Question

1\frac{2}{4} and 2\frac{4}{9}

Explanation:

Assuming the problem is to compare or perform an operation (like addition, subtraction) with the mixed numbers \(1\frac{2}{4}\) and \(2\frac{4}{9}\). First, simplify the fractions.

Step 1: Simplify \(1\frac{2}{4}\)

Simplify the fractional part \(\frac{2}{4}=\frac{1}{2}\), so \(1\frac{2}{4} = 1\frac{1}{2}=\frac{3}{2}\) (or as a mixed number, it's simplified to \(1\frac{1}{2}\)).

Step 2: Analyze \(2\frac{4}{9}\)

The fractional part \(\frac{4}{9}\) is already in simplest form since 4 and 9 have no common factors other than 1.

If we were to add them:
First, convert to improper fractions.
\(1\frac{1}{2}=\frac{2\times1 + 1}{2}=\frac{3}{2}\)
\(2\frac{4}{9}=\frac{9\times2+4}{9}=\frac{22}{9}\)
Find a common denominator, which is \(2\times9 = 18\).
\(\frac{3}{2}=\frac{3\times9}{2\times9}=\frac{27}{18}\)
\(\frac{22}{9}=\frac{22\times2}{9\times2}=\frac{44}{18}\)
Add them: \(\frac{27}{18}+\frac{44}{18}=\frac{27 + 44}{18}=\frac{71}{18}=3\frac{17}{18}\)

If we were to subtract them (assuming \(2\frac{4}{9}-1\frac{1}{2}\)):
\(\frac{22}{9}-\frac{3}{2}=\frac{44 - 27}{18}=\frac{17}{18}\)

Since the problem isn't fully specified (what to do with the two mixed numbers), but if we assume simplifying or comparing:

\(1\frac{2}{4}=1\frac{1}{2}\), \(2\frac{4}{9}\) is as is. Comparing, \(1\frac{1}{2}=1.5\) and \(2\frac{4}{9}\approx2.44\), so \(1\frac{1}{2}<2\frac{4}{9}\)

Answer:

If simplifying \(1\frac{2}{4}\), it becomes \(1\frac{1}{2}\) (or \(\frac{3}{2}\)). If adding, the result is \(3\frac{17}{18}\); if subtracting (\(2\frac{4}{9}-1\frac{1}{2}\)), the result is \(\frac{17}{18}\). (Depends on the operation, but the most basic simplification of \(1\frac{2}{4}\) is \(1\frac{1}{2}\))