How many bricks, each measuring 25 cm × 11.25 cm × 6 cm, will be needed to build a wall 8 m × 6 m × 22.5 cm?

### Concept & Volume Division for Object Counts To find the number of standard units (bricks) needed to form a larger volume (wall), simply divide the total volume by the unit volume, provided all dimensions are in the same measurement unit. $$ Number = \frac{Total Volume}{Volume of One Unit} $$ ### Step-by-Step Solution 1. **Standardize the Units**: - Convert all wall dimensions from meters to centimeters to match the brick dimensions. - Wall Length = $8 \text{ m} = 800 \text{ cm}$ - Wall Height = $6 \text{ m} = 600 \text{ cm}$ - Wall Thickness = 22.5 cm 2. **Set Up the Ratio**: - Number of bricks = $\frac{800 \times 600 \times 22.5}{25 \times 11.25 \times 6}$ 3. **Simplify and Cancel**: - Notice that $22.5$ is exactly double $11.25$. So, $\frac{22.5}{11.25} = 2$. - The expression becomes: $\frac{800 \times 600 \times 2}{25 \times 6}$ - Cancel the 6 from 600: $\frac{800 \times 100 \times 2}{25}$ - Cancel 25 from 100: $800 \times 4 \times 2$ 4. **Final Calculation**: - Number of bricks = $800 \times 8 = 6400$ ### Exam Strategy & Shortcut Never multiply all dimensions to find total volumes before dividing. Instead, write them out as a single large fraction and cancel common factors directly. Spotting relationships like $22.5 = 2 \times 11.25$ instantly cuts the calculation time in half. ### Common Pitfall A classic error is failing to convert the 8 m and 6 m dimensions into centimeters, leading to an answer that is orders of magnitude too small. ### Final Answer Therefore, the correct answer is **6400**.