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

Question

Responses

3 5/8⋅9/4>3 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

5 2/9⋅78>5 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

17/4⋅3/2<17/4
Start Fraction 17 over 4 End Fraction times Start Fraction 3 over 2 End Fraction less than Start Fraction 17 over 4 End Fraction

4 1/2⋅5/4<4 1/2

Answer 1

Let's evaluate each statement to determine which one is true.

1. \(3 \frac{5}{8} \cdot \frac{9}{4} > 3 \frac{5}{8}\)

   First, 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, calculate: \[ \frac{29}{8} \cdot \frac{9}{4} = \frac{29 \times 9}{8 \times 4} = \frac{261}{32} \] Now compare \(\frac{261}{32}\) and \(\frac{29}{8}\): To compare, we can convert \(\frac{29}{8}\) to a denominator of 32: \[ \frac{29}{8} = \frac{29 \times 4}{8 \times 4} = \frac{116}{32} \] Since \(\frac{261}{32} > \frac{116}{32}\), this statement is true.

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

   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 calculate: \[ \frac{47}{9} \cdot \frac{7}{8} = \frac{47 \times 7}{9 \times 8} = \frac{329}{72} \] Now compare \(\frac{329}{72}\) and \(\frac{47}{9}\): Convert \(\frac{47}{9}\) to a denominator of 72: \[ \frac{47}{9} = \frac{47 \times 8}{9 \times 8} = \frac{376}{72} \] Since \(\frac{329}{72} < \frac{376}{72}\), this statement is false.

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

   Calculate: \[ \frac{17}{4} \cdot \frac{3}{2} = \frac{17 \times 3}{4 \times 2} = \frac{51}{8} \] Compare \(\frac{51}{8}\) with \(\frac{17}{4}\): Convert \(\frac{17}{4}\) to a denominator of 8: \[ \frac{17}{4} = \frac{17 \times 2}{4 \times 2} = \frac{34}{8} \] Since \(\frac{51}{8} > \frac{34}{8}\), this statement is false.

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

   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 calculate: \[ \frac{9}{2} \cdot \frac{5}{4} = \frac{9 \times 5}{2 \times 4} = \frac{45}{8} \] Compare \(\frac{45}{8}\) with \(\frac{9}{2}\): Convert \(\frac{9}{2}\) to a denominator of 8: \[ \frac{9}{2} = \frac{9 \times 4}{2 \times 4} = \frac{36}{8} \] Since \(\frac{45}{8} > \frac{36}{8}\), this statement is false.

Based on the computations, the only true statement is:

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