Fraction Calculator guide

Fraction Rules — Add, Subtract, Multiply & Divide

Fractions represent exact ratios of whole numbers. Understanding denominator, equivalent fractions, and greatest common divisor makes calculation and simplification reliable.

What the numerator and denominator mean

For a fraction a/b, the numerator a counts parts and the denominator b gives the number of equal parts in the whole. The denominator cannot be zero. Fractions a/b and ka/kb are equivalent for any nonzero integer k.

Adding and subtracting

Find a common denominator, preferably the least common multiple of the two denominators. Scale both numerators by the matching factor, then add or subtract. For example, 1/6 + 1/4: the LCD is 12, so 2/12 + 3/12 = 5/12. For subtraction, 3/4 − 5/8 = 6/8 − 5/8 = 1/8.

Multiplication

Multiply numerator by numerator and denominator by denominator: (a/b)×(c/d) = ac/bd, then reduce. For example, 2/3 × 9/10 = 18/30 = 3/5. Multiplying two negative fractions gives a positive result.

Division

Divide by multiplying by the reciprocal: (a/b)÷(c/d) = (a/b)×(d/c), where c is nonzero. For example, 7/8 ÷ 14/3 = 7/8 × 3/14 = 3/16. Dividing by a fraction equal to zero is not defined.

Reduce to lowest terms

Find the greatest common divisor (GCD) of the numerator and denominator, divide both by it, and normalize a negative denominator to positive. For example, 12/8 reduces using GCD 4 to 3/2. A result with denominator one is a whole number.

Mixed numbers and negatives

The mixed number 2 1/3 is 7/3. For negative mixed numbers, the minus applies to the entire quantity: -2 1/3 = -7/3. Convert mixed numbers to improper fractions before performing arithmetic. For -7/3, the mixed display is -2 1/3, not -2 + 1/3.

Fractions and decimals

A finite ordinary decimal becomes a fraction using its place value: 2.75 = 275/100 = 11/4. Some fractions end in decimals, such as 1/8 = 0.125; others repeat without ending, such as 1/3. A 12-place rounded decimal is an approximation of a repeating fraction, not a replacement for the exact rational.