To determine which symbol (either '<' or '>') should be placed between the fractions [tex]\(\frac{4}{9}\)[/tex] and [tex]\(\frac{3}{7}\)[/tex], we need to compare the two fractions. Here’s a step-by-step comparison strategy:
1. Identify the fractions:
- First fraction: [tex]\(\frac{4}{9}\)[/tex]
- Second fraction: [tex]\(\frac{3}{7}\)[/tex]
2. Compare the fractions:
- Fractions can be compared by considering their values or by cross-multiplication.
3. Considering their values (we do not show intermediate steps here but this is how it should be done for visualization purposes):
- Calculate the decimal values of [tex]\(\frac{4}{9}\)[/tex] and [tex]\(\frac{3}{7}\)[/tex].
4. Compare the results:
- If the first fraction ([tex]\(\frac{4}{9}\)[/tex]) is less than the second fraction ([tex]\(\frac{3}{7}\)[/tex]), we use the symbol '<'.
- If the first fraction ([tex]\(\frac{4}{9}\)[/tex]) is greater than the second fraction ([tex]\(\frac{3}{7}\)[/tex]), we use the symbol '>'.
Given the comparison:
[tex]\[
\frac{4}{9} > \frac{3}{7}
\][/tex]
Hence, the correct symbol to place between [tex]\(\frac{4}{9}\)[/tex] and [tex]\(\frac{3}{7}\)[/tex] is [tex]\(>\)[/tex]. So, it would be:
[tex]\[
\frac{4}{9} > \frac{3}{7}
\][/tex]
