Percentages: find the right whole.
Percent means per hundred. The hard part is often choosing the quantity that represents 100%, then answering the question actually asked.
Reviewed · Official ASVAB scope and calculator guidance. Examples are original AptiStep material.
Name the whole before calculating
If a $60 jacket is discounted by 15%, the original $60 price is the whole. A discount is an amount removed from that whole. The discount and the final price are different answers.
An increase starts from the original amount
A monthly cost rises from $80 to $100. The change is $20. To find the percentage increase, divide the change by the original cost: 20/80 = 1/4 = 25%. Dividing by the new cost would answer a different question.
For a known percentage increase, add the increase to the original value. Increasing 80 by 25% gives 80 + 20 = 100. A later 25% reduction of 100 gives 75, not 80, because the whole has changed.
Try it without a calculator
A container is 35% full and has a capacity of 80 liters. How much liquid is inside?
Show the solution
Ten percent of 80 is 8. Thirty percent is 24, and five percent is 4. Together, 35% is 28 liters. The result should be less than half the capacity because 35% is less than 50%.
Use an estimate to catch a misplaced decimal
For 15% of 60, the answer must be less than 60 and a little larger than 6, which is 10%. An answer of 90 is impossible. Estimate first when the numbers are unfamiliar; the estimate can rule out a result even before you repeat the calculation.
Four fresh questions
Try each example before opening its answer. Then explain the step you used in your own words.
A $90 bag is 20% off. What is its sale price before tax?
Show answer and reasoning
$72
Ten percent is $9, so 20% is $18. Subtract the discount: $90 − $18 = $72. The amount saved is not the requested sale price.
A weekly cost rises from $50 to $60. What is the percentage increase?
Show answer and reasoning
20%
The increase is $10. Divide by the original $50: 10/50 = 1/5 = 20%. The new $60 amount is not the base for this increase calculation.
Eighteen of 60 seats are occupied. What percentage is occupied?
Show answer and reasoning
30%
The occupied share is 18/60 = 3/10. Three tenths is 30 out of 100, or 30%. The 60 seats represent the whole.
A $100 price rises 10%, then the new price falls 10%. Is it back to $100?
Show answer and reasoning
No; it is $99
The increase makes $110. Ten percent of the new $110 is $11, so the reduction gives $99. Equal percentage changes do not cancel when their starting amounts differ.
Can you explain the method without looking?
Saved on this browser only.