Theory:

There are two cases in simplifying the ratio.
  1. Simplifying ratios of the same unit.
  2. Simplifying ratios of the different unit.
Simplifying ratios of the same unit
The general rule to simplify the ratios of the same unit.
 
Step \(1\): Write the ratio in fraction form.
Step \(2\): Divide each of the ratios with a suitable number.
Example:
1. Simplify the ratio \(45\) to \(6\).
 
The fraction form of the ratio is 456.
 
Divide each of the ratios by \(3\).
 
That is 45÷36÷3=152=15:2.
 
Thus, the simplified form of the ratio is 15:2.
 
 
2. Simplify the ratio of \(750\) \(gm\) to \(25\) \(gm\).
 
The fraction form of the ratio is 75025.
 
Divide each of the ratios by \(25\).
 
That is 750÷2525÷25=301=30:1.
 
Thus, the simplified form of the ratio is 30:1.
Simplifying ratios of different units.
The general rule to simplify the ratios of the different unit.
 
Step \(1\): Convert the ratios to the same unit.
Step \(2\): Write the ratio in fraction form.
Step \(3\): Divide each of the ratios with a suitable number.
Example:
Simplify the ratio \(5\) \(m\) to \(700\) \(cm\).
 
Step \(1\): Convert \(5\) \(m\) to \(cm\). We know that \(1m = 100cm\). Thus, \(5m = 5 × 100 = 500cm\).
 
Step \(2\): Write the ratio in fraction form. The fraction form of the given ratios is 500700.
 
Step \(3\): Divide each number by \(100\). 500700=57=5:7.
 
Thus, the simplified form of the ratio is 5:7.