Theory:

Applying the equivalent ratio method, we can determine whether the given ratios are equivalent or not.
 
Let's see a few steps to understand this concept.
Equivalent ratios: 
 
Step 1: First write the given ratios in the form of fractions.
 
Step 2: Compare the fractions by converting into like fractions. (Take LCM if needed)
 
Step 3: Now if the fractions are equal, then the ratios are said to be equivalent otherwise not.
Check whether the ratios 1:4 and 4:8 are equivalent?
 
Step 1: Write the given ratios in the form of fractions.
 
14and48
 
Step 2: Hence the denominators 4 and 8 is not equal. We should take LCM for 4 and 8.
 
That is LCM of 4 and 8 is \(16\).
 
Then we get,
 
1×44×4and4×28×2416and816
 
Now we can compare the ratios 416and816.
 
Since416816
 
That is \(4\)\(/\)16 is lesser than 8\(/\)16.
 
Therefore the given ratios 1:4 and 4:8 are not equivalent.