Percentages pervade our lives, and so it's important to have a good "feel" for them. On-the-fly estimates involving money, medicine, politics, and the like often require their calculation. Percent questions also frequently appear on the SAT/ACT.
In a nutshell, percents are fractions with denominator 100. The “50-25-10” rule enables use of simple unit fractions as guides in estimating percentages: 50% = 1/2. 25% = 1/4. 10% = 1/10.
Example 1
To estimate 62% of 48,300, first, round 62% to 60%, and 48,300 to 48,000, for convenience. 60% is 10% more than half. Half of $48,000 is 24,000, and 10% of 48,000 is 4,800. Altogether, this makes $28,800. Since we rounded down, adjust the answer up a little, to perhaps 30,000. The correct answer is 29,760.
To work out tricky SAT/ACT percent problems, it’s sometime best to pick a sample value to work with, and see what happens. In such a case, 100 is a good default choice.
Example 2
On your test you’re asked to find the percent of change when a number is first increased by 10% and then decreased by 10%. The trap answer is to assume this is a wash, that there’s no change at all. But using 100 as a sample value enables us to find the surprising answer quite easily. Increasing 100 by 10% yields 110. 10% of 110 is 11, and decreasing 110 by 11 produces 99, which is 1% less than 100. The percent of change is 1%, not 0%.
Problems involving “percent of increase or decrease” would seem to require two calculations, but in practice these questions can easily be answered in a single step. First, simply add or subtract the percent of increase/decrease to/from 100 percent. A 70% decrease equates to direct calculation of 30% of the number. For a 60% increase, take 160% of the number.
Example 3
Suppose your dentist gives a 5% discount to patients who pay at the time of service. Your dental work will cost $420. You could first find 5% of 420, and then subtract this number from 420. But that requires two steps. Instead, remember that 5% off is the same as 95% on! So, simply calculate 95% of 420, and you’ve got your answer: $399.
To estimate 62% of 48,300, first, round 62% to 60%, and 48,300 to 48,000, for convenience. 60% is 10% more than half. Half of $48,000 is 24,000, and 10% of 48,000 is 4,800. Altogether, this makes $28,800. Since we rounded down, adjust the answer up a little, to perhaps 30,000. The correct answer is 29,760.
To work out tricky SAT/ACT percent problems, it’s sometime best to pick a sample value to work with, and see what happens. In such a case, 100 is a good default choice.
Example 2
On your test you’re asked to find the percent of change when a number is first increased by 10% and then decreased by 10%. The trap answer is to assume this is a wash, that there’s no change at all. But using 100 as a sample value enables us to find the surprising answer quite easily. Increasing 100 by 10% yields 110. 10% of 110 is 11, and decreasing 110 by 11 produces 99, which is 1% less than 100. The percent of change is 1%, not 0%.
Problems involving “percent of increase or decrease” would seem to require two calculations, but in practice these questions can easily be answered in a single step. First, simply add or subtract the percent of increase/decrease to/from 100 percent. A 70% decrease equates to direct calculation of 30% of the number. For a 60% increase, take 160% of the number.
Example 3
Suppose your dentist gives a 5% discount to patients who pay at the time of service. Your dental work will cost $420. You could first find 5% of 420, and then subtract this number from 420. But that requires two steps. Instead, remember that 5% off is the same as 95% on! So, simply calculate 95% of 420, and you’ve got your answer: $399.
Example 4
You’re having dinner out and it’s time to pay. The cost of the meal is $74, total, and a 15% tip is standard. You could first calculate 18% of 74 and add that back, but again that’s two calculations. Instead, realizing that a 15% increase produces 115% of the original number, you could simply multiply 74 by 1.15, to arrive at the amount to pay: $85.10.
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For practice, search Google for “SAT ACT percent problem worksheets,” pick a worksheet that provides answers, complete the worksheet, analyze any mistakes, and redo it until you can complete that worksheet with no errors. Then repeat, with additional worksheets, as needed, until you’ve mastered this material.
You’re having dinner out and it’s time to pay. The cost of the meal is $74, total, and a 15% tip is standard. You could first calculate 18% of 74 and add that back, but again that’s two calculations. Instead, realizing that a 15% increase produces 115% of the original number, you could simply multiply 74 by 1.15, to arrive at the amount to pay: $85.10.
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For practice, search Google for “SAT ACT percent problem worksheets,” pick a worksheet that provides answers, complete the worksheet, analyze any mistakes, and redo it until you can complete that worksheet with no errors. Then repeat, with additional worksheets, as needed, until you’ve mastered this material.
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