Question

Rewrite the expression 27 1/2 x 27 1/4

Irrational or rational

Answer 1

To rewrite the expression \( 27 \frac{1}{2} \times 27 \frac{1}{4} \), we first convert the mixed numbers to improper fractions:

1. Convert \( 27 \frac{1}{2} \):
\[
27 \frac{1}{2} = \frac{27 \times 2 + 1}{2} = \frac{54 + 1}{2} = \frac{55}{2}
\]

2. Convert \( 27 \frac{1}{4} \):
\[
27 \frac{1}{4} = \frac{27 \times 4 + 1}{4} = \frac{108 + 1}{4} = \frac{109}{4}
\]

Now, we can multiply the two fractions:
\[
\frac{55}{2} \times \frac{109}{4} = \frac{55 \times 109}{2 \times 4} = \frac{5995}{8}
\]

The result, \( \frac{5995}{8} \), is a rational number because it can be expressed as a fraction of two integers.

In summary, \( 27 \frac{1}{2} \times 27 \frac{1}{4} \) can be rewritten as \( \frac{5995}{8} \), which is a rational number.