How do you write 160% as a fraction or mixed number in simplest form?
The Correct Answer and Explanation is :
To express 160% as a fraction or mixed number in simplest form, follow these steps:
- Convert Percent to Fraction: The term “percent” means “per hundred.” Therefore, 160% can be written as:
[
160\% = \frac{160}{100}
] - Simplify the Fraction: To simplify the fraction (\frac{160}{100}), we need to find the greatest common divisor (GCD) of the numerator (160) and the denominator (100). The GCD of 160 and 100 is 20. We can divide both the numerator and denominator by 20:
[
\frac{160 \div 20}{100 \div 20} = \frac{8}{5}
] - Convert to Mixed Number: The fraction (\frac{8}{5}) is an improper fraction since the numerator is greater than the denominator. To convert it to a mixed number, divide the numerator by the denominator:
[
8 \div 5 = 1 \quad \text{with a remainder of } 3.
]
This means (\frac{8}{5}) can be expressed as:
[
1 \frac{3}{5}
]
In summary, 160% can be expressed as the fraction (\frac{8}{5}) or as the mixed number (1 \frac{3}{5}).
Explanation:
Understanding percentages is crucial, especially in fields like finance, healthcare, and education. Percentages represent a part of a whole, making it easier to compare values. By converting percentages to fractions, we gain a clearer view of ratios and relationships between numbers. This conversion is particularly useful in calculations involving proportions or when integrating percentage-based data into more complex mathematical models.
Moreover, simplifying fractions and converting them into mixed numbers enhances our numerical literacy. It allows us to express values in various forms, making it easier to interpret data. For instance, in healthcare, presenting dosages as fractions or mixed numbers can clarify medication instructions, ensuring patient safety and compliance. Thus, mastering these skills not only aids in academic success but also fosters practical application in everyday scenarios.