Let's analyze Macy's work step by step to determine which statement is true.
Macy is comparing the ratios 4:5 and 19:30. To do this, we convert the ratios to fractions:
- The ratio 4:5 can be written as the fraction \( \frac{4}{5} \).
- The ratio 19:30 can be written as the fraction \( \frac{19}{30} \).
Next, let's compare these two fractions. To do this, we can find a common denominator. The common denominator for 5 and 30 is 30.
Now, we convert \( \frac{4}{5} \) to have a denominator of 30:
\[ \frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30} \]
Now we have:
- \( \frac{4}{5} = \frac{24}{30} \)
- \( \frac{19}{30} \)
Next, we compare \( \frac{24}{30} \) and \( \frac{19}{30} \):
\[ \frac{24}{30} \text{ compared to } \frac{19}{30} \]
Since the denominators are the same, we can compare the numerators directly:
24 is greater than 19.
Thus,
\[ \frac{24}{30} > \frac{19}{30} \]
Now, let's evaluate the original statements about Macy's work:
-
Macy did not correctly write the ratios as fractions. - This is not true, as she did write the ratios as fractions correctly (as \( \frac{4}{5} \) and \( \frac{19}{30} \)).
-
Macy did not find a common denominator for the fractions. - This is not true either; she found a common denominator of 30.
-
Macy did not find the correct equivalent fraction with the denominator of 30. - This is true, as she incorrectly stated that \( \frac{4}{5} \) is \( \frac{18}{30} \) instead of \( \frac{24}{30} \).
-
Macy did not correctly compare the numerators. - This is true as well; because her final comparison was incorrect based on her incorrect equivalent fraction.
Given the analysis, the most accurate statement regarding Macy's work is:
Macy did not find the correct equivalent fraction with the denominator of 30.