Write the fraction as a percent: 1 13/20.
The correct answer and explanation is:
The fraction given is a mixed number: 1 13/20. To convert this mixed number to a percent, follow these steps:
- Convert the mixed number to an improper fraction.
The mixed number 1 13/20 means 1 whole plus 13/20.
To write it as an improper fraction, multiply the whole number by the denominator and add the numerator:
1×20+13=20+13=331 \times 20 + 13 = 20 + 13 = 33.
So, 11320=33201 \frac{13}{20} = \frac{33}{20}. - Convert the improper fraction to a decimal.
Divide the numerator by the denominator:
3320=33÷20=1.65\frac{33}{20} = 33 \div 20 = 1.65. - Convert the decimal to a percent.
To convert a decimal to a percent, multiply by 100:
1.65×100=165%1.65 \times 100 = 165 \%.
Therefore, 113201 \frac{13}{20} as a percent is 165%.
Explanation
A mixed number like 1 13/20 combines a whole number and a fraction. To work with it more easily, it helps to convert it into an improper fraction, which is a single fraction where the numerator is larger than the denominator. The formula for converting a mixed number abca \frac{b}{c} to an improper fraction is a×c+bc\frac{a \times c + b}{c}.
In this case, 1 whole is the integer part, and 13/20 is the fractional part. By multiplying the whole number 1 by the denominator 20, then adding the numerator 13, we get the numerator of the improper fraction: 33. The denominator remains 20.
Next, dividing 33 by 20 gives the decimal equivalent. Dividing 33 by 20 yields 1.65. This decimal form is easier to convert to a percentage.
To convert a decimal to a percentage, multiply it by 100. Multiplying 1.65 by 100 moves the decimal two places to the right, resulting in 165. This means the original mixed number is equivalent to 165 percent.
This method of converting mixed numbers to percentages is common in many practical situations, such as calculating discounts, interest rates, or any context where fractions need to be expressed as percentages. Understanding the conversion steps allows accurate and meaningful interpretation of fractions as percentages.