Start with a few familiar values rather than a long conversion table. Quarters, halves and fifths give exact decimals and percentages that are easy to check. Once those connections are clear, use them to find a percentage of a quantity.
Start with a small set of exact values
| Fraction | Decimal | Percent | One way to check |
|---|---|---|---|
| 1/4 | 0.25 | 25% | 1/4 = 25/100 |
| 1/2 | 0.5 | 50% | 1/2 = 50/100 |
| 3/4 | 0.75 | 75% | 3/4 = 75/100 |
| 1/5 | 0.2 | 20% | 1/5 = 20/100 |
Choose two rows first. Cover one column and ask for the missing representation, then ask how it was checked. For 1/4, multiplying numerator and denominator by 25 gives 25/100. That is 0.25 in decimal notation and 25% in percent notation. All three name the same proportion; the percent sign says the number is being expressed per hundred.
Fractions and decimalsUse a short fraction-and-decimal sheet to check the first connection.Check the place value, not just the digits
Compare 0.5 and 0.05 explicitly. The first is five tenths, equal to 50/100 and 50%. The second is five hundredths, equal to 5/100 and 5%. Writing a percent symbol after a decimal without changing the numerical value is not the conversion: 0.5 is 50%, whereas 0.5% is 0.005.
For a second check, start with 75%. Write 75/100, simplify to 3/4, and write the decimal 0.75. Reversing the direction helps you see whether the relationship is being used consistently. These chosen examples terminate exactly; other fractions, such as 1/3, need repeating notation or a stated approximation, so keep them out of this first exact-value set.
Fractions, decimals and percentagesAdd a three-representation task after checking decimal place value.Apply one percent to a quantity
- 1
Find 25% of 80
Use 25% = 1/4. Divide 80 by 4 to obtain 20. Check with the decimal: 0.25 × 80 = 20.
- 2
Find 20% of 45
Use 20% = 1/5. Divide 45 by 5 to obtain 9. Check with the decimal: 0.2 × 45 = 9.
- 3
Name the whole
In the first question the whole quantity is 80; in the second it is 45. The percent describes a proportion of that stated whole, so the answer is a quantity rather than another conversion entry.
Ask why 25% of 80 is not simply 25. One quarter of 100 would be 25, but the whole here is 80. If this distinction needs discussion, use a bar or four equal groups before adding more percentages. Keep units in the answer when the question supplies them: 25% of 80 cm is 20 cm.
Percent of a quantityUse a separate percent-of-quantity sheet for applying the representations.Choose a short review order
| Stage | Suggested task | Review decision |
|---|---|---|
| Representation | Complete two rows from the exact-value table. | If the decimal is misplaced, revisit tenths and hundredths. |
| Reverse conversion | Start at 75% and show both 0.75 and 3/4. | If only one direction works, practice the other direction with a fresh value. |
| Application | Find 25% of 80 and 20% of 45. | If the whole is unclear, name it and use equal groups. |
| Explanation | Explain one answer without reading the key. | Use the explanation to choose the next short sheet. |
Use the table for discussion, then check the keys for the worksheets you generate. If the learner can explain a conversion but struggles to apply a percent, return to naming the whole and sharing it into equal groups. Choose the next short task from the part that needs another explanation.