Fractions represent parts of a whole, expressed as one number (the numerator) divided by another (the denominator). Working with fractions involves four basic operations - addition, subtraction, multiplication, and division - each with its own rules. Mastering fraction operations is essential for cooking, construction, financial calculations, and advanced mathematics.

Fraction Basics

A fraction consists of:

• Numerator: The top number, representing how many parts you have
• Denominator: The bottom number, representing how many equal parts make up the whole
• Fraction bar: The line separating them, which also means "divided by"

For example, in 3/4, the numerator is 3 (you have 3 parts) and the denominator is 4 (the whole is divided into 4 equal parts).

Adding and Subtracting Fractions

To add or subtract fractions, they must have the same denominator (called a common denominator):

1. Same denominators: Add or subtract the numerators, keep the denominator. Example: 2/5 + 1/5 = 3/5
2. Different denominators: Find the least common denominator (LCD), convert both fractions, then add or subtract. Example: 1/3 + 1/4 → 4/12 + 3/12 = 7/12
3. Simplify: Always reduce the answer to lowest terms

Multiplying Fractions

Multiplication is simpler - no common denominator needed:

• Multiply the numerators together
• Multiply the denominators together
• Simplify the result
• Example: 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2

Dividing Fractions

Division uses the "keep, change, flip" method:

• Keep the first fraction as is
• Change the division sign to multiplication
• Flip the second fraction (find its reciprocal)
• Multiply as usual
• Example: 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3 = 2 2/3