The correct option is **A. 0.375**. ### Step-by-Step Explanation To determine which decimal representation is equivalent to the fraction \( \frac{3}{8} \), we need to convert the fraction into its decimal form. This can be done through division. 1. **Understanding the Fraction**: The fraction \( \frac{3}{8} \) means we are dividing 3 by 8. 2. **Performing the Division**: - Set up the division: \( 3 \div 8 \). - Since 3 is less than 8, we know that the result will be less than 1. We can add a decimal point and a zero to 3, making it 30. - Now, we divide 30 by 8: - 8 goes into 30 three times (since \( 8 \times 3 = 24 \)). - Subtract 24 from 30, which gives us 6. - Bring down another 0 (making it 60). - 8 goes into 60 seven times (since \( 8 \times 7 = 56 \)). - Subtract 56 from 60, which gives us 4. - Bring down another 0 (making it 40). - 8 goes into 40 five times (since \( 8 \times 5 = 40 \)). - Subtract 40 from 40, which gives us 0. 3. **Result of the Division**: The result of the division \( 3 \div 8 \) is \( 0.375 \). ### Verification of the Answer To verify, we can multiply the decimal back by the denominator: - \( 0.375 \times 8 = 3 \). This confirms that \( 0.375 \) is indeed equivalent to \( \frac{3}{8} \). ### Analyzing the Other Options Now, let's look at the other options to understand why they are incorrect: - **B. 0.25**: - This decimal represents \( \frac{1}{4} \) (since \( 0.25 \times 4 = 1 \)). - To compare, \( \frac{3}{8} \) is greater than \( \frac{1}{4} \) because \( \frac{3}{8} = 0.375 \) and \( 0.25 < 0.375 \). - **C. 0.5**: - This decimal represents \( \frac{1}{2} \) (since \( 0.5 \times 2 = 1 \)). - Clearly, \( \frac{3}{8} < \frac{1}{2} \) because \( 0.375 < 0.5 \). - **D. 0.625**: - This decimal represents \( \frac{5}{8} \) (since \( 0.625 \times 8 = 5 \)). - Again, \( \frac{3}{8} < \frac{5}{8} \) because \( 0.375 < 0.625 \). ### Summary of Key Points - The fraction \( \frac{3}{8} \) converts to the decimal \( 0.375 \) through division. - The other options (0.25, 0.5, and 0.625) represent different fractions that are not equivalent to \( \frac{3}{8} \). - Always verify your decimal conversion by multiplying back with the denominator to check for accuracy. ### Revision Summary - \( \frac{3}{8} = 0.375 \) through division. - Other options represent different fractions: \( 0.25 = \frac{1}{4} \), \( 0.5 = \frac{1}{2} \), \( 0.625 = \frac{5}{8} \). - Always check your work by reversing the operation (multiplying the decimal by the denominator).