📘 Fractions, Decimals and Percentages (Complete Chapter)
🔹 Introduction
In mathematics, fractions, decimals, and percentages are three different ways to show the same value. Although they look different, they are closely related and can be changed from one form to another.
Understanding the relationship between fractions, decimals, and percentages helps students:
- Compare values easily
- Understand money, marks, and measurements
- Solve real-life problems confidently
This chapter explains these three concepts in a clear, detailed, and plagiarism-free manner, supported by simple examples and visual understanding.
🔹 1. Fractions
✅ Meaning
A fraction shows a part of a whole. It is written in the form:
Numerator / Denominator
📘 Examples
- 1/2 (one half)
- 3/4 (three fourths)
- 5/10 (five tenths)
Visual Understanding
⬛⬛⬜⬜ = 2/4 = 1/2
🔹 2. Decimals
✅ Meaning
A decimal is another way to write a fraction using a decimal point (.). Decimals are based on place value, such as tenths, hundredths, and thousandths.
📘 Examples
- 1/2 = 0.5
- 3/4 = 0.75
- 25/100 = 0.25
Visual Understanding
0.5 = 5 tenths = ⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
🔹 3. Percentages
✅ Meaning
A percentage means per hundred. It shows how many parts out of 100 are taken.
The symbol % is used for percentage.
📘 Examples
- 50% means 50 out of 100
- 25% means 25 out of 100
- 75% means 75 out of 100
Visual Understanding
100 squares → ⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ = 10%
🔹 4. Relationship Between Fractions, Decimals, and Percentages
Fractions, decimals, and percentages are three different names for the same value.
Example:
1/2 = 0.5 = 50%
Visual Comparison
⬛⬛⬜⬜ = 1/2
⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜ = 0.5
50 shaded squares = 50%
🔹 5. Converting Fractions into Decimals
📌 Method
Divide the numerator by the denominator.
Example
3 ÷ 4 = 0.75
So,
👉 3/4 = 0.75
🔹 6. Converting Decimals into Fractions
📌 Method
- Write the decimal without a point as numerator
- Use 10, 100, or 1000 as denominator
- Simplify if needed
Example
0.6 = 6/10 = 3/5
🔹 7. Converting Fractions into Percentages
📌 Method
- Convert the fraction into a decimal
- Multiply by 100
- Add the % sign
Example
1/4 = 0.25 × 100 = 25%
🔹 8. Converting Percentages into Fractions
📌 Method
- Write the percentage over 100
- Remove the % sign
- Simplify
Example
75% = 75/100 = 3/4
🔹 9. Converting Decimals into Percentages
📌 Method
Multiply the decimal by 100 and add %.
Example
0.8 × 100 = 80%
🔹 10. Converting Percentages into Decimals
📌 Method
Divide the percentage by 100.
Example
45% = 0.45
🔹 11. Use of Fractions, Decimals, and Percentages in Daily Life
- Marks in exams (75%)
- Money and discounts (20% off)
- Measurements (0.5 meter)
- Cooking quantities
- Statistics and data
✅ Chapter Summary
- Fractions, decimals, and percentages show the same value in different forms
- Easy methods exist to convert between them
- They are widely used in daily life
- Visual understanding makes learning easier