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Math Tutor's Solution: 120/420 as a percent is 28.571%
Methods
Method 1 from a Tutor – Converting 120/420 Into a Percentage:
The math tutor would start with a quick review of fractions. In a fraction, there are two main elements: the numerator and the denominator. The numerator, which is the number above the line, shows how many pieces there are present. The denominator, which is the number below the line, shows how many pieces there would have to be in order to make up a whole number.
“Percent” means “per hundred”, which means that we want to find out how many pieces of the whole we would have if there are 100 pieces possible. This means that a percent is the same as showing what the numerator of a fraction would be if the denominator, or the number of pieces there would have to be to make up a whole, is 100.
For example, if we look at the percentage 40%, that means we have 40 pieces of the possible 100. Re-writing this in fraction form, we see 40/100.
To start converting a fraction into a percent, we first have to change the fraction so that the denominator will be 100. To do this, we first divide 100 by the denominator:
This means that in order to change the denominator to 100, we will have to multiply it by 28.571. But to do that, we also have to multiply the numerator by the same number:
This works because multiplying both the numerator and the denominator by the same number is like multiplying it by 1. (0.238 / 0.238 = 1)
Once we are done multiplying, we can see that 120/420 as a percentage is 28.571%.
Method 2 from a Math Tutor – Converting 120/420 Into a Percentage Using Decimals:
There are other ways to convert a fraction into a percentage. One other common method is to first convert the fraction into a decimal.
To convert 120/420 into a percentage, you would first convert 120/420 into a decimal. This is done by dividing the numerator by the denominator:
Once you have the decimal, you can multiply it by 100 to get the percentage:
0.286 x 100 = 28.571
And there you have it! When we’re done, we can see that 120/420 as a percentage is 28.571%.
Knowing these two methods will help you convert just about any fraction into a decimal. It’s good to know both methods. In your practice you may find that for some fractions, one method is easier, while the second method may be easier for others.
Give it a go! Grab some paper and try to convert some of your own fractions to percentages. You’ll be an expert in no time!
Math Tutor Tip: Master fraction to percentage problems!
Practice makes perfect, so why not check out some of the other problems from our math tutors where you can convert a fraction to a percentage?
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