To determine which two of the given fractions multiply together to yield [tex]\(\frac{9}{28}\)[/tex], we can manually check each pair through multiplication until we find a match or determine there isn't one. Here are the step-by-step checks:
Given fractions:
[tex]\[
\frac{1}{4}, \frac{6}{23}, \frac{2}{7}, \frac{3}{5}, \frac{9}{8}
\][/tex]
Target fraction:
[tex]\[
\frac{9}{28}
\][/tex]
Now, let's multiply each possible pair of fractions and see if any of them equal [tex]\(\frac{9}{28}\)[/tex].
### 1. Multiply [tex]\(\frac{1}{4}\)[/tex] with each other fraction:
[tex]\[
\frac{1}{4} \times \frac{6}{23} = \frac{1 \times 6}{4 \times 23} = \frac{6}{92} = \frac{3}{46}
\][/tex]
[tex]\[
\frac{1}{4} \times \frac{2}{7} = \frac{1 \times 2}{4 \times 7} = \frac{2}{28} = \frac{1}{14}
\][/tex]
[tex]\[
\frac{1}{4} \times \frac{3}{5} = \frac{1 \times 3}{4 \times 5} = \frac{3}{20}
\][/tex]
[tex]\[
\frac{1}{4} \times \frac{9}{8} = \frac{1 \times 9}{4 \times 8} = \frac{9}{32}
\][/tex]
None of these results match [tex]\(\frac{9}{28}\)[/tex].
### 2. Multiply [tex]\(\frac{6}{23}\)[/tex] with each remaining fraction:
[tex]\[
\frac{6}{23} \times \frac{2}{7} = \frac{6 \times 2}{23 \times 7} = \frac{12}{161}
\][/tex]
[tex]\[
\frac{6}{23} \times \frac{3}{5} = \frac{6 \times 3}{23 \times 5} = \frac{18}{115}
\][/tex]
[tex]\[
\frac{6}{23} \times \frac{9}{8} = \frac{6 \times 9}{23 \times 8} = \frac{54}{184} = \frac{27}{92}
\][/tex]
None of these results match [tex]\(\frac{9}{28}\)[/tex].
### 3. Multiply [tex]\(\frac{2}{7}\)[/tex] with each remaining fraction:
[tex]\[
\frac{2}{7} \times \frac{3}{5} = \frac{2 \times 3}{7 \times 5} = \frac{6}{35}
\][/tex]
[tex]\[
\frac{2}{7} \times \frac{9}{8} = \frac{2 \times 9}{7 \times 8} = \frac{18}{56} = \frac{9}{28}
\][/tex]
Here, we find:
[tex]\[
\frac{2}{7} \times \frac{9}{8} = \frac{9}{28}
\][/tex]
Thus, the two fractions that multiply together to give [tex]\(\frac{9}{28}\)[/tex] are [tex]\(\boxed{\frac{2}{7} \text{ and } \frac{9}{8}}\)[/tex].
