## Ratio

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 $\frac {15}{45}$ or 1:3. Units are not written and ratios may be simplified.

## Rate

Units in rates are different and written with their values. They can be reduced but not written as whole numbers. Example: $\frac {30km}{hour}$.

## Proportions

A proportion is the equality of two ratios (fractions). Among other it's used for scales. A generic proportion is $\frac a b = \frac c d$. Two fractions are proportional if their *cross products* are equal: $a \times d = b \times c$. This makes proportional equations quite easy to solve for one value:

$\frac 5 9 = \frac{x}{45}$
$5 \times 45 = 225$

$9 \times x = 225$ | $\div 9$

$x = 25$

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.

## Percent

Defined as parts of a hundred: $1% = \frac {1}{100} = 0.01$.

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 $25%$ of $84$.

$\frac {is}{of} = \frac { percent } {100}$

$\frac {x}{84} = \frac {25} {100}$