Handle percent of, percent change, successive percent changes, and working backward from a final amount.
You compute percents and, more often, reason about them. Questions ask for a percent of a number, a percent increase or decrease, the original value before a change, or the result of two changes applied one after another. Many are set in context, with discounts, tax, interest, population growth, or survey results. A distinct group asks for percent change between two values pulled from a table or graph, which means picking the right starting value for the denominator.
Percent questions usually appear about 2 to 3 times among the 44 math questions, as part of the roughly 15 percent Problem-Solving and Data Analysis share.
Written for this skill, with the answer explained. 108 more are in the app.
What is 60% of 120?
The price of a stock rose from $40 to $44. What was the percent increase?
Why: The rise is 44 - 40 = $4. Percent increase divides that rise by the starting price: 4/40 = 0.10, so 10%. 4% treats the $4 rise as if it were the percent. 5% of 40 is only $2, which would bring the stock to $42. 15% of 40 is $6, which would bring it to $46.
The bar graph shows the number of visitors to a museum exhibit in each of its first four weeks. By what percent did the number of visitors decrease from week 2 to week 4?
Why: Read the two bars: week 2 is 300 visitors and week 4 is 225. The decrease is 300 - 225 = 75. Percent decrease divides by the starting week: 75/300 = 0.25, or 25%. 33% is 75/225, which divides by the week 4 bar instead of the week 2 bar. 75% mistakes the drop of 75 visitors for the percent. 35% would be a drop of 105, down to 195.
The table shows the weight lifted, in pounds, by each of three athletes before and after a training block. What was the percent increase for athlete B?
Why: The increase is 174 - 150 = 24 pounds, and 24/150 = 0.16, or 16%. Answering 13.79 means you divided the increase by the ending weight. Answering 24 means you gave the increase in pounds rather than a percent. Answering 116 means you gave the ending weight as a percent of the starting weight.
Subtract the original value from the new value, divide that difference by the original value, then multiply by 100. A negative result means a decrease. The original value always goes in the denominator, even when the number got smaller.
Because the second percent applies to the larger amount, not the original. Multiplying by 1.2 and then by 0.8 gives 0.96, so the final value is 4 percent below where it started. Successive percents multiply, they do not add.
Write the final price as the original times the remaining fraction. If an item costs 60 dollars after a 25 percent discount, then 0.75 times the original equals 60, so the original is 60 divided by 0.75, which is 80 dollars.
Questions on percentages alone, with explanations on every one, and the app tracks which ones you keep missing.
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