what percentage is 3 out of 5

eddy2017

eddy2017

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Hi, this is supposed to be easy but I do not understand where the 20 is coming from. This is in answer to a problem that said that if 3 out of 5 customers preferred brand x, then what percentage is that, is 3 out of 5?
I looked it up, found this answer.
let's convert the fraction 3/5 into percent.
Explanation:
Let's change the fraction 3/5 to an equivalent fraction with the denominator equal to 100
(3 × 20) / (5 × 20) = 60/100
Now, 60/100 is expressed as 65% in terms of percentage
it is all good except I do not know why I have to multiply 3 and 5 times 20. if there is a shorter way please, let me know.
thanks to all my tutors,
eddy
i could also divide 3/5 which equals 0.6 and could have gone for the 60% option in the answer but with no certainty of why i did that.
 
Last edited:
The word "percent" means 'per one hundred', so when you convert 3/5 into a percent, you are looking for a fraction with a denominator of 100 that is equivalent to 3/5.

Look at this proportion: [MATH]\frac{3}{5}=\frac{?}{100} [/MATH]
What do you multiply by 5 to get 100? That same number must be multiplied by 3 to make an equivalent fraction.
 
R.M. said:
The word "percent" means 'per one hundred', so when you convert 3/5 into a percent, you are looking for a fraction with a denominator of 100 that is equivalent to 3/5.

Look at this proportion: [MATH]\frac{3}{5}=\frac{?}{100} [/MATH]
What do you multiply by 5 to get 100? That same number must be multiplied by 3 to make an equivalent fraction.
Click to expand...
3 times 100/5 =60, 60%
Got it. But in the example answer that I posted why they multiply both numerator and denominator by 20. I still don't see the why.
i like your quick solution best but i would like to know why times 20
 
Last edited:
The only value you can multiply 3/5 by without changing its value is 1. Now 1 can be written many different ways as a fraction. For example, 7/7=1, -19/-19 = 1, 2/3/2/3=1, 20/20=1, 2/2=1, etc.
Now to get a denominator of 100 from 3/5, we multiply 3/5 by 20/20.
 
Jomo said:
The only value you can multiply 3/5 by without changing its value is 1. Now 1 can be written many different ways as a fraction. For example, 7/7=1, -19/-19 = 1, 2/3/2/3=1, 20/20=1, 2/2=1, etc.
Now to get a denominator of 100 from 3/5, we multiply 3/5 by 20/20.
Click to expand...
thanks Mr jomo. Yes, now I see the why *20 clearly. thanks. it is,like, when we 're trying to find a common denominator we multiply by 1, but instead of writing 1 we just write such fractions. I have heard some teachers refer to them like a 'fancy form of one', which they are, in fact.
 
Another way of writing 1 is 100%. 100%=1. So if you have a number, like 3/5, and you want to introduce a % symbol, then multiply by 100%

[math] Now \dfrac{3}{5} = \dfrac{3}{5}*100\% =60\%[/math]
 
Jomo said:
Another way of writing 1 is 100%. 100%=1. So if you have a number, like 3/5, and you want to introduce a % symbol, then multiply by 100%

[math] Now \dfrac{3}{5} = \dfrac{3}{5}*100\% =60\%[/math]
Click to expand...
I like that!
 
I think like an Algebraist- A mathematician who studies Algebra (very advanced Algebra, not high school algebra).
A very important concept in Algebra is the identity which you would call 1. It is a very powerful number and has gotten me out of jams more than one time while trying to solve a math problem. 0 is also a powerful number. You can add 0 to any expression without changing its value!
 
Jomo said:
I think like an Algebraist- A mathematician who studies Algebra (very advanced Algebra, not high school algebra).
A very important concept in Algebra is the identity which you would call 1. It is a very powerful number and has gotten me out of jams more than one time while trying to solve a math problem. 0 is also a powerful number. You can add 0 to any expression without changing its value!
Click to expand...
Definitely. I could see it when watching some videos from free academy on you tube how 0, and 1 are so useful when graphing equations. makes everything so easy and i suppose in may different mathematical operations.
 
Jomo said:
I think like an Algebraist- A mathematician who studies Algebra (very advanced Algebra, not high school algebra).
A very important concept in Algebra is the identity which you would call 1. It is a very powerful number and has gotten me out of jams more than one time while trying to solve a math problem. 0 is also a powerful number. You can add 0 to any expression without changing its value!
Click to expand...
is there anything written or on youtube that talks about that?. like eg the matheatical power of 0 and 1?
 
Whenever you want to change the way something looks like, you multiply by 1 or add 0. That should be a tool which you have .
As far as a video showing how to use 1 and 0, I have not seen one.
 
Jomo said:
Whenever you want to change the way something looks like, you multiply by 1 or add 0. That should be a tool which you have .
As far as a video showing how to use 1 and 0, I have not seen one.
Click to expand...
Thanks, doc jomo. I will keep it in mind.
 
Jomo said:
When I finish a Phd program in math, then you can call me doc. For now, prof or Jomo is fine.
Click to expand...
Okay, thanks, prof. Thanks for the good info. I will turn in now for the night. A good math day awaits tomorrow!
 
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