The ratio is used for comparing two quantities of the sane kind.

The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in proportion.

The concept of ratio and proportion is majorly based on ratios and fractions.  

Solution:

From the question it is given that, $a+b:a-b=11:8$

$\left( a+b \right)/\left( a-b \right)=11/8$

By cross multiplication we get,

$8\left( a+b \right)=11\left( a-b \right)$

$8a+8b=11a-11b$

Transposing we get,

$11b+8b=11a-8a$

$189b=3a$

$19/3=a/b$

$a:b=19:3$