What is a proper fraction?

A fraction where the numerator is smaller than the denominator, like 3/4. Its value is between 0 and 1.

How do I simplify a fraction?

Divide both the numerator and denominator by their greatest common divisor (GCD). For 12/18, the GCD is 6, so 12/18 = 2/3.

What is a mixed number?

A whole number combined with a fraction, like 2 1/3. To convert to an improper fraction: (2×3+1)/3 = 7/3.

Fractions

Parts of a whole, simplified

Fractions represent parts of a whole. They appear in cooking, measurements, probability, and algebra. Understanding how to operate on fractions — add, subtract, multiply, divide, and simplify — is essential for both daily life and advanced math.

Key Concepts

Equivalent Fractions

Multiply or divide both numerator and denominator by the same number. 2/4 = 1/2 = 3/6 — they all represent the same value.

Adding & Subtracting

Find a common denominator, then add or subtract the numerators. 1/3 + 1/4 = 4/12 + 3/12 = 7/12.

Multiplying

Multiply numerators and denominators directly. 2/3 × 4/5 = 8/15. No common denominator needed.

Dividing

Flip the second fraction and multiply. 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.

Tips & Tricks

To simplify a fraction, divide both parts by their GCD. 12/18 → GCD is 6 → 2/3.
To add fractions, find the LCM of the denominators. 1/6 + 1/8 → LCM of 6 and 8 is 24.
Cross-multiply to compare fractions: 3/4 vs 5/7 → 3×7=21, 4×5=20, so 3/4 > 5/7.
To convert a fraction to a decimal, divide the numerator by the denominator.
Mixed numbers to improper fractions: 2 3/4 = (2×4+3)/4 = 11/4.