# Math Help - Reporting a ratio

1. ## Reporting a ratio

Im doing some online tests and seem to keep getting my ratio expressions wrong,

Example:

QUESTION
What is the ratio of the number of tornados in 2008 to those in 2005?

A) 1.36:1 B) 1:1.28 C) 0.78:1 D)1.26:1

Jets in 2008 = 297
Jets in 2005 = 380

279:380 = 1:1.28

However correct answer is 0.78:1 - why?

Why does it matter whether you express it as "one to..." or "...to one"?

Arent both expressions the same?

If someone could clarify this for me id appreciate it, thanks.

2. Each expression is the reciprocal of other so the order does matter.

If you're asked to find the ratio of A to B then you work out $\dfrac{A}{B}$

In this question you want $\dfrac{n_{2008}}{n_{2005}}$

3. Hi

297:380 or 297/380=0.78

It is 0.78 to 1 as in 2008 you only have 0.78 times the events of 2005, if expressed the other way (1:0.78) you would have less events then in the past. Hope that makes sense but it's hard for me to describe in words - sorry

4. Thanks, that explains the above question, which makes sense - but what about here, that method above doesnt seem to apply:

What is the ratio of women to men working in Audit In 2005?

A) 1:1.12 B) 1.18:1 C) 1:1.31 D) 1.15:1

women working = 26758
men working = 31500

women:men = 26758:31500 = 26758/31500 = 0.849 - not a given answer

Im sure im being thick, but I simply dont see it!

5. Hi

As mentioned above you need the reciprocal to give the answer shown so:

either 26758/31500 = 0.849 then 1/0.849 = 1.18 (b)
or 31500/26758 = 1.18 (b)

As the result is 1.18:1 you can see that you would anticipate that the number of males is more than females as is shown in the table.

6. The Ratio of A to B is essentially how many of B is there for every 1 of A.

In your example it is asking how many men are there for each woman. To this end we can divide both sides by the number of women

$\dfrac{26758}{26758} : \dfrac{31500}{26758}$ which is $1:1.18$.

I believe the question is incorrectly worded though as this is not the same as $1.18:1$ - after all the ratios given imply that there are more women than men which is clearly not the case

7. Notice the order in the question.

First question: "number of tornados in 2008 to those in 2005"
So the ratio is "number of tornados in 2008": " number of tornados in 2005" or 297: 380 which is the same as 1: 380/297= 1.28.
You could have divided the other way: 297/380= 0.78: 1 but- (1) it is more common to write a proportion as 1 and a number greater than 1. (2) (More importantly) None of the given answers say "0.78: 1".

Second question: " ratio of women to men working in Audit In 2005" so the order is "women": "men" or 26758: 31500. Since 26758 is the smaller number, this is 1: 31500/26758= 1.18: 1. You could have written it as 1: 26758/31500= 0.81 but that is not a given answer.

Just make sure you undestand the difference between 1: 0.81 which is correct but not one of the given answers and 0.81: 1 which is NOT correct. 0.81: 1 would be "men": "women", not "men": "women".

8. Hi

Sorry to be pedantic but:

None of the given answers say "0.78: 1".
however from the original post

QUESTION
What is the ratio of the number of tornados in 2008 to those in 2005?

A) 1.36:1 B) 1:1.28 C) 0.78:1 D)1.26:1

9. Hi, thanks for all the replies.

Just to clarify, my question was never "is 1:0.78 the same as 0.78:1" - i know full well these are two different things.

My confusion came from the first question having 1:1.28 and 0.78:1 as possible answers and not know which was right.

The above two posts seem to highlight my point!