Question

Which products are greater than 2 5/6
?

(1 point)
Responses

18×2 5/6


6/5× 2 5/6


5/6×2 5/6



2 5/6×2/3

Answer 1

To determine which products are greater than \(2 \frac{5}{6}\), we first need to convert \(2 \frac{5}{6}\) into an improper fraction:

\[
2 \frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6}
\]

Now we will evaluate each product:

1. **For \(18 \times 2 \frac{5}{6}\):**
\[
18 \times 2 \frac{5}{6} = 18 \times \frac{17}{6} = \frac{18 \times 17}{6} = \frac{306}{6} = 51
\]
\(51 > 2 \frac{5}{6}\) (True)

2. **For \(\frac{6}{5} \times 2 \frac{5}{6}\):**
\[
\frac{6}{5} \times 2 \frac{5}{6} = \frac{6}{5} \times \frac{17}{6} = \frac{6 \times 17}{5 \times 6} = \frac{17}{5}
\]
Now convert \(\frac{17}{5}\) to a mixed number:
\[
\frac{17}{5} = 3 \frac{2}{5}
\]
\(3 \frac{2}{5} > 2 \frac{5}{6}\) (True)

3. **For \(\frac{5}{6} \times 2 \frac{5}{6}\):**
\[
\frac{5}{6} \times 2 \frac{5}{6} = \frac{5}{6} \times \frac{17}{6} = \frac{5 \times 17}{6 \times 6} = \frac{85}{36}
\]
To compare \(\frac{85}{36}\) with \(\frac{17}{6}\), let's convert \(\frac{17}{6}\) to have a common denominator:
\[
\frac{17}{6} = \frac{17 \times 6}{6 \times 6} = \frac{102}{36}
\]
Since \(85 < 102\), \(\frac{85}{36} < \frac{17}{6}\) (False)

4. **For \(2 \frac{5}{6} \times \frac{2}{3}\):**
\[
2 \frac{5}{6} \times \frac{2}{3} = \frac{17}{6} \times \frac{2}{3} = \frac{17 \times 2}{6 \times 3} = \frac{34}{18}
\]
Simplifying \(\frac{34}{18}\):
\[
\frac{34}{18} = \frac{17}{9}
\]
Convert \(\frac{17}{9}\) to a mixed number:
\[
\frac{17}{9} = 1 \frac{8}{9}
\]
Since \(1 \frac{8}{9} < 2 \frac{5}{6}\) (False)

**Final Results:**
- \(18 \times 2 \frac{5}{6}\): Yes
- \(\frac{6}{5} \times 2 \frac{5}{6}\): Yes
- \(\frac{5}{6} \times 2 \frac{5}{6}\): No
- \(2 \frac{5}{6} \times \frac{2}{3}\): No

Thus, the products that are greater than \(2 \frac{5}{6}\) are:
- \(18 \times 2 \frac{5}{6}\)
- \(\frac{6}{5} \times 2 \frac{5}{6}\)