Express as 4/5% as a fraction or a mixed number
The correct answer and explanation is:
To convert 4/5% to a fraction or mixed number, follow these steps:
Step 1: Convert the percentage to a fraction.
- A percentage is essentially a fraction out of 100, so we start by rewriting the percentage as a fraction: 45%=45×1100\frac{4}{5}\% = \frac{4}{5} \times \frac{1}{100}
- Multiply the fractions: 45×1100=4500\frac{4}{5} \times \frac{1}{100} = \frac{4}{500}
- This fraction can be simplified. To do that, find the greatest common divisor (GCD) of 4 and 500, which is 4.
Step 2: Simplify the fraction.
- Divide both the numerator and denominator by 4: 4500=4÷4500÷4=1125\frac{4}{500} = \frac{4 \div 4}{500 \div 4} = \frac{1}{125}
Step 3: Express the result.
Thus, 4/5% as a fraction is: 1125\frac{1}{125}
Explanation:
In this process, we started by converting the percentage into a fraction over 100. Then, we multiplied the fraction by 1/100 to account for the percentage notation. Finally, we simplified the resulting fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). Since 4 and 500 share a GCD of 4, the simplified fraction becomes 1/125.
This approach shows how percentages can be converted into simple fractions, and it is particularly useful in solving real-world problems that involve rates, proportions, or comparisons between percentages.