VI Ratio, Rate, Proportions and Percent


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 1545\frac {15}{45} 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: 30kmhour\frac {30km}{hour}.


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

59=x45\frac 5 9 = \frac{x}{45} 5×45=2255 \times 45 = 225
9×x=2259 \times x = 225 | ÷9\div 9
x=25x = 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.


Defined as parts of a hundred: 11% = \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 2525% of 8484.

isof=percent100\frac {is}{of} = \frac { percent } {100}

x84=25100\frac {x}{84} = \frac {25} {100}