Write 87 1/2% as a fraction in simplest form

The Correct Answer and Explanation is:

To write 87 1/2% as a fraction in its simplest form, follow these steps:

Step 1: Convert the percentage into a fraction

First, recognize that 87 1/2% means “87 and one-half percent.” We need to express this as a fraction.

Step 1a: Express the whole number part as a fraction

The whole number is 87, and since “percent” means “out of 100,” we write:
[
87\% = \frac{87}{100}
]

Step 1b: Convert the fractional part (1/2%) into a fraction

Next, the fractional part is 1/2%. To convert this, remember that “percent” means “out of 100.” So:
[
\frac{1}{2}\% = \frac{1}{2} \times \frac{1}{100} = \frac{1}{200}
]

Step 2: Combine the two parts

Now, combine the whole number part (87%) and the fractional part (1/2%). We do this by adding the two fractions:
[
87\% + \frac{1}{2}\% = \frac{87}{100} + \frac{1}{200}
]

Step 2a: Find a common denominator

To add these fractions, we need a common denominator. The least common denominator (LCD) between 100 and 200 is 200.

Step 2b: Rewrite the fractions with the common denominator

We rewrite (\frac{87}{100}) with a denominator of 200:
[
\frac{87}{100} = \frac{87 \times 2}{100 \times 2} = \frac{174}{200}
]
Now, add the fractions:
[
\frac{174}{200} + \frac{1}{200} = \frac{175}{200}
]

Step 3: Simplify the fraction

Now that we have the fraction (\frac{175}{200}), we simplify it by finding the greatest common divisor (GCD) of 175 and 200. The GCD of 175 and 200 is 25.

Step 3a: Divide the numerator and denominator by 25

[
\frac{175 \div 25}{200 \div 25} = \frac{7}{8}
]

Final Answer:

Thus, 87 1/2% as a fraction in its simplest form is:
[
\frac{7}{8}
]

Explanation:

The process of converting a percentage to a fraction involves two key steps: first, breaking down the whole number part and fractional part of the percentage, and second, simplifying the resulting fraction by finding the greatest common divisor. This approach helps in ensuring the final fraction is in the simplest form.