Sure, let's break down the problem step-by-step:
1. Total length of the cloth:
Ahmed has purchased a piece of cloth that is 12 meters long.
2. Cloth used by Ahmed:
Ahmed uses [tex]\(\frac{3}{4}\)[/tex] of the total cloth. Therefore, the amount of cloth he uses is:
[tex]\[
\frac{3}{4} \times 12 \text{ meters} = 9 \text{ meters}
\][/tex]
3. Remaining cloth after usage:
After Ahmed has used 9 meters of the cloth, the remaining length of the cloth is:
[tex]\[
12 \text{ meters} - 9 \text{ meters} = 3 \text{ meters}
\][/tex]
4. Damaged portion of the remaining cloth:
Out of the remaining 3 meters, [tex]\(\frac{1}{9}\)[/tex] is damaged. Therefore, the amount of damaged cloth is:
[tex]\[
\frac{1}{9} \times 3 \text{ meters} = \frac{3}{9} \text{ meters} = 0.333... \text{ meters}
\][/tex]
5. Cloth left over after considering the damaged portion:
To find out how much usable cloth is left after considering the damaged portion, subtract the damaged length from the remaining cloth:
[tex]\[
3 \text{ meters} - 0.333... \text{ meters} = 2.667 \text{ meters}
\][/tex]
Therefore, after using [tex]\(\frac{3}{4}\)[/tex] of the cloth and considering the damaged portion of the remaining cloth, Ahmed will have approximately 2.667 meters of cloth left over.
