Fractions, Decimals, Percents

A fraction is just one of three ways to write the same value. Divide the top by the bottom and you get a decimal; slide that decimal two places and you get a percent. So 1/2 = 0.5 = 50%, and 3/4 = 0.75 = 75% are the same number in three outfits.

This is why a 1/4-off sale and a 25%-off sale mean exactly the same discount. Switching between forms lets you pick whichever one makes the math easiest.

Scales, maps, and currency conversions all run on equivalent fractions. A map's "1 inch = 50 miles" is just the ratio 1 inch : 50 miles held constant, and "$1 = 135 yen" is one giant equivalent ratio held steady. (A scale written as a pure ratio like 1:50 means 1 unit equals 50 of the same unit, so it works only when both sides share a unit — for example, 1 cm to 50 cm.) As long as both sides grow or shrink by the same factor, the relationship stays true — convert 2 inches and you instantly read 100 miles.