what is 156% as a fraction reduced form
The correct answer and explanation is:
Answer:
156% as a fraction in reduced form is 3925\frac{39}{25}.
Explanation (300 words):
To convert a percentage to a fraction, you start by understanding what the percentage means. A percentage is a number out of 100. So, 156% literally means 156 per 100, or: 156%=156100156\% = \frac{156}{100}
This fraction can be simplified by dividing both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD).
- Write the percentage as a fraction:
156%=156100156\% = \frac{156}{100}
- Find the Greatest Common Divisor (GCD) of 156 and 100:
- Factors of 156 include: 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156
- Factors of 100 include: 1, 2, 4, 5, 10, 20, 25, 50, 100
The greatest common factor both share is 4.
- Divide numerator and denominator by 4:
156÷4100÷4=3925\frac{156 \div 4}{100 \div 4} = \frac{39}{25}
- Check if the fraction can be simplified further:
- 39 factors: 1, 3, 13, 39
- 25 factors: 1, 5, 25
They have no common factors other than 1, so 3925\frac{39}{25} is the fraction in simplest form.
Additional notes:
- Since the numerator (39) is greater than the denominator (25), this is an improper fraction, which means the fraction represents a value greater than 1.
- If you want, you can also convert this improper fraction into a mixed number:
3925=11425\frac{39}{25} = 1 \frac{14}{25}
This means 156% is the same as 1 whole and 1425\frac{14}{25} extra.
Summary:
- Step 1: Write percentage as fraction: 156100\frac{156}{100}
- Step 2: Simplify by dividing numerator and denominator by 4
- Step 3: Final reduced fraction: 3925\frac{39}{25}
That’s how you convert 156% into a simplified fraction!