A ratio compares two numbers. Every fraction is a ratio if both numbers represent the same unit. 15 miles out of 45 miles may be written as or 1:3. Units are not written and ratios may be simplified.
Units in rates are different and written with their values. They can be reduced but not written as whole numbers. Example: .
A proportion is the equality of two ratios (fractions). Among other it's used for scales. A generic proportion is . Two fractions are proportional if their cross products are equal: . This makes proportional equations quite easy to solve for one value:
This can be applied to many problems. Imagine a certain amount of material costs a certain amount. This techniques calculates how much a different amount of the material would cost.
Defined as parts of a hundred: .
A decimal is converted to a percent by moving the digits 2 places to the left.
A percent is converted to a decimal by moving the digits 2 places to the right.
A fraction is converted to a percent by multiplying by 100.
Equations dealing with percentages can be solved using the cross product of two equivalent fractions. e.g. Find of .