How to read this expression? How can I read this expression :

$$\frac{1}{4} \le a \lt b \le 1$$ 

Means $a,b$ lies between $\displaystyle \frac{1}{4}$ and $1$?
Or is $a$ less the $b$ also less than equal to $1$?
So $a+b$ won't be greater than $1$?

Think of the number line.  The numbers $\{\tfrac{1}{4}, a, b, 1\}$ are arranged from left to right.  The weak inequalities on either end indicate that $a$ could be $\tfrac{1}{4}$ and $b$ could be $1$.  However, the strict inequality in the middle indicates that $a$ never equals $b$.
