To solve this problem, let's start by simplifying the given expression. We have \(18 \div \frac{4}{5}\). The division of any number by a fraction is equivalent to multiplying the number by the reciprocal of the fraction. So we can rewrite the expression as \(18 \times \frac{5}{4}\).
Now let's go through each option provided and verify which one is equivalent to our simplified expression:
a. \(18 \times \frac{4}{5}\) - This is not equivalent to our simplified expression because the numerator and denominator are switched compared to our expression.
b. \(\frac{1}{18} \times \frac{4}{5}\) - This is not equivalent to our expression. The numerator and denominator are different from our expression.
C. \(\frac{18}{18} \times \frac{5}{4}\) - This is equivalent to \(1 \times \frac{5}{4}\), which simplifies to \(\frac{5}{4}\). It is not equal to our expression.
d. \(18 \times \frac{5}{4}\) - This is our simplified expression and is equivalent to our original expression \(18 \div \frac{4}{5}\).
Therefore, the correct option is d. \(18 \times \frac{5}{4}\).
Double-checking our work:
We can verify this by evaluating both expressions. \(18 \div \frac{4}{5}\) is equal to multiplying 18 by the reciprocal of \(\frac{4}{5}\), which gives us \(18 \times \frac{5}{4}\), resulting in the correct answer.
In conclusion, the correct option is d. \(18 \times \frac{5}{4}\).
we get the exact same values when doing the evaluation at these two points.
Based on those results, one may think the expressions may be equivalent, but they are not equivalent. Because at any other x-value, their results are different. See for example that for x = 0 the first one gives "2" while the second one gives -18.
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