Insert `ltorgt` in the box.
`22/(44)square13/(23)`

Answer

To solve the problem of comparing the fractions \( \frac{22}{44} \) and \( \frac{13}{23} \), we will follow these steps:

### Step 1: Simplify \( \frac{22}{44} \)
First, we simplify the fraction \( \frac{22}{44} \).

\[ \frac{22}{44} = \frac{22 \div 22}{44 \div 22} = \frac{1}{2} \]

### Step 2: Write the fractions to compare
Now we have two fractions to compare:
- \( \frac{1}{2} \) (which is the simplified form of \( \frac{22}{44} \))
- \( \frac{13}{23} \)

### Step 3: Find a common denominator
To compare \( \frac{1}{2} \) and \( \frac{13}{23} \), we need a common denominator. The denominators are 2 and 23. The least common multiple (LCM) of 2 and 23 is:

\[ \text{LCM}(2, 23) = 2 \times 23 = 46 \]

### Step 4: Convert both fractions to have the common denominator
Now we convert both fractions to have the denominator of 46.

For \( \frac{1}{2} \):
\[ \frac{1}{2} = \frac{1 \times 23}{2 \times 23} = \frac{23}{46} \]

For \( \frac{13}{23} \):
\[ \frac{13}{23} = \frac{13 \times 2}{23 \times 2} = \frac{26}{46} \]

### Step 5: Compare the numerators
Now we compare the two fractions:
- \( \frac{23}{46} \)
- \( \frac{26}{46} \)

Since \( 26 > 23 \), we can conclude that:
\[ \frac{26}{46} > \frac{23}{46} \]

### Step 6: Write the final comparison
Thus, we can write:
\[ \frac{13}{23} > \frac{1}{2} \quad \text{or} \quad \frac{13}{23} > \frac{22}{44} \]

### Final Answer
In the box, we will insert the symbol:
\[ \frac{22}{44} < \frac{13}{23} \]

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