2 1/4 is equal to what percent?
The Correct Answer and Explanation is :
To convert a mixed number like (2 \frac{1}{4}) into a percentage, we can follow a series of straightforward steps.
Step 1: Convert the Mixed Number to an Improper Fraction
A mixed number consists of a whole number and a fraction. In this case, (2 \frac{1}{4}) can be converted to an improper fraction. The formula for this conversion is:
[
\text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator}\right) + \text{Numerator}
]
For (2 \frac{1}{4}):
- The whole number is (2).
- The denominator of the fraction is (4).
- The numerator of the fraction is (1).
Applying the formula:
[
\text{Improper Fraction} = (2 \times 4) + 1 = 8 + 1 = 9
]
Thus, (2 \frac{1}{4}) can be expressed as:
[
\frac{9}{4}
]
Step 2: Convert the Fraction to a Decimal
Next, we need to convert the improper fraction (\frac{9}{4}) into a decimal. This is done by dividing the numerator by the denominator:
[
9 \div 4 = 2.25
]
Step 3: Convert the Decimal to a Percentage
To convert a decimal to a percentage, multiply the decimal by (100) and add a percent sign (%):
[
2.25 \times 100 = 225\%
]
Conclusion
Thus, (2 \frac{1}{4}) is equal to (225\%). This means that if you had an original quantity of 100%, then (2 \frac{1}{4}) times that quantity would yield 225% of it. This conversion is particularly useful in various fields such as finance, statistics, and education, where understanding proportions and their percentage representations is critical. Knowing how to perform these conversions helps in making informed decisions based on quantitative data.