Easy way to relate tenths and hundredths to fractions

📚 Understanding Tenths and Hundredths

Tenths and hundredths are special types of fractions where the denominator (the bottom number) is either 10 or 100, respectively. Understanding them is crucial because they form the basis of decimal numbers and percentages.

📜 Historical Context

The concept of dividing a whole into ten or a hundred parts has ancient roots, appearing in various forms across different cultures. However, the systematic use of decimal fractions, as we know them today, gained prominence in the 16th century, largely due to the needs of commerce and scientific measurement. Simon Stevin, a Flemish mathematician, is often credited with popularizing decimal fractions in Europe.

🔑 Key Principles

• 📏 Tenths:
Represent one out of ten equal parts of a whole. As a fraction, a tenth is written as $\frac{1}{10}$.
• 💯 Hundredths:
Represent one out of one hundred equal parts of a whole. As a fraction, a hundredth is written as $\frac{1}{100}$.
• 🤝 Relationship:
Tenths and hundredths are related because ten hundredths make up one tenth. This can be expressed as: $\frac{1}{10} = \frac{10}{100}$.
• ↔️ Conversion:
To convert a tenth to a hundredth, multiply both the numerator and denominator by 10. For example, $\frac{3}{10} = \frac{3 \times 10}{10 \times 10} = \frac{30}{100}$.

➕ Adding Tenths and Hundredths

Before adding tenths and hundredths, they must have the same denominator (100). Convert the tenths to hundredths and then add the numerators.

For example: $\frac{2}{10} + \frac{35}{100} = \frac{20}{100} + \frac{35}{100} = \frac{55}{100}$

🌍 Real-World Examples

• 🍕 Pizza Slices:
If a pizza is cut into 10 slices, each slice represents one-tenth of the pizza.
• 🍫 Chocolate Bar:
If a chocolate bar is divided into 100 squares, each square represents one-hundredth of the bar.
• 💰 Money:
One dime is one-tenth of a dollar ($\frac{1}{10}$), and one cent is one-hundredth of a dollar ($\frac{1}{100}$).
• 📊 Graphs:
Hundredths are commonly used to represent data in percentage form on graphs, such as pie charts.

📝 Practice Quiz

Convert the following fractions:

1. $\frac{7}{10}$ to hundredths
2. $\frac{90}{100}$ to tenths
3. $\frac{4}{10} + \frac{12}{100}$ to a single fraction

Answers:

1. $\frac{70}{100}$
2. $\frac{9}{10}$
3. $\frac{52}{100}$

✅ Conclusion

Understanding the relationship between tenths and hundredths and how they relate to fractions is vital for grasping more advanced mathematical concepts, especially decimals and percentages. With practice, these conversions and calculations will become second nature!