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 $1$?


$$\frac{1}{4} \le a \lt b \le 1 \iff \;\; \frac 14 \leq a\;\;\;\text{AND}\;\;a\lt b\;\;\;\text{AND} \;\;b \leq 1$$ 

Most directly, this means that both $a$ and $b\;$ lie on the interval ranging from $\large \frac{1}{4}$ and $1$, inclusive, with the added qualification that $a\lt b$.
Another way to think of this inequality is to think of it as the set values, $\;a,\; b\;$ for which $$\;a \lt b\;\;\text{ and}\;\;\;[a, b]\; \subseteq \;[1/4, 1]$$
Yes, it could be that $a + b > 1$. For example, if $a = 1/2, \;b = 1$, then $\;a+b>1$
But it could also be that $a + b < 1:$  for example, if $a = 1/4, \; b = 1/2$, then the inequality is satisfied, but $a + b = 3/4 \lt 1$
