Fractions represent parts of a whole or parts of a group. The bottom number (denominator) tells how many equal parts the whole is divided into, while the top number (numerator) tells how many of those parts we have. This concept appears everywhere — from pizza slices to musical notes.

Understanding fractions requires grasping that the same amount can be written different ways. One-half (1/2) equals two-fourths (2/4) equals three-sixths (3/6). These equivalent fractions represent the same portion of a whole, just divided into different numbers of pieces.

Comparing fractions develops number sense. When denominators are the same, compare numerators: 3/8 < 5/8. When numerators are the same, the larger denominator means smaller pieces: 1/4 > 1/6. For fractions with different numerators and denominators, find a common denominator or convert to decimals.

Operations with fractions follow specific rules. Adding or subtracting requires common denominators. Multiplying fractions means multiplying numerators and denominators separately. Understanding why these rules work — not just memorizing them — leads to lasting success with fractions.