Write 4 1/4 as a percent.
The Correct Answer and Explanation is :
To express 4 1/4 as a percentage, let’s first convert the mixed number into an improper fraction and then into a percentage.
Step-by-Step Process:
- Convert 4 1/4 to an improper fraction:
- 4 1/4 means 4 plus 1/4.
- Convert 4 into a fraction: (4 = \frac{4 \times 4}{4} = \frac{16}{4}).
- Now add 1/4 to 16/4: (\frac{16}{4} + \frac{1}{4} = \frac{17}{4}).
- Convert the fraction to a decimal:
- Divide 17 by 4: ( \frac{17}{4} = 4.25 ).
- Convert the decimal to a percentage:
- To convert a decimal to a percentage, multiply it by 100:
( 4.25 \times 100 = 425\% ).
So, 4 1/4 as a percentage is 425%.
Explanation:
The concept of percentages is essentially a way to express a number as a fraction of 100. When converting any number into a percentage, you multiply by 100 to shift the decimal point two places to the right.
For the mixed number 4 1/4, we first turned it into an improper fraction because it makes calculations easier. The improper fraction ( \frac{17}{4} ) simply tells us that there are 17 parts, each part being one-quarter. Dividing 17 by 4 gives us the exact decimal form, 4.25.
Multiplying this decimal by 100 gives the equivalent percentage. In this case, it is 425%, meaning that 4 1/4 is equivalent to 425% of a whole.
This makes sense because any number greater than 1, when converted to a percentage, results in a value greater than 100%, as it’s more than a complete whole unit.