowest terms), decimal 0.8333, percent 83.33%. Same number, three notations.

For mixed numbers like 2¾ (two and three-quarters), convert to an improper fraction first: 2¾ = (2×4 + 3)/4 = 11/4. Enter the improper form. The calculator works exclusively with improper fractions internally, since they’re cleaner to add and multiply.

Fractions are just division wearing a costume. 3/4 is 3 ÷ 4 — a number waiting to become 0.75 the moment you stop calling it a fraction. The notation looks scarier than the math actually is: a number on top (the numerator, “how many slices you have”), a line, and a number on the bottom (the denominator, “how many slices the whole pizza was cut into”).

So why do we keep using fractions instead of just decimals? Because some numbers refuse to play nicely as decimals. 1/3 as a decimal is 0.333333... forever. 1/7 is 0.142857142857... also forever. As fractions, both are exact and tidy. Fractions are also how the world actually measures things: 1/2 cup of flour, 3/8 wrench, 5/16 drill bit, 1/4 pound of cheese. Try ordering “0.25 pounds of provolone” at a deli counter. (Don’t. Just say a quarter pound.)

This calculator does the four operations — add, subtract, multiply, divide — then automatically simplifies the answer and shows it three ways: as a fraction, as a decimal, and as a percent. The trickiest of those four operations is addition, because adding fractions requires that the denominators match before you can combine the numerators. (Try adding eighths to fifths in your head and you’ll see what you escape by using a calculator.) Multiplication is the easy one: just multiply across the top and across the bottom. Division is multiplication in disguise — flip the second fraction upside down and multiply.

Two quirks worth flagging up front. First, every fraction has infinite equivalent forms: 1/2 = 2/4 = 50/100 = 9/18. They’re all the same number, but only one is in simplest form. The calculator always shows you both the raw cross-multiplied result and the fully reduced version. Second, fractions can be negative — just put the minus sign on the numerator. The calculator handles signs automatically and always returns a positive denominator (because nobody likes reading 3/−4 when they could read −3/4 instead).

The four operations on fractions a/b and c/d:

• Addition: a/b + c/d = (a×d + c×b) / (b×d)
• Subtraction: a/b − c/d = (a×d − c×b) / (b×d)
• Multiplication: a/b × c/d = (a×c) / (b×d)
• Division: a/b ÷ c/d = (a×d) / (b×c)  —  same as multiplying a/b by the reciprocal d/c

The intuition behind addition and subtraction: you can’t directly combine pieces of different sizes. Two thirds and one quarter aren’t comparable until both are expressed in the same units — in this case, twelfths. The cross-multiplication formula (a×d + c×b)/(b×d) does exactly that: it converts both fractions to a common denominator of b×d, then adds the numerators. The result often isn’t in simplest form because b×d is rarely the smallest possible common denominator, but that’s what the simplification step is for.

After the operation, both numerator and denominator are divided by their greatest common divisor (GCD), found using the Euclidean algorithm. For example, 9/18 has GCD(9,18) = 9, so it simplifies to 1/2. For decimal output, the calculator divides numerator by denominator and rounds to four decimal places. For percent output, it multiplies that decimal by 100.

Example 1 — Adding fractions with different denominators. Calculate 1/3 + 1/6.

• Cross-multiply for the raw result: (1×6 + 1×3) / (3×6) = 9/18
• GCD(9, 18) = 9, so simplified result: 1/2
• Decimal: 0.5  |  Percent: 50%

Notice 9/18 isn’t the most efficient cross-multiplication possible — the lowest common denominator is 6, not 18 — but the formula doesn’t care. Simplification cleans up whatever the formula produces.

Example 2 — Multiplying fractions. Calculate 2/5 × 3/4.

• Multiply across: (2×3) / (5×4) = 6/20
• GCD(6, 20) = 2, so simplified: 3/10
• Decimal: 0.3  |  Percent: 30%

This is why multiplication is the easy fraction operation: no common denominator hunting required.

Example 3 — Dividing fractions (the “flip and multiply” trick). Calculate 5/8 ÷ 1/2.

• Flipping 1/2 gives the reciprocal 2/1, then multiply: (5×2) / (8×1) = 10/8
• GCD(10, 8) = 2, so simplified: 5/4 (an improper fraction, equal to 1¼)
• Decimal: 1.25  |  Percent: 125%

The “dividing makes it bigger?!” surprise here is real and worth pausing on: dividing by a number less than 1 always makes the result larger than the original. 5/8 is less than 1, but 5/8 ÷ 1/2 = 5/4, which is more than 1. Asking “how many halves fit inside 5/8?” the answer is 1.25 halves. Math checks out.

Example 4 — Subtracting fractions. Calculate 7/8 − 1/4.

• Cross-multiply: (7×4 − 1×8) / (8×4) = (28 − 8) / 32 = 20/32
• GCD(20, 32) = 4, so simplified: 5/8
• Decimal: 0.625  |  Percent: 62.5%

A useful sanity check: when subtracting two positive fractions, your answer must be smaller than the larger fraction. 7/8 = 0.875, and 5/8 = 0.625, which is smaller. Looks right.