Fractions, ratio and percent
Whole numbers count whole things. How do you say how much of a thing you have, how two amounts compare, or how big a share is out of every hundred?
Where you are 3 inside
What this area is about
Three ways of describing amounts that whole numbers alone cannot. A fraction names part of a whole. A ratio compares two amounts by how many times one fits in the other. A percent is a ratio measured against 100. Each one builds on the one before.
How these fit together
Fractions is the foundation: a fraction \displaystyle \frac{a}{b}, for whole numbers a and b \neq 0, is a pieces of a whole cut into b equal parts, and then a number on the line that can be renamed, compared, added, multiplied and divided.
Ratio uses that multiplying. A ratio a : b stays the same when both amounts are multiplied by one positive number, which gives equivalent ratios, unit rates, proportions, proportional relationships and scale drawings.
Percent is a ratio with a fixed second amount: p\% means p for every 100. It gives one scale for comparing parts of different wholes, and handles percent change, discounts, tax and interest.
A path through it
Fractions first, then ratio, then percent. Each depends on the one before: ratio needs multiplying fractions, and percent is defined as a ratio.
Fractions lead on to rational numbers, ratio to similarity in geometry, and the whole area to probability, measuring how likely something is.