Question

1. which rectangle has the greater area, a rectangle with length \\(\frac{1}{12}\\) foot and width \\(\frac{3}{4}\\) foot or a rectangle with length \\(\frac{1}{16}\\) foot and width \\(\frac{4}{5}\\) foot?

Explanation:

Step1: Calculate Area of 1st Rectangle

Multiply length and width:
$\text{Area}_1 = \frac{1}{12} \times \frac{3}{4} = \frac{1 \times 3}{12 \times 4} = \frac{3}{48} = \frac{1}{16}$ square feet

Step2: Calculate Area of 2nd Rectangle

Multiply length and width:
$\text{Area}_2 = \frac{1}{16} \times \frac{4}{5} = \frac{1 \times 4}{16 \times 5} = \frac{4}{80} = \frac{1}{20}$ square feet

Step3: Compare the Two Areas

Convert to decimals for clarity:
$\frac{1}{16} = 0.0625$, $\frac{1}{20} = 0.05$
Since $0.0625 > 0.05$, $\frac{1}{16} > \frac{1}{20}$

Answer:

The rectangle with length $\frac{1}{12}$ foot and width $\frac{3}{4}$ foot has the greater area.