To solve the problem "180 is 40 percent of what number?", you want to set up an equation that represents this relationship.
Let \( x \) be the unknown number. The statement can be translated into the equation:
\[ 180 = 0.4 \times x \]
From this equation, you can find \( x \) by dividing both sides by 0.4:
\[ x = \frac{180}{0.4} \]
Now let's analyze the options you provided:
- \( \frac{40 \times 4.5}{100 \times 4.5} = \frac{180}{450} \)
- \( \frac{180 \times 0.4}{100 \times 0.4} = \frac{72}{40} \)
- \( \frac{40 \times 1}{180 \times 1} = \frac{40}{180} \)
- \( \frac{100 \times 4.5}{40 \times 4.5} = \frac{450}{180} \)
The first option simplifies to \( \frac{180}{450} \) but is not directly derived from the original question. The second option can be derived from rearranging the equation but doesn't represent the percentage right. The third option is not relevant as it doesn't address the entire equation. The fourth option is also not the correct representation.
None of these directly represent the original problem using the correct equation.
However, if rearranged and simplified appropriately, you could go from \( 180 = 0.4x \) to other forms, but the simplest expression is \( \frac{180}{0.4} \) to find \( x \).
In essence, none of these options directly translate to solving for \( x \) using the original percentage equation. The best approach to find \( x \) directly from the problem should be done as mentioned earlier:
\[ x = \frac{180}{0.4} \] or equivalently understood as \( 180 = 0.4 \times x \).
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