Understanding Mixed Numbers
Mixed numbers consist of a whole number and a proper fraction. To convert a mixed number into an improper fraction, follow a simple formula.
Conversion Formula
- To convert a mixed number, use the formula:
Whole Number × Denominator + Numerator / Denominator
Step-by-step Conversion of 1/3
1. Identify the Mixed Number:
In this case, it is 1/3, but we need to treat it as a mixed number. Let's represent it as 0 whole parts and 1/3.
2. Use the Formula:
- Whole Number = 0
- Denominator = 3
- Numerator = 1
3. Apply the Formula:
0 × 3 + 1 = 0 + 1 = 1
4. Write as an Improper Fraction:
Now, since we have only the fraction part:
1/3 can be expressed as 1/3 (no whole part).
Example Conversion Explained
- For 6 1/2:
- Whole Number = 6
- Denominator = 2
- Numerator = 1
Calculation:
6 × 2 + 1 = 12 + 1 = 13/2
- For 1/3:
- Whole Number = 0
- Denominator = 3
- Numerator = 1
Calculation:
0 × 3 + 1 = 0 + 1 = 1/3
Conclusion
Converting mixed numbers into improper fractions helps in simplifying calculations. The process is straightforward and essential for various mathematical operations. Understanding this concept is beneficial for exams like UPSC.