# Why am I getting two different results? 15% of what is 7?

#### mesmerized

##### New member
Hi all,

Question: 15% of what is 7? Here's how I approach this problem:

Method 1:

15% = 0,15
0.15 x (n) = 7
0.15n = 7 /divide by 0.15
n = 7/15
n= 46.66 or as a fraction n=46 and 66/100ths which can be simplified into 46 and 33/50ths

Method 2 (using proportions):

percent over 100 = amount over base
15/100 = 7/n
15n = 700 /divide by 15
n = 700/15
n = 46 and 10/15ths which gets simplified into 46 and 2/3rds

Now, 46 and 33/50ths isn't the same as 46 and 2/3rds, is it? Why am I getting different results? How come I can't simplify the first result (46 and 33/50ths) into 46 and 2/3rds?

It all comes down to rounding.
2/3 as a decimal is a repeating decimal and goes on infinitely as: .6666666666666666666666666....
Sometimes you'll see it written as: 0.6666667.

So your method one answer if rounded to two decimal places would be 46.67 but in reality, the 6 is repeating infinitely showing that your answer is 46 and 2/3
When you do 7 divided by .15 you get 46 with a remainder of 10/15 which is 2/3.

I hope this helped explain why you're getting different results!

7/0.15 = 46.66666666666...
That is the never ending decimal
0.66666666.... is 2/3
To see this, let n be 0.6666666...
Then 10n = 6.666666
So, 10n - n = 9n = 6
solve for n. n = 6/9 = 2/3 !

You forgot the [imath]100[/imath] in [imath]0.15[/imath] in the first method.

[imath]0.15 \times n = 7[/imath]
[imath]\therefore \frac{1}{0.15} \times 0.15 \times n = 7 \times \frac{1}{0.15} = 1 \times n = n = \frac{7}{0.15} = \frac{700}{15}[/imath]

You forgot the [imath]100[/imath] in [imath]0.15[/imath] in the first method.

[imath]0.15 \times n = 7[/imath]
[imath]\therefore \frac{1}{0.15} \times 0.15 \times n = 7 \times \frac{1}{0.15} = 1 \times n = n = \frac{7}{0.15} = \frac{700}{15}[/imath] (Mathematical drivel!)
Again! Doesn't answer the question! (Or contribute to the OP's understanding of the problem s/he has presented!)

Please STOP just posting any old rubbish that just occurs to you (as here too!).

Thank you.

Now, 46 and 33/50ths isn't the same as 46 and 2/3rds, is it? Why am I getting different results? How come I can't simplify the first result (46 and 33/50ths) into 46 and 2/3rds?
You are getting different results because you can't "simplify" the first result (46.66) the way you have tried to!

46⅔ is the correct answer and both your methods arrived at that, or would have if you hadn't done something very wrong (and unforgiveable in Maths) at the end of your first attempt!

You wrote: n = 7/15 then n = 46.66. I presume (since your previous line was correct) that you meant to write: n = 7/0.15 then n = 46.66.

But how did you get 46.66?

Did you use a calculator?

If I do that sum on my little cheap (Poundland) calculator, my (10 digit) display shows: 46.66666667 (Note the 7 at the end!)

46.66 is an incorrectly rounded value for that answer; to 2 d.p. it would be 46.67!

Because ⅔ = 0.666666... recurring (ie: the 6's go on forever) and 7/0.15 = 46⅔ (as correctly evaluated in your second attempt) you cannot just take the (incorrect) .66 and say it is 66 hundredths (or even take a correctly rounded .67 and say it is 67 hundredths) because these are rounded decimal values!

(⅔ cannot be accurately expressed as a decimal number which is why it is often better to leave it as a common fraction when it crops up in calculations.)

The correct answer at the end of your first procedure should have been: n = 7/0.15 ⇒ n 46.67.
(Note the use of an 'approximately equal to' sign as opposed to an 'equals' sign!)

Hope that helps.

Last edited:
Let's keep it simple.
Method 1:

15% = 0,15
0.15 x (n) = 7
0.15n = 7 /divide by 0.15
n = 7/0.15
n= 46.66 or as a fraction n=46 and 66/100ths which can be simplified into 46 and 33/50ths
Using a rounded decimal value changes the answer. Evaluating as a fraction instead, you get 7/0.15 = 700/15 = 140/3 = 46 2/3.

The answer you wrote is an approximation of this, obtained by (inaccurately) rounding 46.666... to 46.66. This is a reason to avoid dividing by a decimal, if you care about precision, because you will usually have to round.

Method 2 (using proportions):

percent over 100 = amount over base
15/100 = 7/n
15n = 700 /divide by 15
n = 700/15
n = 46 and 10/15ths which gets simplified into 46 and 2/3rds
This is exactly the same, but because you used proportions, you stuck with fractions, and got an exact answer.

Now, 46 and 33/50ths isn't the same as 46 and 2/3rds, is it? Why am I getting different results? How come I can't simplify the first result (46 and 33/50ths) into 46 and 2/3rds?
The two answers you compare are, respectively, 46.66 and 46.666..., which are not very different. The latter is exact (when treated as a fraction or a repeating decimal); the former is rounded. That's all.

In general, rounding means intentionally changing a number to one you can work with more easily in the chosen form. When you round, you a;ways need to be aware that the result will be inaccurate; don't expect the result to be exact.

Hi all,

Question: 15% of what is 7? Here's how I approach this problem:

Method 1:

15% = 0,15
0.15 x (n) = 7
0.15n = 7 /divide by 0.15
n = 7/15
You say that you are planning on dividing the 7 by 0.15, but instead you divided by 15!

You say that you are planning on dividing the 7 by 0.15, but instead you divided by 15!
Actually, they did the right division, since they got 46.66, not 0.4666. They just didn't write what they did. The "error" is in the rounding, not the dividing.

15% of what is 7?
Our "base" equation for percentages is: original amount * percentage = result. Let's substitute the numbers in and we get: original amount * 0.15 = 7. For now, we'll call original amount 'a'.

Now, we can solve this equation: a * 0.15 = 7. We need to divide both sides by 0.15 so they cancel out. We get: a = 46.66667 or 46 and 2/3. Let's check using a calculator (is 15% of 46 and 2/3 7)? Yes it is!

Therefore, our answer is 46.666667 or 46 and 2/3.

15% of what is 7?
Our "base" equation for percentages is: original amount * percentage = result. Let's substitute the numbers in and we get: original amount * 0.15 = 7. For now, we'll call original amount 'a'.

Now, we can solve this equation: a * 0.15 = 7. We need to divide both sides by 0.15 so they cancel out. We get: a = 46.66667 or 46 and 2/3. Let's check using a calculator (is 15% of 46 and 2/3 7)? Yes it is!

Therefore, our answer is 46.666667 or 46 and 2/3.
Your arithmetic and handling of a calculator are, without doubt, unimpeachable!

However your post does not, in any way, address the original question which was to provide an explanation of how the OP was getting two different answers.