Fraction Calculator

How to use the fraction calculator

Type the first fraction in box a and the second in box b, then choose an operation. The answer updates as you type. Each box accepts several formats:

You type	Read as	Example meaning
3/4	A simple fraction	three quarters
1 1/2	A mixed number (note the space)	one and a half
−2/5	A negative fraction	minus two fifths
7	A whole number	7/1
0.75	A decimal	75/100, which simplifies to 3/4

Pick Simplify a to reduce a single fraction or turn a decimal into a fraction. Every result is shown four ways: as a simplified fraction, as a mixed number, as a decimal (with any repeating digits marked in brackets) and as a percentage.

Fraction formulas

For fractions a/b and c/d:

• Addition: a/b + c/d = (a × d + c × b) ÷ (b × d), or rewrite both over the least common denominator (LCD) and add the numerators.
• Subtraction: a/b − c/d = (a × d − c × b) ÷ (b × d), or use the LCD the same way.
• Multiplication: a/b × c/d = (a × c) ÷ (b × d).
• Division: a/b ÷ c/d = a/b × d/c = (a × d) ÷ (b × c). This is often called cross-multiplying.

After any operation, divide the numerator and denominator by their greatest common divisor (GCD) to get the answer in lowest terms. The calculator uses the LCD for addition and subtraction because it keeps the numbers small and matches how fractions are taught in school.

Worked examples

Adding with unlike denominators: 3/4 + 5/6. The LCD of 4 and 6 is 12. Rewrite: 3/4 = 9/12 and 5/6 = 10/12. Add the numerators: 9 + 10 = 19, so the sum is 19/12. Since 19 ÷ 12 = 1 remainder 7, that is 1 7/12, or about 1.583333.

Subtracting mixed numbers: 5 1/4 − 2 2/3. Convert to improper fractions: 5 1/4 = 21/4 and 2 2/3 = 8/3. The LCD is 12, so 21/4 = 63/12 and 8/3 = 32/12. Subtract: 63 − 32 = 31, giving 31/12 = 2 7/12.

Multiplying mixed numbers: 2 1/3 × 1 1/2. Convert: 7/3 × 3/2. Multiply across: 21/6. The GCD of 21 and 6 is 3, so the answer simplifies to 7/2 = 3 1/2 = 3.5.

Dividing: 3/4 ÷ 2/5. Flip the second fraction and multiply: 3/4 × 5/2 = 15/8 = 1 7/8 = 1.875.

Problem	Exact answer	Mixed number	Decimal
3/4 + 5/6	19/12	1 7/12	1.58(3)
5 1/4 − 2 2/3	31/12	2 7/12	2.58(3)
2 1/3 × 1 1/2	7/2	3 1/2	3.5
3/4 ÷ 2/5	15/8	1 7/8	1.875

How to simplify a fraction

A fraction is in simplest form when the numerator and denominator share no common factor other than 1. To get there in one step, divide both by their GCD. For 18/24, the factors of 18 are 1, 2, 3, 6, 9 and 18, and 6 is the largest that also divides 24, so 18/24 = 3/4. For large numbers, the calculator finds the GCD with Euclid’s algorithm: keep replacing the larger number with the remainder of dividing it by the smaller one until the remainder is zero. The GCF and LCM calculator shows that process in full.

Fractions, decimals and percentages

Every fraction is a division. Dividing the numerator by the denominator gives a decimal that either stops or repeats forever:

• 3/8 = 0.375 = 37.5% (stops, because 8 = 2 × 2 × 2)
• 1/8 = 0.125 = 12.5%
• 1/3 = 0.(3) = 0.333…
• 2/7 = 0.(285714), a six-digit repeating block

A fraction in lowest terms gives a terminating decimal only when its denominator has no prime factors other than 2 and 5. That is why fifths, eighths and twentieths stop, while thirds, sixths and sevenths repeat. Going the other way, 0.75 = 75/100 = 3/4. For percentage problems such as discounts and marks, the percentage calculator is a better fit.

Common mistakes with fractions

• Adding the denominators. 1/2 + 1/3 is not 2/5. The pieces are different sizes, so convert to sixths first: 3/6 + 2/6 = 5/6.
• Forgetting to convert mixed numbers. Multiplying 2 1/3 × 1 1/2 as (2 × 1) and (1/3 × 1/2) gives 2 1/6, which is wrong. Convert to 7/3 and 3/2 first to get 3 1/2.
• Flipping the wrong fraction. When dividing, flip only the second fraction (the divisor), never the first.
• Misreading negative mixed numbers. −1 1/2 means −(1 + 1/2) = −3/2, not −1 + 1/2.
• Rounding too early. Working in decimals, 1/3 + 1/6 might become 0.33 + 0.17 = 0.50 by luck, but other sums drift. Exact fractions avoid that, and so does this calculator. For ratios such as 3:4, the ratio calculator uses the same simplifying rules.