VI Ratio, Rate, Proportions and Percent

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: $1$.

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 $84$.

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

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