Question

Which is greater 7 1/2 or 15/4

Answer 1

To compare \( 7 \frac{1}{2} \) and \( \frac{15}{4} \), we first convert \( 7 \frac{1}{2} \) into an improper fraction.

1. **Convert \( 7 \frac{1}{2} \)**:
\[
7 \frac{1}{2} = 7 + \frac{1}{2} = \frac{14}{2} + \frac{1}{2} = \frac{15}{2}
\]

Now we have:
- \( 7 \frac{1}{2} = \frac{15}{2} \)
- \( \frac{15}{4} \)

2. **Convert both fractions to have a common denominator**:
The least common multiple of the denominators \(2\) and \(4\) is \(4\).

- Convert \( \frac{15}{2} \) to have a denominator of \(4\):
\[
\frac{15}{2} = \frac{15 \times 2}{2 \times 2} = \frac{30}{4}
\]

3. **Now compare \( \frac{30}{4} \) and \( \frac{15}{4} \)**:
Since they have the same denominator, we can directly compare the numerators:
\[
30 > 15
\]

Therefore, \( \frac{30}{4} > \frac{15}{4} \).

Thus, \( 7 \frac{1}{2} (which is \frac{15}{2}) \) is greater than \( \frac{15}{4} \).

So, we conclude:
\[
7 \frac{1}{2} > \frac{15}{4}
\]