Question

Use computation to determine which of the following statements is true.(1 point)
Responses

4/7⋅10/3<4/7
Start Fraction 4 over 7 End Fraction times Start Fraction 10 over 3 End Fraction less than Start Fraction 4 over 7 End Fraction

1/10⋅5/2<1/10
Start Fraction 1 over 10 End Fraction times Start Fraction 5 over 2 End Fraction less than Start Fraction 1 over 10 End Fraction

11/13⋅1/8<11/13
Start Fraction 11 over 13 End Fraction times Start Fraction 1 over 8 End Fraction less than Start Fraction 11 over 13 End Fraction

13/6⋅4/7>13/6

Answer 1

To determine which of the statements is true, we can compute each one separately.

1. **Statement:** \( \frac{4}{7} \cdot \frac{10}{3} < \frac{4}{7} \)
**Computation:**
\[
\frac{4}{7} \cdot \frac{10}{3} = \frac{4 \times 10}{7 \times 3} = \frac{40}{21}
\]
To compare \( \frac{40}{21} \) and \( \frac{4}{7} \), we can cross-multiply:
\( 40 \times 7 = 280 \) and \( 4 \times 21 = 84 \).
Since \( 280 > 84 \),
\[ \frac{40}{21} > \frac{4}{7} \]
**This statement is false.**

2. **Statement:** \( \frac{1}{10} \cdot \frac{5}{2} < \frac{1}{10} \)
**Computation:**
\[
\frac{1}{10} \cdot \frac{5}{2} = \frac{1 \times 5}{10 \times 2} = \frac{5}{20} = \frac{1}{4}
\]
Compare \( \frac{1}{4} \) and \( \frac{1}{10} \) by cross-multiplying:
\( 1 \times 10 = 10 \) and \( 1 \times 4 = 4 \).
Since \( 10 > 4 \),
\[ \frac{1}{4} > \frac{1}{10} \]
**This statement is false.**

3. **Statement:** \( \frac{11}{13} \cdot \frac{1}{8} < \frac{11}{13} \)
**Computation:**
\[
\frac{11}{13} \cdot \frac{1}{8} = \frac{11 \times 1}{13 \times 8} = \frac{11}{104}
\]
Compare \( \frac{11}{104} \) and \( \frac{11}{13} \) by cross-multiplying:
\( 11 \times 13 = 143 \) and \( 11 \times 104 = 1144 \).
Since \( 1144 > 143 \),
\[ \frac{11}{104} < \frac{11}{13} \]
**This statement is true.**

4. **Statement:** \( \frac{13}{6} \cdot \frac{4}{7} > \frac{13}{6} \)
**Computation:**
\[
\frac{13}{6} \cdot \frac{4}{7} = \frac{13 \times 4}{6 \times 7} = \frac{52}{42} = \frac{26}{21}
\]
Compare \( \frac{26}{21} \) and \( \frac{13}{6} \) by cross-multiplying:
\( 26 \times 6 = 156 \) and \( 13 \times 21 = 273 \).
Since \( 156 < 273 \),
\[ \frac{26}{21} < \frac{13}{6} \]
**This statement is false.**

In conclusion, the only true statement is:

**3:** \( \frac{11}{13} \cdot \frac{1}{8} < \frac{11}{13} \)