Strategy #14 Know how to work with ratios, rates, proportions, percents and probabilities

• The ratio of a to b is written as:  \(a/b\) or as:   a:b:c if there are three values.
• A proportion is an equality between two or more ratios such as:  \(\frac{a}{b}= \frac{c}{b}\).
• Similar Triangles have sides whose ratios form a proportion
• Percent means, how much out of 100. It is a ratio and can be found by dividing the PART we are interested in by the WHOLE, then multiplying by 100:  \[\frac{part}{whole}\times 100\]
• The probability of an event is the ratio between the number of favorable outcomes (the part you are interested) to the number of all possible outcomes (the whole). If we want percent probability, then we’d multiply by 100:
 \[\frac{favorable\ outcomes}{all\ possible\ outcomes}\times 100\]

• To convert a decimal to a percent – move the decimal to the right two places.
• To convert a percent to a decimal – move the decimal to the left two places.
• To calculate the percent increase or decrease from the old value to the new value:
  \[\frac{new\ value}{old\ value}\times 100\]

• Know the formulas for density and speed. These are both ratios that express rates of change: the amount of change in the numerator for each unit change in the denominator.

1. \(speed\ = \frac{distance\ }{time\ }\), or R = D • t.   It expresses how distance changes for each unit change in time.
2. \(density\ = \frac{mass\ }{volume\ }\), or D = M • V.  It expresses how mass changes for each unit change of volume.

• Rates of change (or just rates) are simply ratios. 
• The slope is the rate of change for a graphed line of a linear equation. It's the ratio: \(\frac{change\ in\ y\ }{change\ in\ x\ }\)
and it expresses how y changes for each unit change in x. The usual formula is:  \(\frac{y\ _{2}-y\ _{1}}{x\ _{2}-x\ _{2}\ }\).