What percentage is the first quantity of the second quantity

J

Joshua76

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Hi, i am stuck on this area of percentages. Can i see a formula to help me out
 
Ok. Imagine you got 8 out of 240 on a test (eeek!). What percentage did you get?
 
The formula applied to your example is

[MATH]\dfrac{8}{240} * 100 \approx 3.33\%.[/MATH]
It is just that simple.

[MATH]\dfrac{\text {part}}{\text {whole}} * 100 = \text {percentage}.[/MATH]
 
JeffM said:
The formula applied to your example is

[MATH]\dfrac{8}{240} * 100 \approx 3.33\%.[/MATH]
It is just that simple.

[MATH]\dfrac{\text {part}}{\text {whole}} * 100 = \text {percentage}.[/MATH]
Click to expand...
JeffM, I am sorry but I can not agree with what you said. After all, \(\displaystyle \frac{8}{240}*100 >1\). So how can the answer be 3.33%???

The formula applied to your example is

[MATH]\dfrac{8}{240} * 100\% \approx 3.33\%.[/MATH]
It is just that simple.

[MATH]\dfrac{\text {part}}{\text {whole}} * 100\% = \text {percentage}.[/MATH]
 
Jomo said:
JeffM, I am sorry but I can not agree with what you said. After all, \(\displaystyle \frac{8}{240}*100 >1\). So how can the answer be 3.33%???

The formula applied to your example is

[MATH]\dfrac{8}{240} * 100\% \approx 3.33\%.[/MATH]
It is just that simple.

[MATH]\dfrac{\text {part}}{\text {whole}} * 100\% = \text {percentage}.[/MATH]
Click to expand...
?????

1% of 240 is 2.4 so 8 as a percentage of 240 is clearly greater than 1%. Who is drinking what?
 
JeffM said:
?????

1% of 240 is 2.4 so 8 as a percentage of 240 is clearly greater than 1%. Who is drinking what?
Click to expand...
I am drinking Bosco.

I never wrote that anything is greater than 1%. I wrote that something is greater than 1 which equals 100%.
 
\(\displaystyle \frac{8}{240}*100\) is clearly greater than 1 while 3.33% is less than 1. Are the two quantities really equal??
 
Yes, they are equal.

[MATH]3.33\% \equiv \dfrac{3.33}{100}.[/MATH]
What in the world are we confusing the poor student about?

[MATH]1\% = \dfrac{1}{100} << 1.[/MATH]
Please tell me explicitly what error I made.
 
I'm going to butt in and say I agree with Jomo.

Jeff said \(\displaystyle \frac{8}{240} * 100 \approx 3.33\%\)

Jomo said \(\displaystyle \frac{8}{240} * 100\% \approx 3.33\%\)

Jeff, you left out the % sign next to the 100 on the LHS.
 
Jomo said:
Please tell me explicitly what error I made.
Click to expand...
Sure, you said that [MATH]\dfrac{8}{240} * 100\% \approx 3.33\%.[/MATH] which is not true. The lhs is greater than 1 while the rhs is less than 1. Please look carefully.
 
Jomo said:
Sure, you said that [MATH]\dfrac{8}{240} * 100\% \approx 3.33\%.[/MATH] which is not true. The lhs is greater than 1 while the rhs is less than 1. Please look carefully.
Click to expand...
No Jomo, that statement is correct. Jeff didn't have the % sign on the LHS. See #10.
 
Jomo said:
Sure, you said that [MATH]\dfrac{8}{240} * 100\% \approx 3.33\%.[/MATH] which is not true. The lhs is greater than 1 while the rhs is less than 1. Please look carefully.
Click to expand...
Actually you said [MATH]\dfrac{8}{240} * 100\ \approx 3.33\%.[/MATH] which is not true. The lhs is greater than 1 while the rhs is less than 1.
 
Jomo

I am not upset. Yes, I agree. We should treat the percent sign as a unit. That is the correct formalism. I agree. (There, I have now said it three times.) After Harry clarified what was being said, I guess I should have said "Mea maxima culpa."

Had I understood what you were objecting to in your very first post, namely the misuse of units, this whole thread could have been truncated long ago. Of course, for a student who seemed not to understand the arithmetic of computing a percentage, a discussion of the proper use of unit symbols may have been wasted. For that student, what you put into a calculator is

[MATH]\dfrac{8}{240} * 100 \approx 3.33.[/MATH] Then write % after the 3.33.

It is that simple operationally. I was giving a procedure, not really an equation.

By the definition of percent, short for per centum meaning in proportion to 100, and by the meaning of the symbol %,

[MATH]\dfrac{8}{240} * 100 \approx 3.33 \implies \dfrac{8}{240} * \dfrac{100}{100} \approx \dfrac{3.33}{100} \implies \dfrac{8}{240} \approx 3.33\%.[/MATH]
That is a logical justification for what we actually do operationally. I am not sure, however, that such an explanation or this thread has helped this student.
 
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