Fraction Calculator

A fraction represents a part of a whole, consisting of a numerator (the top number indicating how many parts we have) and a denominator (the bottom number indicating how many equal parts the whole is divided into). Working with fractions is a core skill in mathematics, baking, construction, and finance.

Adding and Subtracting Fractions

To add or subtract fractions, the denominators must be the same. This is because you can only combine parts of equal size. If the denominators are different, you must find a Least Common Denominator (LCD):

1. Find the LCD: Find the smallest multiple that both denominators share. For example, to calculate 3/4 + 1/6, the multiples of 4 are (4, 8, 12, 16) and the multiples of 6 are (6, 12, 18). The LCD is 12.
2. Convert the Fractions: Multiply the numerator and denominator of each fraction by the factor needed to get the LCD.
   3/4 = (3 × 3)/(4 × 3) = 9/12
1/6 = (1 × 2)/(6 × 2) = 2/12
3. Add or Subtract: Combine the numerators while keeping the common denominator:
   9/12 + 2/12 = (9 + 2)/12 = 11/12

Multiplying Fractions

Unlike addition, multiplying fractions is extremely straightforward because you do not need a common denominator. Simply multiply the numerators together and the denominators together:
(a/b) × (c/d) = (a × c) / (b × d)For example, to multiply 2/3 × 4/5:
(2 × 4)/(3 × 5) = 8/15

Dividing Fractions

To divide fractions, you use the classic math rule: "Keep, Change, Flip":

1. Keep the first fraction exactly as it is.
2. Change the division sign into a multiplication sign.
3. Flip the second fraction (find its reciprocal by swapping the top and bottom numbers).
4. Multiply the two fractions as usual.

For example, to calculate (2/3) ÷ (4/5):
= 2/3 × 5/4 = 10/12 = 5/6

Working with Mixed Fractions

A mixed fraction (or mixed number) consists of a whole number combined with a proper fraction (e.g., 2 1/2). To easily perform math operations on mixed numbers, it is best to first convert them into improper fractions:

1. Multiply the whole number by the denominator.
2. Add the numerator to that result to get the new numerator.
3. Keep the original denominator.

For example, to convert 3 1/4:
(3 × 4) + 1 = 13, giving the improper fraction 13/4.

Frequently Asked Questions (FAQ)