A survey: 18 of 60 choose cycling
- Part / whole = 18/60 = 3/10.
- 3/10 = 30/100, so 30% choose cycling.
- The other 42 of 60 represent 70%; the shares total 100%.
Understand percent
Name the whole before you name the percent.
Percent means per hundred
A percent is a ratio with a reference total of 100. In 35%, 35 describes how much corresponds to every 100 equal parts of the whole. The whole might be a class, a length, a price or an amount of time. It does not have to contain exactly 100 objects.
See the whole and its parts.
Predict first. Change one value, then explain what stays the same and what changes. All bars use the same scale within a model.
Keep the reference whole visible
If 7 of 20 students walk to school, the part is 7 and the whole is 20. Scaling both quantities by 5 gives 35 out of 100, or 35%. This compares the share of the class, not a count of 35 students. In a diagram, label the entire rectangle as 100% before shading a part.
The same percent can describe different amounts
Half of 20 is 10; half of 80 is 40. Both are 50%, because the part-to-whole ratio is the same. Comparing percentages helps compare groups of different sizes, but the original totals still matter. A larger percent of a smaller whole can be a smaller amount.
Worked examples
Compare two teams
- Team A wins 8 of 10 games: 8/10 = 80%.
- Team B wins 12 of 20 games: 12/20 = 60%.
- B has more wins, but A has the greater winning percentage.
Guided Practice
A class of 25 has 10 students wearing blue. What percent is that?
A first hint
Scale 25 to 100, and scale 10 by the same factor.
Compare your reasoning
10/25 = 40/100 = 40%. The other 15 students represent 60%.
Practice
Fresh questions · useful feedback
Build fluency, one decision at a time.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
0 of 8 questions completed
This round saves on this device. It is practice, not a school mark.
Connections
Two clubs each report 25% participation. One has 24 members and the other 80. Explain how both reports can be true, and find each participation count.
Use it in Extreme Couponing
Record the whole, the percent multiplier and the result with units. For each coupon, use the eligible amount at that step. State whether a resale percentage means percent of cost or markup on cost.