How the Fraction Calculator Works

Adding Fractions

To add fractions with different denominators, you need to find a common denominator first:

Example: 1/2 + 1/3 = (1×3 + 2×1)/(2×3) = (3 + 2)/6 = 5/6

Subtracting Fractions

Similar to addition, find a common denominator first:

Example: 1/2 - 1/3 = (1×3 - 2×1)/(2×3) = (3 - 2)/6 = 1/6

Multiplying Fractions

To multiply fractions, multiply the numerators and denominators:

Example: 1/2 × 1/3 = (1×1)/(2×3) = 1/6

Dividing Fractions

To divide fractions, multiply by the reciprocal of the second fraction:

Example: 1/2 ÷ 1/3 = 1/2 × 3/1 = (1×3)/(2×1) = 3/2 = 1 1/2

Simplifying Fractions

To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD):

Example: 8/12 = (8÷4)/(12÷4) = 2/3

Converting Between Fractions and Decimals

To convert a fraction to a decimal, divide the numerator by the denominator:

Example: 3/4 = 3 ÷ 4 = 0.75

To convert a decimal to a fraction:

1. Count the number of decimal places (n)
2. Multiply the decimal by 10^n to get the numerator
3. Set the denominator to 10^n
4. Simplify the fraction

Example: 0.75 = 75/100 = 3/4

Converting Between Improper Fractions and Mixed Numbers

To convert an improper fraction to a mixed number:

1. Divide the numerator by the denominator
2. The quotient is the whole number part
3. The remainder is the new numerator
4. The denominator stays the same

Example: 11/4 = 2 3/4

To convert a mixed number to an improper fraction:

Example: 2 3/4 = (2×4 + 3)/4 = 11/4