Whis the percent as a fraction or mixed number in simplest form. 87.5%
The Correct Answer and Explanation is:
To convert 87.5% to a fraction or mixed number in its simplest form, follow these steps:
- Write the percent as a fraction:
Percent means “per 100,” so 87.5% can be written as:
[
87.5\% = \frac{87.5}{100}
] - Eliminate the decimal:
To get rid of the decimal point in 87.5, multiply both the numerator and the denominator by 10:
[
\frac{87.5}{100} = \frac{875}{1000}
] - Simplify the fraction:
Find the greatest common divisor (GCD) of 875 and 1000. The GCD of 875 and 1000 is 125. Now, divide both the numerator and denominator by 125:
[
\frac{875 \div 125}{1000 \div 125} = \frac{7}{8}
]
Therefore, 87.5% as a fraction in simplest form is ( \frac{7}{8} ). - Convert to a mixed number (if necessary):
In this case, ( \frac{7}{8} ) is already a proper fraction, so it cannot be converted into a mixed number because the numerator (7) is less than the denominator (8). Hence, the simplest form of 87.5% is ( \frac{7}{8} ).
Detailed Explanation:
Percentages are a way of expressing a number as a portion of 100. The term “percent” means “per hundred.” So, when you see a percentage like 87.5%, it means 87.5 out of 100. To convert this into a fraction, you follow a straightforward process:
- First, express the percentage as a fraction over 100. This is because the definition of percentage is out of 100. So, ( 87.5\% ) becomes ( \frac{87.5}{100} ).
- Since fractions typically shouldn’t have decimals in the numerator, we multiply both the top and bottom of the fraction by 10. This converts the decimal into a whole number, giving us ( \frac{875}{1000} ).
- To simplify the fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator. Simplifying fractions reduces them to their lowest terms, which is done by dividing both the numerator and the denominator by their GCD.
- In this case, the GCD of 875 and 1000 is 125, so dividing both by 125 gives us ( \frac{7}{8} ).
Thus, 87.5% expressed as a fraction in simplest form is ( \frac{7}{8} ).