\(\tfrac{12}{75} \, ... \, \tfrac{32}{200}\)
\(\tfrac{12}{75} \, = \, \tfrac{32}{200}\)
Goal: Check if the two fractions are equal.
Method 1: Simplify both fractions
\(\dfrac{12}{75}\) → divide top and bottom by \(3\)
Top: \(12 \div 3 = 4\)
Bottom: \(75 \div 3 = 25\)
So, \(\dfrac{12}{75} = \dfrac{4}{25}\)
\(\dfrac{32}{200}\) → divide top and bottom by \(8\)
Top: \(32 \div 8 = 4\)
Bottom: \(200 \div 8 = 25\)
So, \(\dfrac{32}{200} = \dfrac{4}{25}\)
Both became \(\dfrac{4}{25}\), so they are equal.
Method 2: (Quick check with decimals)
\(\dfrac{4}{25} = 0.16\)
So, \(\dfrac{12}{75} = 0.16\) and \(\dfrac{32}{200} = 0.16\).
Conclusion: \(\dfrac{12}{75} \, \underline{=} \, \dfrac{32}{200}\)