Change the mixed fraction 6 5/8 to a percent
The Correct Answer and Explanation is:
To convert the mixed fraction ( 6 \frac{5}{8} ) into a percentage, we can follow a step-by-step process:
Step 1: Convert the mixed fraction to an improper fraction.
A mixed fraction consists of a whole number and a fraction. The whole number is ( 6 ), and the fraction is ( \frac{5}{8} ).
To convert this into an improper fraction, we multiply the whole number by the denominator of the fraction and then add the numerator. Here’s the calculation:
[
6 \frac{5}{8} = \frac{(6 \times 8) + 5}{8} = \frac{48 + 5}{8} = \frac{53}{8}
]
Step 2: Convert the improper fraction to a decimal.
Now, we divide the numerator ( 53 ) by the denominator ( 8 ) to obtain the decimal equivalent:
[
\frac{53}{8} = 6.625
]
Step 3: Convert the decimal to a percentage.
To convert a decimal to a percentage, we multiply the decimal by 100:
[
6.625 \times 100 = 662.5
]
Thus, the mixed fraction ( 6 \frac{5}{8} ) is equivalent to 662.5%.
Explanation:
A mixed fraction consists of a whole number and a fraction. In this case, ( 6 \frac{5}{8} ) combines the whole number 6 with the fraction ( \frac{5}{8} ). The first step in converting to a percentage is to eliminate the mixed fraction by converting it into an improper fraction. The improper fraction ( \frac{53}{8} ) represents the same value as ( 6 \frac{5}{8} ).
Next, converting this improper fraction to a decimal involves dividing the numerator (53) by the denominator (8), which results in 6.625. Finally, multiplying the decimal by 100 converts it into a percentage. The final result is 662.5%.
This process demonstrates how a mixed fraction can be transformed into a decimal and then into a percentage, allowing you to express the value in a different format. Understanding these steps is important for working with fractions and percentages in both academic and real-life situations.