{"id":1814,"date":"2019-08-24T13:22:30","date_gmt":"2019-08-24T18:22:30","guid":{"rendered":"http:\/\/www.kaptest.com\/blog\/prep\/?p=1814"},"modified":"2023-08-29T20:53:20","modified_gmt":"2023-08-29T20:53:20","slug":"psat-math-rates-ratios-proportions-percentages","status":"publish","type":"post","link":"https:\/\/wpapp.kaptest.com\/study\/psat\/psat-math-rates-ratios-proportions-percentages\/","title":{"rendered":"PSAT Math: Rates and Measurements"},"content":{"rendered":"

By now, you\u2019ve become adept at using algebra to answer many PSAT math questions, which is great, because you\u2019ll need those algebra skills to answer questions involving rates. You\u2019re likely already familiar with many different rates\u2014kilometers per hour, meters per second, and even miles per gallon are all considered rates.<\/p>\n

A fundamental equation related to rates is \u201camount = rate \u00d7 time\u201d. If you have two of the three components of the equation, you can easily find the third.<\/p>\n

You\u2019ll notice units of measurement are important for rate questions (and others that require a unit conversion) and, therefore, also an opportunity to fall for trap answers if you\u2019re not careful. How can\u00a0you avoid this? Use the factor-label method (also known as dimensional analysis). The factor-label method is a simple yet powerful way to ensure you\u2019re doing your calculations correctly and getting an answer with the requested units.<\/p>\n

For example, suppose you\u2019re asked to find the number of cups there are in two gallons. First, identify your starting quantity\u2019s units (gallons) and then identify the end quantity\u2019s units (cups). The next step is to piece together a path of relationships that will convert gallons into cups, canceling out units as you go. Keep in mind that you will often have multiple stepping stones between your starting and ending quantities, so don\u2019t panic if you can\u2019t get directly from gallons to cups.<\/p>\n

The test makers won\u2019t expect you to know English measurements by heart. Instead, they\u2019ll provide conversion factors when needed. For example, a gallon is the same as 4 quarts, every quart contains 2 pints, and a pint equals 2 cups. And there you have it! Your map from gallons to cups is complete. The last step is to put it together as a giant multiplication problem. Each relationship, called a conversion factor, is written as a fraction. The basic rules of fraction multiplication apply, so you can cancel a unit that appears in both the numerator and denominator.<\/p>\n

The PSAT<\/span> will not require you to memorize conversions for conventional units. If the test asks you to convert miles into inches, for example, you will be provided with enough conversion factors to solve the problem.<\/p>\n

Follow along as we convert from gallons to quarts to pints to cups using the factor-label method:<\/p>\n

\"psat<\/p>\n

distance = rate x time is actually a variation of this process. Suppose you travel at 60 mph for 5 hours. You would calculate the distance traveled using the equation d = r x t = 60mi \u00d7 5h = 300 \u00a0miles. The units for hours cancel out, leaving only miles, which is precisely what you’re looking for, a distance. This built-in check is a great way to ensure your path to the answer is correct. If your units are off, check your steps for mistakes along the way. The PSAT<\/span> will never ask you for a quantity such as miles or gallons, so if you end up with funky units like that, you\u2019ve made an error somewhere in your work.<\/p>\n