Rahul bought a ribbon of total length $12\frac{1}{2}\text{ m}$. He cut off $3\frac{3}{4}\text{ m}$ to use for his art project and divided the remaining ribbon equally among $5$ of his friends. How many metres of ribbon did each friend receive?

Step-by-step solution

1. Step 1: Convert the mixed fraction for the total length of the ribbon into an improper fraction: Total length $=12\frac{1}{2}\text{ m}=\frac{25}{2}\text{ m}$.
2. Step 2: Convert the mixed fraction for the length cut off into an improper fraction: Cut length $=3\frac{3}{4}\text{ m}=\frac{15}{4}\text{ m}$.
3. Step 3: Subtract the cut length from the total length to find the remaining length: $\text{Remaining length}=\frac{25}{2}-\frac{15}{4}=\frac{50-15}{4}=\frac{35}{4}\text{ m}$.
4. Step 4: Divide the remaining length by $5$ to find each friend's share: $\text{Share of each friend}=\frac{35}{4}÷5=\frac{35}{4}\times \frac{1}{5}=\frac{7}{4}\text{ m}$.
5. Step 5: Convert the improper fraction $\frac{7}{4}$ back into a mixed fraction: $\frac{7}{4}\text{ m}=1\frac{3}{4}\text{ m}$.

Concept tested: Operations on Rational Numbers in Word Problems

Published 20 August 2026 · How this solution was prepared and checked

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