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.
• Aproportionis an equality between two or more ratios such as: ab=cb.
•Similar Triangleshave sides whose ratios form a proportion
•Percentmeans, 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:
part whole×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:
favorable outcomes all possible outcomes×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:
new value old value×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.
speed =distance time
, or R = D • t. It expresses how distance changes for each unit change in time.
density =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: change in y change in x
and it expresses how y changes for each unit change in x. The usual formula is: y 2−y 1x 2−x 2 .