The correct option is **B. 3/4**. ### Step-by-Step Explanation 1. **Understanding the Decimal**: The decimal 0.75 represents a number that is three-quarters of a whole. To convert this decimal into a fraction, we need to express it in terms of a numerator (the top part of the fraction) and a denominator (the bottom part of the fraction). 2. **Converting Decimal to Fraction**: - The decimal 0.75 can be read as "75 hundredths," which can be written as the fraction \( \frac{75}{100} \). - To simplify this fraction, we need to find the greatest common divisor (GCD) of 75 and 100. The GCD of 75 and 100 is 25. 3. **Simplifying the Fraction**: - We divide both the numerator and the denominator by their GCD: \[ \frac{75 \div 25}{100 \div 25} = \frac{3}{4} \] - Thus, \( 0.75 = \frac{3}{4} \). 4. **Verifying the Answer**: To ensure that \( \frac{3}{4} \) is indeed equal to 0.75, we can perform the division: - Divide 3 by 4: \[ 3 \div 4 = 0.75 \] - This confirms that \( \frac{3}{4} \) is equivalent to 0.75. ### Why the Other Options are Incorrect - **Option A: \( \frac{1}{2} \)**: - \( \frac{1}{2} \) equals 0.5, which is less than 0.75. Therefore, it cannot be equivalent to 0.75. - **Option C: \( \frac{2}{3} \)**: - To convert \( \frac{2}{3} \) to a decimal, divide 2 by 3: \[ 2 \div 3 \approx 0.6667 \] - This value is also less than 0.75, making it an incorrect option. - **Option D: \( \frac{4}{5} \)**: - To convert \( \frac{4}{5} \) to a decimal, divide 4 by 5: \[ 4 \div 5 = 0.8 \] - This value is greater than 0.75, so it cannot be equivalent to 0.75. ### Summary of Key Points - The decimal 0.75 can be expressed as \( \frac{75}{100} \) and simplifies to \( \frac{3}{4} \). - The GCD of 75 and 100 is 25, which is used to simplify the fraction. - The other options (A, C, D) do not equal 0.75 when converted to decimals. - Always verify your fraction by converting it back to a decimal to ensure accuracy. This thorough understanding of converting decimals to fractions and verifying them will help you in similar problems in the future!