LEMMA

Applied arithmetic

Percent increase and decrease

TEAS math

Percent change always measures against the original value, never the new one.

What this covers

% change=oldnew−old​⋅100
  • Find the percent of the ORIGINAL value first.
  • An increase adds that amount; a decrease subtracts it.
  • To find the percent itself, divide the change by the original and multiply by 100.
  • Find the sign from new minus original: positive means increase, negative means decrease. If the amount grew, a negative percent cannot be right.
  • Doubling is a 100% increase, but halving is only a 50% decrease — the original you compare against is different each way.
  • Sanity-check the direction: an increase must land above the original.

Worked example

Worked example

A 300 mg dose is increased by 25%. Find the new dose.

  1. 300⋅10025​=75The increase is a quarter of the original 300.
  2. 300+75=375An increase adds the change onto what was there.
Another worked example

Compare the percent change from 80 to 100 with the change from 100 to 80.

  1. 80100−80​⋅100%=25%Use the initial 80 as denominator on the first trip.
  2. 10080−100​⋅100%=−20%The return trip begins at 100; the denominator and sign change.

A common mistake

A mistake Lemma catches

From

100100−80​⋅10080100−80​⋅100

“Percent change compares the change with where you started. Going from 80 to 100 starts at 80: 20/80 = 0.25, a 25% increase. Dividing by 100, the new value, gives 20/100 = 20% — the size of the change going back down from 100 to 80.”

Try one

Sample problem

A medication order of 240 mg is increased by 30%. What is the new dose in milligrams? Enter the number.

240+10030​⋅240

Practice percent change free

No account, no email. Every line you type is checked by the same computer algebra system as the worked example above.

Where this fits

Before this