Fraction Calculator with Steps

1/2 + 1/3 = 5/6. Because the denominators (2 and 3) are different, first find their least common denominator (LCD), which is 6. Convert each fraction to an equivalent form (3/6 + 2/6) and add the numerators: 3 + 2 = 5, giving 5/6 in simplest form.

3/4 − 1/3 = 5/12. Find the lowest common denominator of 4 and 3, which is 12. Convert each fraction: 3/4 = 9/12 and 1/3 = 4/12. Subtracting the numerators yields (9 − 4)/12 = 5/12.

3/4 ÷ 1/2 = 3/2 (or 1 ½ as a mixed number). Using Keep-Change-Flip (multiplying by the reciprocal), change the division into multiplication: 3/4 × 2/1 = 6/4. Dividing numerator and denominator by 2 simplifies the result to 3/2 = 1 ½ = 1.5.

To add mixed numbers like 2 ½ + 1 ¾, first convert each to an improper (top-heavy) fraction: 2 ½ = 5/2 and 1 ¾ = 7/4. Next, find a common denominator (4) to get 10/4 + 7/4 = 17/4, which simplifies to the mixed number 4 ¼.

To subtract mixed numbers such as 3 ⅓ − 1 ½, first convert them into improper fractions: 3 ⅓ = 10/3 and 1 ½ = 3/2. Find the common denominator (6) to express them as 20/6 − 9/6 = 11/6, which equals 1 ⅚.

Convert both mixed numbers to improper fractions before dividing. For example, 2 ¼ ÷ ¾ becomes 9/4 ÷ 3/4. Multiplying by the reciprocal gives 9/4 × 4/3 = 36/12 = 3.

Divide the numerator (top number) by the denominator (bottom number). The whole quotient is the integer part, and the remainder becomes the new numerator over the original denominator. For example, 29 ÷ 6 = 4 remainder 5, so 29/6 = 4 ⅚.

Divide the amount by the denominator, then multiply by the numerator. For example, to find 3/5 of £40, compute £40 ÷ 5 = £8, then £8 × 3 = £24. Similarly, 3/4 of $20 is 20 ÷ 4 × 3 = $15.

The least common denominator (LCD) is the lowest common multiple (LCM) of the denominators. List the multiples of each denominator until you identify the smallest shared number. For example, the multiples of 4 are 4, 8, 12, 16... and the multiples of 6 are 6, 12, 18... making 12 the LCD of 4 and 6.

Fractions represent equal fractional parts of a whole. Adding 1/2 + 1/3 cannot equal 2/5 (0.4) because 1/2 alone is already 0.5. Denominators indicate part sizes; you must scale them to equal units using a common denominator (6) so that 3/6 + 2/6 = 5/6.

The reciprocal of a fraction is created by swapping its numerator and denominator (flipping it). The reciprocal of 3/4 is 4/3, and the reciprocal of an integer n (n/1) is 1/n. Multiplying any non-zero fraction by its reciprocal always equals 1.

Convert both fractions to have a shared common denominator. For example, to compare 3/5 and 2/3, express both with a denominator of 15: 3/5 = 9/15 and 2/3 = 10/15. Because 10/15 > 9/15, 2/3 is greater than 3/5.

The greatest common factor (GCF in US math) or highest common factor (HCF in UK maths) is the largest whole number that divides evenly into both numerator and denominator. For 18/24, the GCF/HCF is 6, reducing 18/24 to lowest terms: 3/4.

Multiplying fractions does not require a common denominator: multiply the numerators straight across and the denominators straight across: (a/b) × (c/d) = (a × c) / (b × d). For instance, (2/3) × (5/7) = 10/21. Once multiplied, reduce the result to simplest form.

No. Division by zero is mathematically undefined. A denominator represents how many equal pieces divide a whole; because a unit cannot be divided into zero pieces, entering zero as a denominator produces an error.

This calculator accurately handles negative mixed numbers (entering −2 with 3/4 treats the entire quantity as −(2 + ¾) = −11/4). It also computes using arbitrary-precision JavaScript BigInt arithmetic, ensuring 100% exact fractions without 64-bit floating-point rounding errors.