Fraction Calculator

What is a Fraction?

A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number). The numerator tells how many parts we have, and the denominator tells how many equal parts the whole is divided into.

Fraction Operations

Adding Fractions

To add fractions, find a common denominator, convert both fractions, then add the numerators:

a/b + c/d = (a*d + c*b) / (b*d)

Example: 1/4 + 1/6
Common denominator: 12
= 3/12 + 2/12 = 5/12

Subtracting Fractions

Similar to addition, but subtract the numerators:

a/b - c/d = (a*d - c*b) / (b*d)

Example: 3/4 - 1/3
= 9/12 - 4/12 = 5/12

Multiplying Fractions

Multiply numerators together and denominators together:

a/b * c/d = (a*c) / (b*d)

Example: 2/3 * 3/4
= (2*3) / (3*4) = 6/12 = 1/2

Dividing Fractions

Multiply by the reciprocal of the second fraction:

a/b / c/d = a/b * d/c = (a*d) / (b*c)

Example: 2/3 / 4/5
= 2/3 * 5/4 = 10/12 = 5/6

Simplifying Fractions

To simplify a fraction, divide both numerator and denominator by their GCD:

12/18 = ?
GCD(12, 18) = 6
12/18 = (12/6) / (18/6) = 2/3

Converting to Mixed Numbers

When the numerator is larger than the denominator (improper fraction), convert to a mixed number:

17/5 = ?
17 / 5 = 3 remainder 2
17/5 = 3 2/5

Converting to Decimals

Divide the numerator by the denominator:

3/4 = 3 / 4 = 0.75
1/3 = 1 / 3 = 0.333...

Types of Fractions

• Proper Fraction: Numerator less than denominator (e.g., 3/4)
• Improper Fraction: Numerator greater than or equal to denominator (e.g., 7/4)
• Mixed Number: Whole number plus a fraction (e.g., 1 3/4)
• Unit Fraction: Numerator is 1 (e.g., 1/5)

Applications of Fractions

Cooking

Recipe measurements often use fractions (1/2 cup, 3/4 teaspoon).

Construction

Measurements in inches often include fractions (3 1/2 inches).

Music

Time signatures and note values are expressed as fractions (3/4 time, half notes).

Probability

Chances and odds are expressed as fractions.