Ratios / Rates / Proportions

Understanding the difference between ratios, rates and proportions is important for getting a high math score on the SAT. We are going to take a look at some of the basic information that should be known about ratios, rates and proportions when it comes to the math section of the SAT.  Ratios Ratios are used to establish a relationship between two groups of numbers. They can be written down as fractions, as a series of numbers separated by a colon, or written as words.  TIP: On the SAT math section, if a question gives a ratio in a form other than fraction form, it is advisable to set it up as a fraction to make it easier to deal with and get the correct answer.  Other questions may be more complicated and ask for an answer that is derived from ratios. For example, they may give you a ratio of pizza to pasta and ask for the total number of dishes or plates of food.  EXAMPLE The ratio of slices of pie to slices of cake to bowls of ice cream at the party was five to four to seven.  If there were 52 slices of pie at the party, how many other food choices were also available? To solve, it is simply a matter of adding up the ratios to find the total number of pieces in the ratio.  Ratios are not real numbers so they should never be mixed with real numbers in a fraction.  Proportions Proportions on the SAT math section are a different type of ratio problem that may be asked. For proportion questions, they will typically give two ratios that work together. In word problems, it is important to look for pairs of items that get repeated in the question.  Like ratios, proportion problems need to be set up in the right way to make sure the correct answer is received. Numerators should refer to a single thing - the denominator of the other.  TIP: In some cases they may give you information in hours and also minutes. It is important to pick one and translate one to the other. So, 3 hours and 54 minutes would be 180 minutes and 54 minutes.  The most common type of proportions are called direct proportions or direct variation.   Another type of proportion is called an indirect proportion.  They may also be referred to as an inverse proportion, indirect variation or even an inverse variation. These are used in cases where increasing one thing decreases another thing. For example, if one worker can get so much done in four hours, it does not make sense to say getting three people to help would make it take sixteen hours. This is what is known as an indirect proportion.  In SAT math word problems that use indirect proportions it is important to make sure it is indirect and not a direct proportion question. Remember that test makers are trying to trick test takers into getting the wrong answer.  BONUS:  An additional way to think about the difference between direct and indirect variations is to define them as if x/y = a constant like t while indirect if yx = t.  Rate On the SAT math section, a rate is a ratio that deals with time. For example, a car driving 42 mph, a runner doing 2 miles in 15 minutes.