Which scenario matches the given expression?

Question

-3/5 / -2/5
 A.
On the first day of mining a metal, a miner goes  of a kilometer below ground level. On the second day, he goes  of a kilometer below ground level. How many times further below ground level does the miner go on the second day than on the first day?
 B.
Rick spent  of an hour studying. Later, he spent  of an hour watching television. How much more time did Rick spend studying than watching television?
 C.
A builder uses  of an acre of land for constructing a building. He uses  of an acre of land for a garden. How much more of an acre does he use for the building than the garden?
 D.
A tuna swims  of a meter below sea level. A sardine swims  of a meter below sea level. How many times more below sea level does the sardine swim than the tuna?

Answer 1

To solve this problem, we first need to interpret the expression \(-\frac{3}{5} / -\frac{2}{5}\).

When we divide two negative fractions, the negatives cancel out, resulting in a positive value. The division of the fractions can be rewritten as:

\[ -\frac{3}{5} / -\frac{2}{5} = \frac{3/5}{2/5} = \frac{3}{5} \times \frac{5}{2} = \frac{3 \times 5}{5 \times 2} = \frac{3}{2} = 1.5 \]

This means the expression essentially finds how many times \(-\frac{2}{5}\) fits into \(-\frac{3}{5}\) or how much larger \(-\frac{3}{5}\) is compared to \(-\frac{2}{5}\) when both are considered as negative values.

Now let's analyze the options given:

• A: Talks about a miner going below ground level, measuring distance below ground. This doesn't align with the division of how many times further below ground one day compared to another, as the focus is on distances, not multiples.

• B: Discusses time spent studying versus watching television. This simply measures the difference in time, not how much more one time spent compared to another.

• C: Compares land used for a building versus a garden, again talking about difference, not comparison between two amounts.

• D: This option compares how much deeper (in meters) the sardine swims compared to the tuna. Since both are below sea level and the question asks how many times further one is compared to the other, this fits the scenario of comparing the magnitudes of two negative values, making it a suitable match for our expression.

Thus, the scenario that matches the expression \(-\frac{3}{5} / -\frac{2}{5}\) is:

D: A tuna swims \(-\frac{3}{5}\) of a meter below sea level. A sardine swims \(-\frac{2}{5}\) of a meter below sea level. How many times more below sea level does the sardine swim than the tuna?