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,
$11b+8b=11a-8a$
$189b=3a$
$19/3=a/b$
$a:b=19:3$