How do you write 450% as a fraction or mixed number in simplest form?
The correct answer and explanation is:
To express 450% as a fraction or mixed number in its simplest form, we start by converting the percentage to a fraction.
- Understanding the Percentage: A percentage is simply a fraction out of 100. Therefore, 450% means 450 out of 100, or: 450%=450100450\% = \frac{450}{100}
- Simplifying the Fraction: Next, we simplify the fraction by dividing both the numerator (450) and the denominator (100) by their greatest common divisor (GCD). The GCD of 450 and 100 is 50, so we divide both by 50: 450100=450÷50100÷50=92\frac{450}{100} = \frac{450 \div 50}{100 \div 50} = \frac{9}{2} Therefore, 450% as a simplified fraction is 92\frac{9}{2}.
- Converting to a Mixed Number: To convert 92\frac{9}{2} into a mixed number, we divide 9 by 2. The quotient is 4 and the remainder is 1. So, 92\frac{9}{2} is equivalent to the mixed number 4 12\frac{1}{2}. 92=412\frac{9}{2} = 4 \frac{1}{2}
- Final Answer: Thus, 450% as a fraction in its simplest form is 92\frac{9}{2}, and as a mixed number, it is 4124 \frac{1}{2}.
In conclusion, to convert a percentage into a fraction or mixed number, you first convert the percentage into a fraction by dividing by 100, then simplify the fraction by finding the GCD, and finally, if necessary, convert it into a mixed number.