Percent or percentage points? Read the change clearly
Compare two percentages, choose the right starting value, and spot a misleading change. Includes seven original questions with worked answers.
Two questions, two useful answers
A percentage tells you a part out of 100. A percentage point tells you the gap between two percentages. A percentage change tells you how large a change is compared with its starting value. The same change can have both a percentage-point answer and a percentage-change answer.
All people, groups and numbers in this lesson are invented for practice. Suppose the share of people who cycle to a fictional learning center rises from 24% to 30%. First write down the starting value, 24%, and the new value, 30%. Check that the figures use the same definition and comparable groups and dates before interpreting the change.
For percentage points, subtract
Find the gap: 30 − 24 = 6. The cycling share rose by 6 percentage points. Write the words “percentage points” to show that you subtracted two percentages.
Think of 100 equal spaces. The original share fills 24; the new share fills 30. Six more spaces are filled. If both groups had exactly 100 people, this would mean 6 more cyclists. If the group sizes differ, the percentages alone do not tell you the change in the number of cyclists.
For percentage change, divide by the starting value
Ask how big that gap is compared with where you began. Use (new value − starting value) ÷ starting value × 100. Here, (30 − 24) ÷ 24 × 100 = 25%. The cycling share rose by 25% relative to its old value.
Check it backwards: 25% of 24 is 6, and 24 + 6 = 30. Both descriptions are correct: up 6 percentage points, or up 25% relative to the starting share. Saying only “up 6%” gives a different calculation: 24 × 1.06 = 25.44, not 30.
Keep matching units in the subtraction and division. Using 0.24 and 0.30 instead gives (0.30 − 0.24) ÷ 0.24 × 100 = 25%. Do not mix 24 with 0.30.
A decrease uses the same starting-value rule
A fictional survey rate falls from 50% to 35%. The percentage-point change is 35 − 50 = −15: a fall of 15 percentage points. The percentage change is (35 − 50) ÷ 50 × 100 = −30%: a fall of 30% relative to the starting rate. The minus sign shows the direction.
Changing back does not use the same percentage. Going from 35% back to 50% is a rise of 15 percentage points, but the relative increase is 15 ÷ 35 × 100, about 42.9%. The starting value is now 35, so the calculation has a different base. Round only at the end and say when an answer is approximate.
Check the group behind the percentage
In one invented month, 20 of 100 visitors choose an evening class: 20%. In another month, 30 of 200 visitors choose it: 15%. The number choosing the class increased from 20 to 30, but the share decreased from 20% to 15%. Counts and percentages answer different questions.
Before accepting a headline, ask: What is being counted? Out of how many? Which dates or groups are compared? Does the wording mean a gap in percentage points, a relative percentage change, or a change in the number of people? A larger percentage change does not by itself explain the cause or importance of the result.
If the starting value is zero, the usual percentage-change formula would divide by zero, so it does not give a defined percentage change. You can still state the two values and their percentage-point gap when both values are percentages. Do not invent a “100% increase” from zero.
One small routine to keep
Write starting value → new value. If asked for percentage points, subtract. If asked for percentage change, subtract, divide by the starting value, then multiply by 100. Finish with the direction and the correct unit.
This is original practice in reading percentages, not a GED® test question set or a readiness score. The linked GED educator guide, dated June 2016, includes percent increase and decrease in math target Q.3.d; that does not mean every question here is a separate named test target. ONS guidance explains percentage-point wording. Both public sources were checked on October 21, 2026. For a gentler first step, use Percentages without panic in the related lessons below.
Your turn.
Try each question before opening the explanation. These are FinishHigh practice examples, not GED® test questions.
An invented participation rate rises from 32% to 40%. Find the increase in percentage points and the percentage increase relative to the original rate.
Show the answer and why
Up 8 percentage points: 40 − 32 = 8. Up 25% relative to the starting rate: 8 ÷ 32 × 100 = 25%. Check: 32 × 1.25 = 40.
A fictional survey rate falls from 75% to 60%. Describe the decrease in both ways.
Show the answer and why
Down 15 percentage points: 60 − 75 = −15. Down 20% relative to the starting rate: −15 ÷ 75 × 100 = −20%. The final rate is 60%; neither change is the final rate.
Start at 40%. What is the new rate after an increase of 10 percentage points? What is it after an increase of 10% relative to the starting rate?
Show the answer and why
A 10-percentage-point increase gives 40% + 10 percentage points = 50%. A relative 10% increase gives 40 × 1.10 = 44%. The wording changes the answer.
An invented rate rises from 2% to 3%. A headline says it “rose by 1%.” What clear descriptions should replace that headline?
Show the answer and why
It rose by 1 percentage point, since 3 − 2 = 1. It also rose by 50% relative to its starting value, since 1 ÷ 2 × 100 = 50%. A relative rise of only 1% would give 2 × 1.01 = 2.02%, not 3%.
Month A has 20 evening-class visitors out of 100 visitors. Month B has 30 out of 200. Find each share and its percentage-point change. Did the count and the share move in the same direction?
Show the answer and why
Month A: 20 ÷ 100 × 100 = 20%. Month B: 30 ÷ 200 × 100 = 15%. The share fell by 5 percentage points. The count rose by 10 people (a 50% increase from 20), so count and share moved in opposite directions. The total group doubled; comparing counts alone misses that change.
An invented rate goes from 0% to 6%. Can you report a percentage-point increase? Can you use the usual relative percentage-change formula?
Show the answer and why
The increase is 6 percentage points: 6 − 0 = 6. The usual percentage change is undefined because (6 − 0) ÷ 0 would divide by zero. State the starting and ending rates; do not call it a 100% increase.
A fictional rate rises from 40% to 50%, then returns to 40%. Find each relative percentage change. Explain why the percentages do not have equal size.
Show the answer and why
The rise is (50 − 40) ÷ 40 × 100 = 25%. The fall is (40 − 50) ÷ 50 × 100 = −20%. The base changes from 40 to 50. Each move is 10 percentage points in size, but the relative percentages have different starting values.
Trusted sources and further study
Sources guide the topics and factual information. The lesson wording, examples, and questions are original FinishHigh material.
- Math: official assessment targets for educators ↗GED Testing Service · checked 2026-10-21
- ONS: percentages and percentage points ↗Office for National Statistics (United Kingdom) · checked 2026-10-21
Another small step
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