To rewrite the expression "27 and a half times 27 and 1/4" in mathematical form, we first convert the mixed numbers to improper fractions.
-
Convert "27 and a half" to an improper fraction: \[ 27 \frac{1}{2} = 27 + \frac{1}{2} = \frac{54}{2} + \frac{1}{2} = \frac{55}{2} \]
-
Convert "27 and 1/4" to an improper fraction: \[ 27 \frac{1}{4} = 27 + \frac{1}{4} = \frac{108}{4} + \frac{1}{4} = \frac{109}{4} \]
Now, we can express the product of these two mixed numbers: \[ \left(27 \frac{1}{2}\right) \times \left(27 \frac{1}{4}\right) = \frac{55}{2} \times \frac{109}{4} \]
To further simplify, we multiply the fractions: \[ \frac{55 \times 109}{2 \times 4} = \frac{5995}{8} \]
Thus, the expression "27 and a half times 27 and 1/4" can be rewritten as: \[ \frac{5995}{8} \]
Alternatively, if you want the result as a mixed number, you can convert it back: \[ \frac{5995}{8} = 749 \frac{3}{8} \]
So, the final answers are:
- As an improper fraction: \(\frac{5995}{8}\)
- As a mixed number: \(749 \frac{3}{8}\)
5 answers