Sure! Let's break down the question into the two main tasks and solve each step-by-step.
### Part 1: Cost of 4.75 Meters of Cloth
The cost per meter of cloth is given as 275.80. We need to find the cost of 4.75 meters of this cloth.
To find the total cost, multiply the cost per meter by the number of meters needed:
[tex]\[ \text{Total Cost} = \text{Cost per meter} \times \text{Meters needed} \][/tex]
[tex]\[ \text{Total Cost} = 275.80 \, \text{(Cost per meter)} \times 4.75 \, \text{(Meters needed)} \][/tex]
[tex]\[ \text{Total Cost} = 1310.05 \][/tex]
So, the cost of 4.75 meters of cloth is 1310.05.
### Part 2: Fraction Division
#### (i) [tex]\( \frac{4}{9} \div \frac{2}{3} \)[/tex]
To divide fractions, we multiply by the reciprocal of the fraction we are dividing by:
[tex]\[ \frac{4}{9} \div \frac{2}{3} = \frac{4}{9} \times \frac{3}{2} \][/tex]
Now, perform the multiplication:
[tex]\[ \frac{4}{9} \times \frac{3}{2} = \frac{4 \times 3}{9 \times 2} = \frac{12}{18} \][/tex]
To simplify [tex]\( \frac{12}{18} \)[/tex]:
[tex]\[ \frac{12}{18} = \frac{2}{3} = 0.6666666666666666 \][/tex]
Thus, [tex]\( \frac{4}{9} \div \frac{2}{3} = \frac{2}{3} \)[/tex] or 0.6666666666666666.
#### (ii) [tex]\( \frac{2}{3} \div \frac{10}{9} \)[/tex]
Similarly, for this division:
[tex]\[ \frac{2}{3} \div \frac{10}{9} = \frac{2}{3} \times \frac{9}{10} \][/tex]
Now, perform the multiplication:
[tex]\[ \frac{2}{3} \times \frac{9}{10} = \frac{2 \times 9}{3 \times 10} = \frac{18}{30} \][/tex]
To simplify [tex]\( \frac{18}{30} \)[/tex]:
[tex]\[ \frac{18}{30} = \frac{3}{5} = 0.6 \][/tex]
Thus, [tex]\( \frac{2}{3} \div \frac{10}{9} = \frac{3}{5} \)[/tex] or 0.6.
### Summary of Answers
1. The cost of 4.75 meters of cloth is 1310.05.
2. [tex]\( \frac{4}{9} \div \frac{2}{3} = 0.6666666666666666 \)[/tex] or [tex]\( \frac{2}{3} \)[/tex]
3. [tex]\( \frac{2}{3} \div \frac{10}{9} = 0.6 \)[/tex] or [tex]\( \frac{3}{5} \)[/tex]
These are the step-by-step solutions to the given problems.
