Question

rewrite the following expressions 27 1/2 • 27 1/4. answers: 27 1/6, 27 3/4, 4 on the top of the square root and 27 under it, or 3 on tile of the square root and 27 under it

Answer 1

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

1. **Convert to Improper Fractions:**
- \(27 \frac{1}{2} = \frac{55}{2}\)
- \(27 \frac{1}{4} = \frac{109}{4}\)

2. **Multiply the Two Improper Fractions:**
\[
\frac{55}{2} \times \frac{109}{4} = \frac{55 \times 109}{2 \times 4}
\]
(Calculating \( 55 \times 109 \) gives \( 5995 \), and \( 2 \times 4 = 8 \)):
\[
\frac{5995}{8}
\]

3. **Convert to Mixed Number:**
To convert \( \frac{5995}{8} \) into a mixed number:
\[
5995 \div 8 = 749 \quad \text{remainder } 3
\]
Therefore:
\[
\frac{5995}{8} = 749 \frac{3}{8}
\]

Now for the expressions given in the prompt:

- **27 1/6:** This is not equivalent to \( 27 \frac{1}{2} \times 27 \frac{1}{4} \).

- **27 3/4:** This is also not equivalent to the product.

- **Square Root Forms:**
- \( \sqrt{27} = 3\sqrt{3} \) or can also be expressed with \( 27 \) under it in some context to simplify or solve \( \sqrt{27} \).
- If you're trying to express \( \sqrt{27} \), it doesn’t correlate directly with \( 27 \frac{1}{2} \times 27 \frac{1}{4} \).

In conclusion, none of the suggested answers seem correct based on the calculation we've done. The correct product of \( 27 \frac{1}{2} \) and \( 27 \frac{1}{4} \) is \( 749 \frac{3}{8} \).