The Correct Answer and Explanation is:
Of course. Here is the correct answer and a detailed explanation.
Correct Answer: 43.3̅% (or 43 1/3%)
Explanation
The goal of this problem is to convert the fraction 13/30 into a percentage. The word “percent” literally means “per one hundred,” so converting a fraction to a percent is a way of finding its equivalent value out of 100. There are two common methods to achieve this.
Method 1: Convert to a Decimal First
The most direct way to convert any fraction to a percentage is to first turn it into a decimal and then multiply by 100.
- Divide the Numerator by the Denominator: To convert the fraction 13/30 into a decimal, you perform the division 13 ÷ 30.
When you perform this division, you will find that it results in a repeating decimal.
13 ÷ 30 = 0.43333…
The digit ‘3’ repeats infinitely. In mathematics, we can represent this repeating decimal by placing a bar over the repeating digit, which looks like this: 0.43̅. - Multiply by 100: To convert the decimal into a percentage, you multiply it by 100 and add a percent sign (%). Multiplying by 100 is the same as moving the decimal point two places to the right.
0.4333… × 100 = 43.333…%
Using the bar notation, the final answer is 43.3̅%.
Method 2: Using a Proportion
Another way to think about this is to set up a proportion to find the equivalent fraction with a denominator of 100. We want to find a number, let’s call it ‘x’, that makes the following equation true:
13/30 = x/100
- Solve for x: To find the value of x, you can use cross-multiplication. Multiply the numerator of the first fraction by the denominator of the second, and set it equal to the denominator of the first fraction multiplied by the numerator of the second.
13 × 100 = 30 × x
1300 = 30x - Isolate x: Now, divide both sides of the equation by 30 to solve for x.
x = 1300 / 30
x = 130 / 3 - Calculate the Percentage: When you divide 130 by 3, you get 43 with a remainder of 1. This can be expressed as the mixed number 43 1/3.
Since x represents the value per one hundred, the percentage is 43 1/3%.
Both 43.3̅% and 43 1/3% are the same value and are the correct answer, as the fraction 1/3 is equal to the repeating decimal 0.3̅.
