The Correct Answer and Explanation is:
The correct answer is 77.5%.
To convert the fraction 31/40 into a percent, you need to find its equivalent value out of 100. There are two common methods to achieve this.
The first and most direct method is to convert the fraction into a decimal and then multiply by 100. To turn a fraction into a decimal, you divide the numerator (the top number) by the denominator (the bottom number). In this case, you perform the division:
31 ÷ 40 = 0.775
Once you have the decimal form, you convert it to a percentage. The word “percent” means “per hundred,” so you multiply the decimal by 100. An easy way to do this is to move the decimal point two places to the right.
0.775 × 100 = 77.5
Finally, you add the percent symbol (%) to indicate it is a percentage. Thus, 31/40 is equal to 77.5%.
A second method involves setting up a proportion to find an equivalent fraction with a denominator of 100. You want to find a number, let’s call it ‘x’, that makes the following equation true:
31/40 = x/100
To solve for x, you can cross multiply the terms. This means you 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.
31 × 100 = 40 × x
3100 = 40x
Now, to find the value of x, you isolate it by dividing both sides of the equation by 40:
x = 3100 ÷ 40
x = 77.5
This result means that 31/40 is equivalent to 77.5/100, which by definition is 77.5%. Both methods confirm that 31/40 as a percent is 77.5%.
