1. **State the problem:** A shop had 40 newspapers and sold \(\frac{3}{8}\) of them. We need to find how many newspapers were sold.\n\n2. **Formula used:** To find the part of a total quantity sold, multiply the total by the fraction sold: \n\n$$ \text{Number sold} = \text{Total newspapers} \times \text{Fraction sold} $$\n\n3. **Apply the values:** \n\n$$ \text{Number sold} = 40 \times \frac{3}{8} $$\n\n4. **Simplify the multiplication:** \n\n$$ 40 \times \frac{3}{8} = \frac{40 \times 3}{8} = \frac{120}{8} $$\n\n5. **Divide numerator by denominator:** \n\n$$ \frac{120}{8} = 15 $$\n\n6. **Conclusion:** The shop sold 15 newspapers.