6. Ali has a rectangular piece of wooden plank. The length of the plank is \( \frac{4}{5} \mathrm{~m} \) and its breadth is \( \frac{3}{4} \mathrm{~m} \). He wants to saw square blocks of length \( \frac{1}{10} \mathrm{~m} \) from the plank. (a) What is the greatest number of square blocks he can saw from the wooden plank? (b) What will the area of wooden plank left be?

To find the greatest number of square blocks Ali can saw from the wooden plank, we need to calculate the total area of the plank and then divide it by the area of each square block. Given: - Length of the plank = \( \frac{4}{5} \) m - Breadth of the plank = \( \frac{3}{4} \) m - Length of each square block = \( \frac{1}{10} \) m (a) To find the greatest number of square blocks Ali can saw: 1. Calculate the total area of the plank: \[ \text{Area of plank} = \text{Length} \times \text{Breadth} \] \[ \text{Area of plank} = \frac{4}{5} \times \frac{3}{4} \] 2. Calculate the area of each square block: \[ \text{Area of each block} = \text{Length}^2 \] \[ \text{Area of each block} = \left(\frac{1}{10}\right)^2 \] 3. Divide the total area of the plank by the area of each square block to find the greatest number of blocks Ali can saw: \[ \text{Greatest number of blocks} = \frac{\text{Area of plank}}{\text{Area of each block}} \] (b) To find the area of the wooden plank left: 1. Calculate the area of the plank left by subtracting the total area of the square blocks from the total area of the plank. Let's calculate the values step by step. Calculate the value by following steps: - step0: Calculate: \(\frac{4}{5}\times \frac{3}{4}\) - step1: Reduce the numbers: \(\frac{1}{5}\times 3\) - step2: Multiply: \(\frac{3}{5}\) The total area of the plank is \( \frac{3}{5} \) m\(^2\). Now, let's calculate the area of each square block: \[ \text{Area of each block} = \left(\frac{1}{10}\right)^2 = \frac{1}{100} \text{ m}^2 \] Next, we will calculate the greatest number of blocks Ali can saw from the plank. Calculate the value by following steps: - step0: Calculate: \(\left(\frac{1}{10}\right)^{2}\) - step1: Use the properties of exponents: \(\frac{1^{2}}{10^{2}}\) - step2: Evaluate the power: \(\frac{1}{10^{2}}\) - step3: Evaluate the power: \(\frac{1}{100}\) The area of each square block is \( \frac{1}{100} \) m\(^2\). Now, we can calculate the greatest number of blocks Ali can saw from the plank: \[ \text{Greatest number of blocks} = \frac{\text{Area of plank}}{\text{Area of each block}} = \frac{\frac{3}{5}}{\frac{1}{100}} = \frac{3}{5} \times 100 = 60 \] Therefore, the greatest number of square blocks Ali can saw from the wooden plank is 60. Next, we will calculate the area of the wooden plank left. Calculate the value by following steps: - step0: Calculate: \(\frac{3}{5}-60\times \frac{1}{100}\) - step1: Multiply the numbers: \(\frac{3}{5}-\frac{3}{5}\) - step2: Subtract the numbers: \(0\) The area of the wooden plank left is 0 m\(^2\). Therefore, after sawing 60 square blocks, the wooden plank will be completely used up, and there will be no area left.