MHB Solve the a/b and 10/11 Problem: Understanding Quantity Relationships

[CharlesLin]

this is a nother problem from my study guide.
it starts with a statement
View attachment 4915

A) a/b

B) 10/11
based on this information you have to choose an answer:

a)quantity A is greater
b)quantity B is greater
c)the two are equal
d)the relationship can not be determined from the information given what I first try was was to change every number into a decimal number. for example 9/10= .9 and 11/12=.916. Then I know that a/b is between .9 and .910 but that did't helped because when I calculated 10/11=.90909 the decimal value is also between .9 and .916. then I'm not sure if the answer is d) the relationship can not be determinde...I suspect this is the answer but I'm not entirely shure.

how would you solve this problem?

I also try to picture the solution drawing the line where every fraction would be but I wasn't able to pictured well. Moreover, I had some problems trying to use LATEX there is any tutorial or guide to use it?

 

[evinda]

If it would hold that $\frac{a}{b}> \frac{10}{11}$ then it would have to hold $\frac{10}{11}< \frac{11}{12} \Rightarrow 10 \cdot 12< 11 \cdot 11$, which is true.

If it would hold $\frac{a}{b}< \frac{10}{11}$ then it would have to hold that $\frac{9}{10}< \frac{10}{11} \Rightarrow 99<100$, which again is true.It also holds that $\frac{9}{10}< \frac{10}{11}< \frac{11}{12}$.

Thus I think that we cannot determine the relationship between $\frac{a}{b}$ and $\frac{10}{11}$ from the given information.

 

[CharlesLin]

I see now
I feel more confident saying that D) is the answer.