Understanding Fractions: A Complete Guide
Everything you need to know about fractions — types, operations, simplification, and conversions. A comprehensive guide for students and parents.
Fractions are one of the most practical math concepts — they appear in cooking, measurements, money, and statistics. This guide covers everything from basic definitions to advanced operations.
What is a fraction?
A fraction represents a part of a whole. It has a numerator (top number) and a denominator (bottom number). 3/4 means 3 out of 4 equal parts. The denominator tells you how many parts the whole is divided into, and the numerator tells you how many of those parts you have.
Types of fractions
Proper: numerator < denominator (3/4). Improper: numerator ≥ denominator (5/3). Mixed: whole number + fraction (2 1/3). Equivalent: same value, different form (1/2 = 2/4 = 3/6).
Simplifying fractions
Divide both numerator and denominator by their greatest common divisor (GCD). 12/18: GCD = 6, so 12/18 = 2/3. A fraction is in simplest form when the numerator and denominator have no common factor other than 1.
Adding and subtracting fractions
Find a common denominator (the LCM of the two denominators), convert each fraction, then add or subtract numerators. 1/3 + 1/4 = 4/12 + 3/12 = 7/12. The denominator stays the same; only the numerators combine.
Multiplying fractions
Multiply numerators together and denominators together. 2/3 × 4/5 = 8/15. No common denominator needed. Simplify the result if possible.
Dividing fractions
Flip the second fraction (take its reciprocal) and multiply. 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6. The mnemonic is "Keep, Change, Flip": keep the first, change ÷ to ×, flip the second.
Converting fractions
To decimal: divide numerator by denominator. 3/4 = 0.75. To percentage: multiply by 100. 3/4 = 75%. From mixed to improper: 2 1/3 = (2×3+1)/3 = 7/3. From improper to mixed: 7/3 = 2 remainder 1 = 2 1/3.
Comparing fractions
Cross-multiply to compare: 3/4 vs 5/7. 3×7 = 21, 4×5 = 20. Since 21 > 20, 3/4 > 5/7. Alternatively, convert to a common denominator and compare numerators.
Practice all these operations with the Math Champion fraction quiz, or use the fraction calculator to check your work.
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