Theory:

Situation \(1\):
 
Consider the following situation. 
 
Reena mother said, Reena completed 13 of the homework exercises.
 
Ravi mother said, Ravi completed 14 of the homework exercises.
 
Can you guess who completed more?
 
Let us express the ratios as a fraction and then find the equivalent fractions, until the denominators are the same, and compare the fractions with common denominators.
 
This situation can be solved by making the denominator the same.
 
Reena's completed workRavi's completed work
13×22=2614×22=28
13×33=3914×33=312¯
13×44=412¯14×44=416
 
Note that the fractions 13 and 14 have the same denominator \(12\) with the values 412 and 312.
 
The numerator value of the fraction 13 is \(4\), and the numerator value of the fraction 14 is \(3\). 
 
Thus, the numerator value is higher for 13.
 
This implies Reena completed more work than Ravi.
 
 
Situation \(2\):
 
A rope of \(8 m\) is cut into two parts \(3 m\) and \(5 m\). This gives the ratio of the two pieces becomes \(3:5\).
Important!
In general, a ratio \(a : b\) is said to have a total of '\(a+b\)' parts in it.