asdusz wrote:

Hi everyone,

I have a question about the notation of ratios.

I do understand the math behind it yet sometimes it seems to me that questions use the notation interchangeably.

Here are two examples of what I mean:

1. Example

If a=2b, 1/2b=c and 4c=3d what is the ratio of d to a?

I thought it's 3/1 but the correct answer is 1/3.

Rephrase "what is the ratio of d to a" algebraically to "d/a=?"

To get a numerical answer for your ratio, you will need the variables to cancel out. Put d in terms of c and a in terms of c (a->b->c)

d=(4/3)c, a=2b=4c. ((4/3)c)/4c = (4/3)/4 = 1/3

**Quote:**

2. Example

Given that a is the average (arithmetic mean) of the first nine positive multiples of six and b is the median of the first twelve positive multiples of six, what is the ratio of a to b?

Same thing. If you rephrase "what is the ratio of a to b" into algebra, you get "a/b=?"

The average of numbers that are evenly spaced apart is the median. The median of the first nine positive multiples of 6 is 30.

Median of the first 12 positive multiples of 6 is the mean of the 6th and 7th positive multiples of 6, so (36+42)/2= 39

30/39 = 10/13

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