24 out of 80 is what percent?
- Use 80 as the whole: 24 ÷ 80 = 0.30.
- 0.30 × 100% = 30%.
- Check: 30% of 80 is 24.
Find the percent or the whole
Identify the missing quantity before choosing an operation.
One relationship, three possible unknowns
The part, whole and percentage describe one relationship: part / whole = percent / 100. Finding a part requires multiplication. Finding a percent requires dividing part by whole and multiplying by 100. Finding a whole requires dividing the part by the decimal percentage.
Keep the reference amount visible.
Predict first. Change one value, then explain what stays the same and what changes. All bars use the same scale within a model.
Ask what represents 100%
If 18 is 30% of a number, 18 is not the whole. Since 0.30 × whole = 18, the whole is 18 ÷ 0.30 = 60. A double number line can pair 30% with 18 and 100% with 60. Substitution back into the original statement checks the solution.
Distinguish reference comparisons
In “520 is what percent of 650?”, 650 is the reference whole. In “650 is what percent of 520?”, the reference is 520 and the answer exceeds 100%. The order matters. A zero whole does not define a part-to-whole percentage; division by zero is undefined.
Worked examples
$42 is 70% of what original price?
- 0.70 × original = 42.
- Original = 42 ÷ 0.70 = $60.
- Check: 70% of $60 is $42.
Guided Practice
15 students are 60% of a club. How many students are in the club?
A first hint
The unknown whole is larger than 15. Divide by 0.60.
Compare your reasoning
15 ÷ 0.60 = 25 students. Check: 0.60 × 25 = 15.
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
A store says $45 is the price after 25% off. Why must you divide by 0.75 to recover the original price, rather than add 25% to $45?
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.