Percents

Percent Change

Compute percent change from an old value to a new value: (new − old) / old × 100.

percent-change To find percent change from old to new: - Diff = new − old. - Ratio = diff / old (in lowest terms). - Pct = ratio × 100.

Example

Compare the change to the original value and name the direction.

highlighted = computed this step

Step 1 — Set up

Set up the relationship.

50→6550 \to 65
Before 50, after 65beforeafter5065Percent change compares the change to the before value.

Step 2 — Find the change

Find the change: 65 - 50 = 15.

65−50=1565 - 50 = \hl{15}
Change: 65 - 50 = 15beforeafter5065change 15The change amount is 15.

Step 3 — Compare to old value

Compare change to old value: 15/50 = 3/10.

1550=310\frac{15}{50} = \hlmath{\frac{3}{10}}
Compare change to old: 15/50 = 3/10beforeafter5065change 1515/50 = 3/10The change is 3 of 10 equal old-value parts.

Step 4 — Convert to percent

Convert to percent: 3/10 x 100 = 30%.

310×100=30%\frac{3}{10} \times 100 = \hl{30\%}
3/10 x 100 = 30%beforeafter5065change 1515/50 = 3/103/10 of 100% is 30%.

Step 5 — Direction

The new value is larger, so this is an increase.

increase\hl{increase}
New value is larger: increasebeforeafter5065change 1515/50 = 3/10Because the after value is larger, call it an increase.

Step 6 — Result

State the percent increase.

30% increase30\% \text{ } \text{increase}
30% increasebeforeafter5065change 1515/50 = 3/10The percent change is 30% increase.