Which is greater in each of the following
`(2)/(3), (5)/(2)`

Answer

To determine which of the two rational numbers, \( \frac{2}{3} \) and \( \frac{5}{2} \), is greater, we can follow these steps:

### Step 1: Identify the two fractions
We have the two fractions:
- \( \frac{2}{3} \)
- \( \frac{5}{2} \)

### Step 2: Find a common denominator
To compare the two fractions, we need to express them with a common denominator. The denominators here are 3 and 2. The least common multiple (LCM) of 3 and 2 is 6.

### Step 3: Convert the fractions to have the same denominator
- To convert \( \frac{2}{3} \) to a fraction with a denominator of 6, we multiply both the numerator and the denominator by 2:
\[ \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \]

- To convert \( \frac{5}{2} \) to a fraction with a denominator of 6, we multiply both the numerator and the denominator by 3:
\[ \frac{5 \times 3}{2 \times 3} = \frac{15}{6} \]

### Step 4: Compare the numerators
Now that we have both fractions with the same denominator, we can compare the numerators:
- \( \frac{4}{6} \) and \( \frac{15}{6} \)

Since 15 is greater than 4, we can conclude:
\[ \frac{15}{6} > \frac{4}{6} \]

### Step 5: State the result
Thus, \( \frac{5}{2} \) is greater than \( \frac{2}{3} \).

### Final Answer:
\[ \frac{5}{2} > \frac{2}{3} \]

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