Write 4.75 as a mixed number with a fraction in simplest form
The Correct Answer and Explanation is :
To convert the decimal 4.75 into a mixed number, we can break it down into its whole number and fractional parts. The whole number part is straightforward; it’s 4. The decimal part, 0.75, needs to be converted into a fraction.
- Understanding the decimal: The decimal 0.75 can be read as “75 hundredths,” which means it can be expressed as the fraction (\frac{75}{100}).
- Simplifying the fraction: To simplify (\frac{75}{100}), we need to find the greatest common divisor (GCD) of 75 and 100. The GCD of 75 and 100 is 25. We divide both the numerator and denominator by 25: [
\frac{75 \div 25}{100 \div 25} = \frac{3}{4}
] Thus, (0.75) simplifies to (\frac{3}{4}). - Combining the whole number and the fraction: Now that we have both parts, we can combine them to express 4.75 as a mixed number: [
4.75 = 4 + 0.75 = 4 + \frac{3}{4}
] This can be written as the mixed number (4 \frac{3}{4}). - Final result: The mixed number representation of 4.75 in simplest form is (4 \frac{3}{4}).
Summary
To recap, the steps taken to convert 4.75 into a mixed number involve separating the whole number from the decimal, converting the decimal into a fraction, simplifying that fraction, and then combining both parts into a mixed number. The key in this process is recognizing the decimal as a fraction and simplifying it correctly, allowing us to arrive at the final answer of (4 \frac{3}{4}). This method can be applied to any decimal to convert it into a mixed number format.