What is 22.5% written as a fraction in simplest form?
The Correct Answer and Explanation is:
Answer:
22.5% written as a fraction in simplest form is 940\boxed{\frac{9}{40}}
Explanation:
To convert 22.5% into a fraction in its simplest form, we follow a step-by-step process.
Step 1: Understand What Percent Means
The word percent means “per hundred.” So: 22.5%=22.510022.5\% = \frac{22.5}{100}
Step 2: Eliminate the Decimal
To make the numerator a whole number, multiply both the numerator and denominator by 10: 22.5100=22.5×10100×10=2251000\frac{22.5}{100} = \frac{22.5 \times 10}{100 \times 10} = \frac{225}{1000}
Now we have a fraction with whole numbers: 2251000\frac{225}{1000}
Step 3: Simplify the Fraction
To simplify, find the greatest common divisor (GCD) of 225 and 1000.
- 225 = 32×523^2 \times 5^2
- 1000 = 23×532^3 \times 5^3
The common factor is 52=255^2 = 25.
Now divide both numerator and denominator by 25: 225÷251000÷25=940\frac{225 \div 25}{1000 \div 25} = \frac{9}{40}
So, the simplest form of 22.5% as a fraction is: 940\boxed{\frac{9}{40}}
Why Simplify?
Simplifying a fraction makes it easier to understand and work with in mathematical problems. It shows the proportion in its most reduced form without changing its value. The fraction 940\frac{9}{40} tells us that for every 40 equal parts, 9 are being considered—which is exactly the same as saying 22.5 out of 100.
Conclusion
Thus, converting a percentage to a fraction involves dividing by 100, removing decimals if needed, and reducing the result to its simplest form. For 22.5%, the correct and fully simplified fraction is: 940\boxed{\frac{9}{40}}
