Question
3. Choose Efficient Methods Why are tenths, fifths, fourths, and halves easy to express as percents?
Ask by Osborne Mccarthy. in the United States
Feb 02,2025
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Answer
Tenths, fifths, fourths, and halves are easy to express as percents because their decimal equivalents are simple and terminate quickly. For example, 1/10 is 0.1 (10%), 1/5 is 0.2 (20%), 1/4 is 0.25 (25%), and 1/2 is 0.5 (50%). These straightforward decimals make it easy to convert them to percentages by multiplying by 100.
Solution
Fractions like tenths, fifths, fourths, and halves are particularly easy to express as percentages for several reasons:
1. **Simple Decimal Equivalents:**
- **Tenths (1/10):** Converts directly to 0.1 in decimal form.
- **Fifths (1/5):** Converts to 0.2.
- **Fourths (1/4):** Converts to 0.25.
- **Halves (1/2):** Converts to 0.5.
These decimal representations are straightforward and terminate after a few decimal places, making the conversion process smooth.
2. **Direct Conversion to Percentages:**
- To convert a decimal to a percentage, you multiply by 100.
- For example:
- 0.1 × 100 = **10%**
- 0.2 × 100 = **20%**
- 0.25 × 100 = **25%**
- 0.5 × 100 = **50%**
Since the decimal equivalents are simple, multiplying by 100 to get the percentage is easy and results in whole or simple fractional percentages.
3. **Common Usage and Familiarity:**
- Fractions like halves, quarters, fifths, and tenths are among the first fractions taught in mathematics.
- They are widely used in everyday contexts (e.g., cutting a pizza into halves or quarters), making their percentage forms more intuitive and easier to recall.
4. **Denominators Relate Conveniently to Base 10:**
- Although not all denominators are direct factors of 10, they often result in finite decimal representations in base 10.
- This compatibility simplifies calculations and conversions between fractions, decimals, and percentages.
5. **Ease in Mental Math:**
- These fractions allow for quick mental conversions without the need for complex calculations.
- For instance, knowing that 1/2 is 50% can be quickly applied in various situations without hesitation.
**Summary:**
Tenths, fifths, fourths, and halves convert easily to decimal form with simple, finite representations. This simplicity allows for straightforward multiplication by 100 to obtain their percentage equivalents. Additionally, their frequent use and familiarity make these conversions intuitive and easy to perform both mentally and in written calculations.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
Tenths, fifths, fourths, and halves are easy to express as percents because they are simple fractions that can be directly converted into percentages using straightforward calculations. For example, a half is 50%, a fourth is 25%, a fifth is 20%, and a tenth is 10%. These common denominators make mental math much simpler for most people, allowing for quick estimations and comparisons. In the real world, understanding these fractions is incredibly beneficial, especially in financial scenarios. For instance, discounts of 10%, 20%, or 50% can easily be visualized as tenths, fifths, and halves of a total price, making it effortless for shoppers to gauge deals and manage their budgets.
