# percentage confusion

Discussion in 'Math' started by TheSpArK505, May 17, 2017.

1. ### TheSpArK505 Thread Starter Member

Sep 25, 2013
101
1
Hello guys, I have some confusions that I need to clarify

In this question, I have used the formula (a-b/b)*100 to solve the problem.Unfortunately it was wrong. I want to know the concept for applying each. In other words, I want to have ta clear understanding when to apply the correct formula.

UK FRANCE

2. ### WBahn Moderator

Mar 31, 2012
20,233
5,756
First off, (a-b/b)*100 is equal to (a-1)*100. You need to pay attention to order of operations.

Second, don't you think it might be at least a bit easier for us to determine where you went wrong in getting that answer you got if you were to, oh, show us the work you did or at the very least tell us what answer you got? We are NOT mind readers!

Their Step 3 is incorrect. 1.166 does NOT equal 16.6%, like they claim. It is 116.6%. They are relying on the reader to understand that this is not the percentage INCREASE in the number of cars, but rather the number of cars in 2005 as a percentage of the number of cars in 1995 and to then infer that this means an increase of 16.6%.

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3. ### djsfantasi AAC Fanatic!

Apr 11, 2010
3,496
1,253
I'm not sure about the rest of your problem, but I am sure that the formula you listed is what you mean. Briefly, the formula as shown, is equivalent to

(A-1)*100

Is this what you want? Do you know why?

OOPS: WBahn beat me to my point. Unsure how I missed his reply.

Last edited: May 17, 2017
4. ### KeepItSimpleStupid Well-Known Member

Mar 4, 2014
2,069
359
First note that there are 2 columns for 1995 and two columns for 2000.

"Between" was an issue for me. If you have 1 2 3 4, between is 2 & 3. That's neither her or there - that's me.

I don't know how you pulled 1.666 = 16.6%

Percentage is a ratio normalized to 100. That's it. So, in the 1.66 example is 1.66/1 * 100 or 166.6%

The 1.66 is likely a repeating decimal, do 166.7% rounding up.

Go over again, the key point percentage is the ratio normalized to 100 (uses the % sign)
Percentage can also be expressed in whole numbers with 1 being 100%

Normalizing to 100 means taking the fractional part and multiplying by 100. e.g. 1/4 --> 1/4*100 and 4/1*100 = 400%

The only real thing you have to worry about is this:

x is y% of z.

y% is y/100
after "of" is the denominator

x/z=y/100

Solve for which one that you need.

==

The b/b is done first, so that one is (a-(b/b))/100 and that already looks wrong.
You might be wanting (a-b)/b*100; or (a-b)*100/b

==

One other comment,

So, you have two columns of 1995 totals and two of 2000 totals, not one. Is one cars and the other trucks or is something missing?

5. ### WBahn Moderator

Mar 31, 2012
20,233
5,756
Can't tell for sure, but I think the first pair of columns is for the U.K. and the second pair is for France.

6. ### KeepItSimpleStupid Well-Known Member

Mar 4, 2014
2,069
359
I see that:

Step #1 is right 1995: 808 (thousand)
Step #2 is right 2000: 942 (thousand)

Step 3 isn't. Hint: What's the total number of cars?

7. ### WBahn Moderator

Mar 31, 2012
20,233
5,756
It's not 1.66, it's 1.166.

It's already rounded up. Why round it again?

The answer carried out a bit further is 1.16584158415841584158415841584158

So there is a repeating decimal, but it is in the 4th sig fig.

Last edited: May 17, 2017
8. ### wayneh Expert

Sep 9, 2010
13,624
4,416
If a = after and b = before, then your only problem appears to be that the "a-b" needs to be within parentheses, to provide the right order of operations. It's equivalent to the steps shown but will not give a step-by-step correlation to the steps shown, which take a shortcut at the end as @WBahn has noted. They omitted the "-1".

For what it's worth, I would usually do it the way the steps are shown. It's faster when using a calculator as you only enter two numbers and one operator, and then you can just subtract one in your head to get the answer. This can become risky, though, when dealing with very large increases such as 1152%. It's easy to forget to subtract 1.

9. ### TheSpArK505 Thread Starter Member

Sep 25, 2013
101
1
Guys, I'm asking about when I use the formula ((a-b)/b)*100 and why the solution( not my solution) used (1-a/b)*100 !!

are they equivalent ??

10. ### wayneh Expert

Sep 9, 2010
13,624
4,416
Yes, except you have the sign wrong in the 2nd expression. Both expressions evaluate to a/b -1, times 100.

11. ### WBahn Moderator

Mar 31, 2012
20,233
5,756
They used ((a/b) - 1)*100%.

Do the algebra.

$
$$\frac{a \; - \; b}{b}$$ \cdot 100%
$$\frac{a}{b} \; - \; \frac{b}{b}$$ \cdot 100%
$$\frac{a}{b} \; -\; 1$$ \cdot 100%
$

12. ### TheSpArK505 Thread Starter Member

Sep 25, 2013
101
1
Many thanks guys, now I understand thank you all.