NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 4: Fractions & Decimals - Problems and Solutions
Question 118

Question. 118

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?

Answer:

\(110\dfrac{1}{20}\,\text{cm}\)

Detailed Answer with Explanation:

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): \(150\dfrac{1}{4} = 150.25\), \(40\dfrac{1}{5} = 40.2\)

\(150.25 - 40.2 = 110.05 = 110\dfrac{1}{20}\,\text{cm}\)

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