15. \( \frac{40 \mathrm{~kg}}{1 \mathrm{~m}}=\frac{x \mathrm{~g}}{1 \mathrm{~cm}} \)

Given the equation \[ \frac{40\,\mathrm{kg}}{1\,\mathrm{m}}=\frac{x\,\mathrm{g}}{1\,\mathrm{cm}}, \] we need to find \( x \). --- **Step 1: Convert kilograms to grams** Recall that \[ 1\,\text{kg} = 1000\,\text{g}. \] Thus, \[ 40\,\text{kg} = 40 \times 1000\,\text{g} = 40000\,\text{g}. \] --- **Step 2: Convert meters to centimeters** Recall that \[ 1\,\text{m} = 100\,\text{cm}. \] Thus, \[ 1\,\text{m} = 100\,\text{cm}. \] --- **Step 3: Substitute the converted values into the equation** Substituting, we have \[ \frac{40000\,\mathrm{g}}{100\,\mathrm{cm}}=\frac{x\,\mathrm{g}}{1\,\mathrm{cm}}. \] --- **Step 4: Simplify the left side** Dividing \( 40000\,\text{g} \) by \( 100\,\text{cm} \) gives \[ \frac{40000}{100} = 400. \] Thus, the equation becomes \[ \frac{400\,\mathrm{g}}{1\,\mathrm{cm}}=\frac{x\,\mathrm{g}}{1\,\mathrm{cm}}. \] --- **Step 5: Solve for \( x \)** Since the denominators are the same, the numerators must be equal: \[ x = 400. \] --- **Final Answer:** \[ x = 400\,\mathrm{g}. \]