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

Question

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. \(358 \cdot 94 > 358\)