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\( 87.5 \% \) is equivalent to what fraction in reduced terms?

Ask by Martin Logan. in the United States
Feb 03,2025

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Answer

\( 87.5\% \) is equal to \( \frac{7}{8} \).

Solution

To convert \( 87.5\% \) to a fraction in its reduced form, follow these steps: 1. **Write the Percentage as a Fraction:** \[ 87.5\% = \frac{87.5}{100} \] 2. **Eliminate the Decimal by Multiplying Numerator and Denominator by 10:** \[ \frac{87.5 \times 10}{100 \times 10} = \frac{875}{1000} \] 3. **Simplify the Fraction:** - Find the greatest common divisor (GCD) of 875 and 1000, which is 125. - Divide both the numerator and the denominator by 125: \[ \frac{875 \div 125}{1000 \div 125} = \frac{7}{8} \] So, \( 87.5\% \) reduced to its simplest fraction form is: \[ \boxed{\dfrac{7}{8}} \]

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Bonus Knowledge

To convert \( 87.5\% \) to a fraction, you can start by writing it as \( \frac{87.5}{100} \). To eliminate the decimal, multiply both the numerator and denominator by 10 to get \( \frac{875}{1000} \). Next, simplify this fraction. Both numbers can be divided by 125, yielding \( \frac{7}{8} \). Thus, \( 87.5\% \) can be expressed as \( \frac{7}{8} \). Now, here’s a fun fact about percentages: The concept of percentages dates back to ancient Rome with a system for calculating taxes! The Romans used a form of "percent" called "centesima," which means one hundredth, to calculate tax rates and expenses! If you want to deepen your understanding of fractions, try playing with fractional recipes in the kitchen! Adjusting ingredients and converting measures like cups and tablespoons can give you hands-on experience in manipulating fractions, making it a delicious way to learn!

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