Question

Using computation, which of the following statements is true?(1 point)
Responses

529⋅78>529
5 Start Fraction 2 over 9 End Fraction times Start Fraction 7 over 8 End Fraction greater than 5 Start Fraction 2 over 9 End Fraction

412⋅54<412
4 Start Fraction 1 over 2 End Fraction times Start Fraction 5 over 4 End Fraction less than 4 Start Fraction 1 over 2 End Fraction

358⋅94>358
3 Start Fraction 5 over 8 End Fraction times Start Fraction 9 over 4 End Fraction greater than 3 Start Fraction 5 over 8 End Fraction

174⋅32<174

Answer 1

Let's analyze each statement by performing the calculations.

1. **Statement**: \(529 \cdot 78 > 529\)

- Compute \(529 \cdot 78\):
\[
529 \cdot 78 = 41262
\]
- Compare \(41262\) and \(529\):
\[
41262 > 529 \quad \text{(True)}
\]

2. **Statement**: \( \frac{5}{9} \cdot \frac{7}{8} > \frac{5}{9} \)

- Compute \( \frac{5}{9} \cdot \frac{7}{8} \):
\[
\frac{5 \times 7}{9 \times 8} = \frac{35}{72}
\]
- Compare \( \frac{35}{72} \) and \( \frac{5}{9} \):
- Convert \( \frac{5}{9} \) to a common denominator:
\[
\frac{5}{9} = \frac{5 \times 8}{9 \times 8} = \frac{40}{72}
\]
- Compare \( \frac{35}{72} \) and \( \frac{40}{72} \):
\[
\frac{35}{72} < \frac{40}{72} \quad \text{(False)}
\]

3. **Statement**: \(412 \cdot 54 < 412\)

- Compute \(412 \cdot 54\):
\[
412 \cdot 54 = 22248
\]
- Compare \(22248\) and \(412\):
\[
22248 > 412 \quad \text{(False)}
\]

4. **Statement**: \(358 \cdot 94 > 358\)

- Compute \(358 \cdot 94\):
\[
358 \cdot 94 = 33632
\]
- Compare \(33632\) and \(358\):
\[
33632 > 358 \quad \text{(True)}
\]

5. **Statement**: \(174 \cdot 32 < 174\)

- Compute \(174 \cdot 32\):
\[
174 \cdot 32 = 5568
\]
- Compare \(5568\) and \(174\):
\[
5568 > 174 \quad \text{(False)}
\]

**Summary**:
- **True Statements**:
- \(529 \cdot 78 > 529\)
- \(358 \cdot 94 > 358\)

Thus, the true statements that have been verified by computation are:
1. \(529 \cdot 78 > 529\)
2. \(358 \cdot 94 > 358\)