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

Question

Responses

5 and 2/9⋅7/8>5 and 2/9
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

4 and 1/2⋅5/4<4 and 1/2
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

3 and 5/8⋅9/4>3 and 5/8
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

17/4⋅3/2<17/4

Answer 1

To determine which statement is true, let's compute each one individually.

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

   First, convert \(5 \frac{2}{9}\) to an improper fraction: \[ 5 \frac{2}{9} = \frac{5 \times 9 + 2}{9} = \frac{45 + 2}{9} = \frac{47}{9} \] Now, compute the product: \[ \frac{47}{9} \cdot \frac{7}{8} = \frac{47 \times 7}{9 \times 8} = \frac{329}{72} \] Now compare \( \frac{329}{72} \) with \( \frac{47}{9} \): \[ \frac{47}{9} = \frac{47 \times 8}{9 \times 8} = \frac{376}{72} \] So, \[ \frac{329}{72} < \frac{376}{72} \] Thus, \( 5 \frac{2}{9} \cdot \frac{7}{8} < 5 \frac{2}{9} \).

2. Statement: \(4 \frac{1}{2} \cdot \frac{5}{4} < 4 \frac{1}{2}\)

   Convert \(4 \frac{1}{2}\) to an improper fraction: \[ 4 \frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{8 + 1}{2} = \frac{9}{2} \] Now compute the product: \[ \frac{9}{2} \cdot \frac{5}{4} = \frac{9 \cdot 5}{2 \cdot 4} = \frac{45}{8} \] Now compare \( \frac{45}{8} \) with \( \frac{9}{2} \): \[ \frac{9}{2} = \frac{9 \times 4}{2 \times 4} = \frac{36}{8} \] So, \[ \frac{45}{8} > \frac{36}{8} \] Thus, \( 4 \frac{1}{2} \cdot \frac{5}{4} > 4 \frac{1}{2} \).

3. Statement: \(3 \frac{5}{8} \cdot \frac{9}{4} > 3 \frac{5}{8}\)

   Convert \(3 \frac{5}{8}\) to an improper fraction: \[ 3 \frac{5}{8} = \frac{3 \times 8 + 5}{8} = \frac{24 + 5}{8} = \frac{29}{8} \] Now compute the product: \[ \frac{29}{8} \cdot \frac{9}{4} = \frac{29 \cdot 9}{8 \cdot 4} = \frac{261}{32} \] Now compare \( \frac{261}{32} \) with \( \frac{29}{8} \): \[ \frac{29}{8} = \frac{29 \times 4}{8 \times 4} = \frac{116}{32} \] So, \[ \frac{261}{32} > \frac{116}{32} \] Thus, \( 3 \frac{5}{8} \cdot \frac{9}{4} > 3 \frac{5}{8} \).

4. Statement: \( \frac{17}{4} \cdot \frac{3}{2} < \frac{17}{4} \)

   Compute the product: \[ \frac{17}{4} \cdot \frac{3}{2} = \frac{17 \cdot 3}{4 \cdot 2} = \frac{51}{8} \] Now compare \( \frac{51}{8} \) with \( \frac{17}{4} \): \[ \frac{17}{4} = \frac{17 \times 2}{4 \times 2} = \frac{34}{8} \] Thus, \[ \frac{51}{8} > \frac{34}{8} \] Therefore, \( \frac{17}{4} \cdot \frac{3}{2} > \frac{17}{4} \).

Summary:

• Statement 1: False
• Statement 2: False
• Statement 3: True
• Statement 4: False

The true statement is Statement 3: \(3 \frac{5}{8} \cdot \frac{9}{4} > 3 \frac{5}{8}\).