Write 4 1/4 as a percent.
The Correct answer and Explanation is:
To convert the mixed number ( 4 \frac{1}{4} ) into a percentage, we follow these steps:
- Convert the mixed number to an improper fraction:
[
4 \frac{1}{4} = \frac{4 \times 4 + 1}{4} = \frac{17}{4}
] - Convert the improper fraction to a decimal:
Divide ( 17 ) by ( 4 ):
[
\frac{17}{4} = 4.25
] - Convert the decimal to a percentage:
Multiply ( 4.25 ) by ( 100 ):
[
4.25 \times 100 = 425\%
]
Thus, ( 4 \frac{1}{4} ) as a percentage is 425%.
Explanation
Percentages are a way of expressing a number as a fraction of 100. The word “percent” literally means “per hundred.” When converting a fraction or mixed number to a percentage, the key is to first convert the number into a decimal form, and then multiply that decimal by 100.
In this problem, ( 4 \frac{1}{4} ) is a mixed number. The first step is converting it into an improper fraction, which makes it easier to manipulate mathematically. Multiplying the whole number (4) by the denominator (4), and adding the numerator (1), gives ( \frac{17}{4} ).
Next, you divide ( 17 ) by ( 4 ) to convert the fraction into a decimal. The result is ( 4.25 ). Decimal numbers are easier to convert into percentages—just multiply by 100. So, ( 4.25 \times 100 = 425 ), meaning that ( 4 \frac{1}{4} ) equals 425%.
This makes sense because any number greater than 1, when converted to a percentage, will exceed 100%. Since ( 4 \frac{1}{4} ) is greater than 4, its percentage representation is more than 400%.