How do you write 156% as a fraction or mixed number in simplest form?
The Correct Answer and Explanation is:
To convert 156% into a fraction or mixed number in its simplest form, follow these steps:
- Understand the Percentage: A percentage is a fraction with a denominator of 100. Therefore, 156% can be expressed as:
[
156\% = \frac{156}{100}
] - Simplify the Fraction: To simplify the fraction (\frac{156}{100}), we need to find the greatest common divisor (GCD) of the numerator (156) and the denominator (100).
- Finding the GCD:
- The prime factorization of 156 is (2^2 \times 3 \times 13).
- The prime factorization of 100 is (2^2 \times 5^2).
- The common factors are (2^2), so the GCD is (4).
- Dividing by the GCD:
- Divide both the numerator and the denominator by the GCD (4):
[
\frac{156 \div 4}{100 \div 4} = \frac{39}{25}
]
- Expressing as a Mixed Number: Since (\frac{39}{25}) is an improper fraction (the numerator is larger than the denominator), it can also be expressed as a mixed number.
- To convert (\frac{39}{25}) to a mixed number, divide 39 by 25:
- (39 \div 25 = 1) (the whole number part)
- Remainder: (39 – 25 = 14).
- Therefore, (\frac{39}{25}) can be written as:
[
1 \frac{14}{25}
]
- Final Answer: Thus, 156% as a fraction in simplest form is (\frac{39}{25}), and as a mixed number, it is (1 \frac{14}{25}).
Summary
In conclusion, converting percentages to fractions involves expressing the percentage as a fraction over 100, finding the GCD to simplify, and optionally converting improper fractions to mixed numbers. The process not only makes the number easier to understand but also reveals its fundamental relationships within the set of rational numbers.