Cross multiplication

[veronica1]

The below question was answered in two ways. I chose the first and got it right but would like to understand the second method. They cross multiply the 7/9 and the possible answer but I'm not sure I see what the result is telling me. My question is the first example (and correct answer) uses > 7/9 first instead of < 7/9... why?

For ex. (correct answer) 9/11 > 7/9 because 9 × 9 = 81, which is greater than 7 × 11 = 77.
For ex. 7/9 > 5/7 because 7 × 7 = 49, which is greater than 5 × 9 = 45.
For ex. 7/9 = 14/18, which is greater than 13/18
For ex. 3/4 = 0.75 and is therefore less than 7/9
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Question:
All of the following are less than 7/9 EXCEPT


9/11
13/18
3/4
5/7
17/22

Answer:
There are a couple of ways to compare fractions:

I. Compare the decimal equivalents of the fractions.

1/9 is equal to 0.111... (since it is 1/3 of 1/3). 7/9 then, is equal to 0.777..., 7 times 1/9.

II. Use the cross multiplication trick:

[atharshiraz]

The below question was answered in two ways. I chose the first and got it right but would like to understand the second method.
II. Use the cross multiplication trick:

Suppose you are to compare two fractions x/y and a/b

you put x/y on the left hand side and a/b on the right hand side, and you put a question mark in the middle (this question mark will change to either < or > or =) :

x/y ? a/b

then you cross multiply:

x*b ? y*a

then you look at the LHS (left hand side) and RHS if xb is greater you change the "?" to ">" if ya is greater than you change the "?" to "<" and if xb and ya are equal then you change "?" to "=".

I think this is all explained in the guides.

[jnelson0612]

Thanks atharshiraz! Good explanation.

Please let us know if you need further clarification. :-)