Solved problems: Converting fractions to decimals to percents explained

📚 Understanding Fractions, Decimals, and Percents

Fractions, decimals, and percents are different ways of representing the same value – a part of a whole. Converting between them is a fundamental skill in mathematics and crucial for everyday life.

📜 A Brief History

While the concept of fractions dates back to ancient civilizations like Egypt and Mesopotamia, the decimal system, as we know it, evolved much later. Simon Stevin is often credited with popularizing decimal fractions in Europe during the late 16th century. Percentages also emerged during this period, primarily for calculating interest and taxes.

🔑 Key Principles for Conversion

• 🧮 Fraction to Decimal: Divide the numerator (top number) by the denominator (bottom number).
• ➗ Decimal to Percent: Multiply the decimal by 100 and add the percent sign (%).
• ⅕ Fraction to Percent: Convert the fraction to a decimal first, then convert the decimal to a percent. Alternatively, make the denominator 100.
• 💯 Percent to Decimal: Divide the percent by 100.
• 📝 Decimal to Fraction: Express the decimal as a fraction with a denominator of 10, 100, 1000, etc., then simplify.
• ➗ Percent to Fraction: Write the percent as a fraction with a denominator of 100, then simplify.

➗ Converting Fractions to Decimals

To convert a fraction to a decimal, perform the division indicated by the fraction. The numerator (top number) is divided by the denominator (bottom number).

• 🔢 Example 1: Convert $\frac{1}{4}$ to a decimal. Divide 1 by 4: $1 \div 4 = 0.25$.
• ➗ Example 2: Convert $\frac{3}{5}$ to a decimal. Divide 3 by 5: $3 \div 5 = 0.6$.
• ✍️ Example 3: Convert $\frac{5}{8}$ to a decimal. Divide 5 by 8: $5 \div 8 = 0.625$.

📈 Converting Decimals to Percents

To convert a decimal to a percent, multiply the decimal by 100 and add the percent sign (%). This essentially shifts the decimal point two places to the right.

• 💯 Example 1: Convert 0.25 to a percent. $0.25 \times 100 = 25\%$.
• ➕ Example 2: Convert 0.6 to a percent. $0.6 \times 100 = 60\%$.
• 📐 Example 3: Convert 0.625 to a percent. $0.625 \times 100 = 62.5\%$.

🔄 Converting Fractions to Percents

The easiest way to convert a fraction to a percent is usually to first convert the fraction to a decimal, and then convert the decimal to a percent.

• 🧭 Method 1: Via Decimal
  Convert the fraction to a decimal by dividing the numerator by the denominator. Then, multiply the decimal by 100 and add the percent sign.
• ⚙️ Method 2: Direct Conversion
  If possible, find an equivalent fraction with a denominator of 100. The numerator then represents the percentage directly. For example, $\frac{1}{4} = \frac{25}{100} = 25\%$.
• 💡Example: Convert $\frac{3}{4}$ to a percent.
  First, convert $\frac{3}{4}$ to a decimal: $3 \div 4 = 0.75$. Then, convert 0.75 to a percent: $0.75 \times 100 = 75\%$.

🌍 Real-World Applications

These conversions are essential in many aspects of life:

• 🛍️ Shopping: Calculating discounts (e.g., 20% off).
• 🏦 Finance: Understanding interest rates on loans or investments.
• 📊 Statistics: Interpreting data presented in various formats.
• 🍳 Cooking: Adjusting recipe quantities.

📝 Practice Quiz

Convert the following:

⭐ Conclusion

Mastering the conversion between fractions, decimals, and percentages will give you a strong foundation in math and allow you to confidently tackle a wide range of problems in school and in the real world. Keep practicing, and you'll become an expert in no time!