How do you write 190% as a fraction or mixed number in simplest form?
The Correct Answer and Explanation is :
To convert 190% to a fraction or mixed number in simplest form, follow these steps:
Step 1: Convert the percentage to a fraction
A percentage is simply a number out of 100. So, to express 190% as a fraction, write it as:
[
190\% = \frac{190}{100}
]
This fraction represents 190 out of 100.
Step 2: Simplify the fraction
To simplify the fraction, find the greatest common divisor (GCD) of 190 and 100. We can start by factoring both numbers.
- 190 factors as: (190 = 2 \times 5 \times 19)
- 100 factors as: (100 = 2^2 \times 5^2)
The common factors between 190 and 100 are 2 and 5. The GCD is (2 \times 5 = 10).
Now, divide both the numerator and denominator of the fraction by 10:
[
\frac{190}{100} = \frac{190 \div 10}{100 \div 10} = \frac{19}{10}
]
Thus, the fraction in simplest form is (\frac{19}{10}).
Step 3: Convert the improper fraction to a mixed number
To convert (\frac{19}{10}) into a mixed number, divide 19 by 10.
- 19 ÷ 10 = 1 remainder 9.
So, the mixed number is:
[
1 \frac{9}{10}
]
Conclusion
Therefore, 190% as a fraction in simplest form is (\frac{19}{10}), and as a mixed number, it is (1 \frac{9}{10}).
In summary:
- 190% = (\frac{19}{10})
- As a mixed number, 190% = (1 \frac{9}{10}).