Compute percent change or the new amount after an increase/decrease.
Free, timed SHSAT practice sets on percent increase & decrease— every question includes a full worked explanation, and there's no account required.
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New amount after a change. Turn the change into one multiplier. An increase of \(p\%\) multiplies by \(1 + \tfrac{p}{100}\); a decrease multiplies by \(1 - \tfrac{p}{100}\). A 42% increase on 80 dollars gives \(80 \times 1.42 = 113.60\) dollars. For a 14% decrease, multiply by 0.86.
Percent change between two values. \(\text{percent change} = \dfrac{\text{new} - \text{original}}{\text{original}} \times 100\) From 50 to 42, the change is 8, and \(8 \div 50 = 0.16\): a 16% decrease.
Traps:
New price \(= \$21.00 \times (1 - 14/100) = \$18.06\). (Reporting only the 14% change instead of the new price gives $2.94. Adding the 14% instead of subtracting it gives $23.94. Subtracting \(\$14\) instead of 14% gives $7.00.) The new price is $18.06.
Percent change \(= \text{change} \div \text{original} \times 100 = \$15.20 \div \$16.00 \times 100 = 95\%\). (Dividing by the new price instead of the original (\(\$15.20 \div \$31.20 \times 100\)) gives about 48.72%. Finding what percent the new price is of the old price (\(\$31.20 \div \$16.00 \times 100\)) gives 195%. Writing the \(\$15.20\) change as a percent gives 15.2%.)
Percent change \(= \text{change} \div \text{original} \times 100 = \$52.56 \div \$73.00 \times 100 = 72\%\). (Dividing by the new price instead of the original (\(\$52.56 \div \$125.56 \times 100\)) gives about 41.86%. Finding what percent the new price is of the old price (\(\$125.56 \div \$73.00 \times 100\)) gives 172%. Writing the \(\$52.56\) change as a percent gives 52.56%.)