APPROACH #1: Use the on-screen calculator

APPROACH #2: Apply a useful property of fractions

Let's first convert $\frac{3}{4}$ to $0.75$, its decimal equivalent, to get: $\frac{0.025 \times 7.5 \times 48}{5 \times 0.0024 \times 0.75}=$

Key property: $\frac{ABC}{DEF} = \frac{A}{D} \times \frac{B}{E} \times \frac{C}{F}$

Strategy: I'm going to use this property to split the original fraction into the product of 3 individual fractions.
There are a few different ways I can split up the fraction. For example, I could pair up 0.025 and 5 to get 0.025/5, but that seems like a pain to calculate.
Similarity, I could pair up 48 and 0.0024 to get 48/0.0024, but that also seems like a pain.
Instead, I'm going to use the fact that the answer choices are extremely spread apart in order to pair up values that I can easily approximate.

So, we get: $\frac{0.025}{0.0024} \times \frac{7.5}{0.75} \times \frac{48}{5}$

Let's evaluate (or approximate) each fraction individually.

$\frac{0.025}{0.0024} ≈ \frac{0.025}{0.0025} ≈ \frac{(1000)(0.025)}{(1000)(0.0025)} ≈ \frac{250}{25} ≈ 10$ [multiplying numerator and denominator by 1000 resulted in a fraction with integer values only, which made it easier to calculate]

$\frac{7.5}{0.75} = \frac{(100)(7.5)}{(100)(0.75)} = \frac{750}{75} = 10$

$\frac{48}{5} ≈ \frac{50}{5} ≈ 10$

Substitute values to get: $\frac{0.025}{0.0024} \times \frac{7.5}{0.75} \times \frac{48}{5} ≈ 10 \times 10 \times 10 ≈ 1000$

Answer: E