What is 7.5% written as a fraction in simplest form?
The Correct Answer and Explanation is:
To write 7.5% as a fraction in simplest form, we start by understanding that percentages represent parts per hundred. Here’s how we can break it down:
- Convert the percentage to a fraction:
Since 7.5% means 7.5 out of 100, we can write this as a fraction:
[
\frac{7.5}{100}
] - Remove the decimal:
To simplify, it’s best to remove the decimal by multiplying both the numerator and the denominator by 10. This moves the decimal point one place to the right, making it easier to work with whole numbers:
[
\frac{7.5 \times 10}{100 \times 10} = \frac{75}{1000}
] - Simplify the fraction:
Next, we simplify (\frac{75}{1000}) by finding the greatest common divisor (GCD) of 75 and 1000, which is 25. We divide both the numerator and the denominator by 25:
[
\frac{75 \div 25}{1000 \div 25} = \frac{3}{40}
]
Thus, 7.5% as a fraction in simplest form is (\frac{3}{40}).
Explanation
Converting percentages to fractions is a key math skill because it helps us work with different forms of numbers and understand their relationships. A percentage, by definition, is a ratio that compares a number to 100, making it easy to turn into a fraction by placing the percentage over 100.
The next step—removing the decimal—simplifies calculations. Multiplying by 10, 100, or any power of 10 is a straightforward way to move decimals and turn numbers into whole numbers.
Finally, simplifying the fraction helps to reach the simplest form, which is usually preferred in mathematical answers for clarity. In this example, we used the GCD of 75 and 1000 to divide both the numerator and the denominator by the largest number that evenly divides them. Simplifying fractions in this way reduces them to their smallest possible terms, making them easier to interpret and work with in future calculations.