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?
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To find the greatest number of square blocks that Ali can saw from the wooden plank, we first need to calculate the area of the plank and the area of each block. The area of the rectangular plank is given by: \[ \text{Area of the plank} = \text{Length} \times \text{Breadth} = \frac{4}{5} \, \text{m} \times \frac{3}{4} \, \text{m} = \frac{12}{20} \, \text{m}^2 = \frac{3}{5} \, \text{m}^2. \] The area of each square block is: \[ \text{Area of each block} = \text{Side} \times \text{Side} = \frac{1}{10} \, \text{m} \times \frac{1}{10} \, \text{m} = \frac{1}{100} \, \text{m}^2. \] Now, we can find the greatest number of such blocks that Ali can saw from the plank: \[ \text{Number of blocks} = \frac{\text{Area of the plank}}{\text{Area of each block}} = \frac{\frac{3}{5} \, \text{m}^2}{\frac{1}{100} \, \text{m}^2} = \frac{3}{5} \times 100 = 60. \] So the greatest number of square blocks he can saw from the wooden plank is **60**. Now, to find the area of the wooden plank left, we first calculate the total area used for the blocks: \[ \text{Area used for blocks} = \text{Number of blocks} \times \text{Area of each block} = 60 \times \frac{1}{100} \, \text{m}^2 = \frac{60}{100} \, \text{m}^2 = \frac{3}{5} \, \text{m}^2. \] So the area left will be: \[ \text{Area left} = \text{Area of the plank} - \text{Area used for blocks} = \frac{3}{5} \, \text{m}^2 - \frac{3}{5} \, \text{m}^2 = 0 \, \text{m}^2. \] Thus, the area of the wooden plank left is **0 m²** after cutting all the blocks! Ali made the most of his plank!
