Write each percent as a fraction. Give answers in lowest terms.
$7.5 percent sign$

Verified step by step guidance

Recall that a percent means 'per hundred,' so 7.5% can be written as the fraction $ \frac{7.5}{100} $.

Convert the decimal 7.5 to a fraction: $ 7.5 = \frac{75}{10} $, so rewrite the fraction as $ \frac{\frac{75}{10}}{100} $.

Simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator: $ \frac{75}{10} \times \frac{1}{100} = \frac{75}{1000} $.

Reduce the fraction $ \frac{75}{1000} $ to its lowest terms by finding the greatest common divisor (GCD) of 75 and 1000 and dividing numerator and denominator by it.

Write the simplified fraction as the final answer representing 7.5% in lowest terms.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Understanding Percentages

A percentage represents a part out of 100. Writing 7.5% means 7.5 parts per 100, which can be expressed as the fraction 7.5/100. Recognizing this relationship is essential for converting percentages to fractions.

Converting Decimals to Fractions

Since 7.5% includes a decimal, converting 7.5 to a fraction involves expressing it as 75/10. This step helps in rewriting the percentage as a fraction before simplifying it.

Simplifying Fractions to Lowest Terms

After converting the percentage to a fraction, simplifying means dividing numerator and denominator by their greatest common divisor. This process ensures the fraction is in its simplest form, making it easier to understand and use.

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