To determine the amount of time it will take Sal to finish his remaining homework, we start by analyzing the information given:
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Sal has completed \( \frac{5}{9} \) of the math problems assigned to him. This means he has \( 1 - \frac{5}{9} = \frac{4}{9} \) of the problems left to solve.
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Each math problem takes \( \frac{3}{5} \) of a minute to complete.
Next, let's denote the total number of math problems assigned as \( N \). The number of problems Sal has left to complete is given by:
\[ \text{Problems left} = N \times \frac{4}{9} \]
Now, to find the time it takes to finish these remaining problems, we multiply the number of remaining problems by the time taken for each problem:
\[ \text{Time} = \left(N \times \frac{4}{9}\right) \times \frac{3}{5} \]
If we express this in a form that allows us to find \( N \) more easily, we can multiply through:
\[ \text{Time} = N \times \left(\frac{4}{9} \times \frac{3}{5}\right) \]
The multiplication of the fractions gives us:
\[ \frac{4 \times 3}{9 \times 5} = \frac{12}{45} = \frac{4}{15} \]
Thus:
\[ \text{Time} = N \cdot \frac{4}{15} \]
However, we need to rewrite this in terms that utilize one of the expressions given in the options. Observe that if \( N = 45 \), the expression simplifies directly to the time it takes to finish the remaining work:
\[ \text{Time} = 45 \cdot \frac{4}{15} \]
Since \( \frac{4}{15} \) is not among the choices, we can directly replace \( N \) with \( 45 \), recognizing how it relates to the fractions provided in the answer options.
Hence, to express this time in a way that matches the answer choices, we might note:
To calculate based on the options, we notice:
- We can rewrite \( N \) in terms of the fraction of problems and how we are dividing or multiplying.
- The choice for which expression calculates Sal's remaining time correctly would utilize the remaining \( \frac{4}{9} \) problems and the time per problem of \( \frac{3}{5} \).
The correct expression that verifies the remaining homework time based on the number of problems left and how long each takes, then check which matches the output combination:
The correct choice based on the options provided would be:
\( 45 \times \frac{4}{9} \times \frac{3}{5} \) can thus be interpreted as \( 45 \times \frac{4}{9} \) multiplied by \( \frac{3}{5} \) leading to
Thus correlating and giving rise to the multiple outputs, points toward:
The acceptable and effective answer based on structural analysis of the options is:
\(\boxed{45 \times \frac{4}{9} \times \frac{3}{5}}\), meaning the expression indeed simplifies toward timing for his homework through systematized output measures while rescaling divides through fraction works.
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