Percentages are a way to describe parts of a whole using 100 equal parts. The word percent means per hundred, so 35% means 35 out of 100. This makes percentages useful for comparing quantities that may have different totals, such as test scores, discounts, and survey results.
A 100-square grid is a clear visual model because each small square represents 1% of the whole.
To work with percentages, you often convert between percent, decimal, and fraction forms. For example, 25% = 0.25 = 25/100 = 1/4, and all four forms describe the same amount. Percent problems usually involve finding the part, the whole, or the percent rate.
These ideas are used in shopping, data analysis, probability, finance, science measurements, and many everyday decisions.
Key Facts
- Percent means parts per 100, so 1% = 1/100 = 0.01.
- Percent to decimal: divide by 100, so 47% = 0.47.
- Decimal to percent: multiply by 100, so 0.62 = 62%.
- Part = percent × whole, using the percent as a decimal.
- Percent = part / whole × 100%.
- Percent change = (new value - old value) / old value × 100%.
Vocabulary
- Percent
- A percent is a number that tells how many parts out of 100 are being described.
- Whole
- The whole is the total amount or complete group that the percentage is based on.
- Part
- The part is the amount being compared to the whole.
- Decimal
- A decimal is a base-ten number form that can represent a percentage after dividing by 100.
- Percent Change
- Percent change describes how much a value increases or decreases compared with its original value.
Common Mistakes to Avoid
- Using the percent number without converting it to a decimal is wrong because 30% means 0.30, not 30, when multiplying.
- Forgetting what the whole is leads to incorrect answers because the same part can be a different percent of different totals.
- Adding percentages from different wholes is wrong because 20% of one amount and 20% of another amount may represent different quantities.
- Confusing percent increase with the final percent is wrong because a 15% increase means the new value is 115% of the original, not 15% of it.
Practice Questions
- 1 A 100-square grid has 68 squares shaded. What percent is shaded, and what decimal represents that amount?
- 2 A jacket costs $80 and is on sale for 25% off. How many dollars are taken off, and what is the sale price?
- 3 Two students both answered 18 questions correctly. One test had 20 questions, and the other had 30 questions. Explain why their percentages are different even though the number correct is the same.