Roma gave a wooden board of length \(150\dfrac{1}{4}\,\text{cm}\) to a carpenter. The carpenter sawed off a piece of \(40\dfrac{1}{5}\,\text{cm}\). What is the length of the remaining piece?
\(110\dfrac{1}{20}\,\text{cm}\)
Idea: Subtract the whole-number parts and the fraction parts separately.
Step 1: Write each length as whole + fraction.
\(150\dfrac{1}{4} = 150 + \dfrac{1}{4}\)
\(40\dfrac{1}{5} = 40 + \dfrac{1}{5}\)
Step 2: Subtract the whole numbers.
\(150 - 40 = 110\)
Step 3: Subtract the fractions. First, make the denominators the same.
\(\dfrac{1}{4} = \dfrac{5}{20}\)
\(\dfrac{1}{5} = \dfrac{4}{20}\)
Now subtract: \(\dfrac{5}{20} - \dfrac{4}{20} = \dfrac{1}{20}\)
Step 4: Combine whole part and fraction part.
\(110 + \dfrac{1}{20} = 110\dfrac{1}{20}\,\text{cm}\)
Quick check (decimal): \(150\dfrac{1}{4} = 150.25\), \(40\dfrac{1}{5} = 40.2\)
\(150.25 - 40.2 = 110.05 = 110\dfrac{1}{20}\,\text{cm}\)