fraction

A fraction is how we name a part of a whole. Slice a pizza into 4 equal pieces and grab 3 of them, and you are holding 3/4 of the pizza. The bottom number (the denominator) says how many equal parts the whole is cut into; the top number (the numerator) says how many of those parts you have.

A fraction a/b stands for a divided by b, written with a numerator on top and a denominator on the bottom (the denominator must be nonzero). When the numerator is smaller than the denominator the fraction is less than 1 (proper); when it is larger the fraction is more than 1 (improper), like 7/4. The same value has many forms: 3/4, 6/8, and 75/100 are all equal, and reducing to lowest terms gives the simplest one.

Fractions are the everyday face of the rational numbers, but the two ideas are not identical: “fraction” usually refers to the written form a/b, while “rational number” refers to the value itself. To add or subtract fractions you first make a common denominator; to multiply you multiply across; to divide you multiply by the reciprocal of the second fraction.