Question
Using computation, which of the following statements is true?(1 point)
Responses
19/20⋅19/20>19/20
Start Fraction 19 over 20 End Fraction times Start Fraction 19 over 20 End Fraction greater than Start Fraction 19 over 20 End Fraction
1 2/3⋅2 1/3<1 2/3
1 Start Fraction 2 over 3 End Fraction times 2 Start Fraction 1 over 3 End Fraction less than 1 Start Fraction 2 over 3 End Fraction
11/10⋅10/11>11/10
Start Fraction 11 over 10 End Fraction times Start Fraction 10 over 11 End Fraction greater than Start Fraction 11 over 10 End Fraction
15/6⋅3 1/4>15/6
Responses
19/20⋅19/20>19/20
Start Fraction 19 over 20 End Fraction times Start Fraction 19 over 20 End Fraction greater than Start Fraction 19 over 20 End Fraction
1 2/3⋅2 1/3<1 2/3
1 Start Fraction 2 over 3 End Fraction times 2 Start Fraction 1 over 3 End Fraction less than 1 Start Fraction 2 over 3 End Fraction
11/10⋅10/11>11/10
Start Fraction 11 over 10 End Fraction times Start Fraction 10 over 11 End Fraction greater than Start Fraction 11 over 10 End Fraction
15/6⋅3 1/4>15/6
Answers
Answered by
GPT-4o mini
Let's evaluate each of the statements one by one.
1. **\( \frac{19}{20} \cdot \frac{19}{20} > \frac{19}{20} \)**:
- First, calculate \( \frac{19}{20} \cdot \frac{19}{20} = \frac{361}{400} \).
- Now, compare \( \frac{361}{400} \) with \( \frac{19}{20} = \frac{380}{400} \).
- Since \( \frac{361}{400} < \frac{380}{400} \), the statement is **false**.
2. **\( 1 \frac{2}{3} \cdot 2 \frac{1}{3} < 1 \frac{2}{3} \)**:
- Convert mixed numbers to improper fractions:
- \( 1 \frac{2}{3} = \frac{5}{3} \)
- \( 2 \frac{1}{3} = \frac{7}{3} \)
- Now compute the product:
- \( \frac{5}{3} \cdot \frac{7}{3} = \frac{35}{9} \).
- Convert \( \frac{35}{9} \) and \( 1 \frac{2}{3} = \frac{5}{3} = \frac{15}{9} \).
- Since \( \frac{35}{9} > \frac{15}{9} \), the statement is **false**.
3. **\( \frac{11}{10} \cdot \frac{10}{11} > \frac{11}{10} \)**:
- Calculate \( \frac{11}{10} \cdot \frac{10}{11} = 1 \).
- Compare \( 1 \) with \( \frac{11}{10} \).
- Since \( 1 < \frac{11}{10} \), the statement is **false**.
4. **\( \frac{15}{6} \cdot 3 \frac{1}{4} > \frac{15}{6} \)**:
- Convert \( 3 \frac{1}{4} \) to an improper fraction:
- \( 3 \frac{1}{4} = \frac{13}{4} \).
- Now compute the product:
- \( \frac{15}{6} \cdot \frac{13}{4} = \frac{195}{24} \).
- Convert \( \frac{195}{24} \) and \( \frac{15}{6} = \frac{60}{24} \).
- Since \( \frac{195}{24} > \frac{60}{24} \), the statement is **true**.
**Conclusion**: The only true statement is:
**4. \( \frac{15}{6} \cdot 3 \frac{1}{4} > \frac{15}{6} \)**.
1. **\( \frac{19}{20} \cdot \frac{19}{20} > \frac{19}{20} \)**:
- First, calculate \( \frac{19}{20} \cdot \frac{19}{20} = \frac{361}{400} \).
- Now, compare \( \frac{361}{400} \) with \( \frac{19}{20} = \frac{380}{400} \).
- Since \( \frac{361}{400} < \frac{380}{400} \), the statement is **false**.
2. **\( 1 \frac{2}{3} \cdot 2 \frac{1}{3} < 1 \frac{2}{3} \)**:
- Convert mixed numbers to improper fractions:
- \( 1 \frac{2}{3} = \frac{5}{3} \)
- \( 2 \frac{1}{3} = \frac{7}{3} \)
- Now compute the product:
- \( \frac{5}{3} \cdot \frac{7}{3} = \frac{35}{9} \).
- Convert \( \frac{35}{9} \) and \( 1 \frac{2}{3} = \frac{5}{3} = \frac{15}{9} \).
- Since \( \frac{35}{9} > \frac{15}{9} \), the statement is **false**.
3. **\( \frac{11}{10} \cdot \frac{10}{11} > \frac{11}{10} \)**:
- Calculate \( \frac{11}{10} \cdot \frac{10}{11} = 1 \).
- Compare \( 1 \) with \( \frac{11}{10} \).
- Since \( 1 < \frac{11}{10} \), the statement is **false**.
4. **\( \frac{15}{6} \cdot 3 \frac{1}{4} > \frac{15}{6} \)**:
- Convert \( 3 \frac{1}{4} \) to an improper fraction:
- \( 3 \frac{1}{4} = \frac{13}{4} \).
- Now compute the product:
- \( \frac{15}{6} \cdot \frac{13}{4} = \frac{195}{24} \).
- Convert \( \frac{195}{24} \) and \( \frac{15}{6} = \frac{60}{24} \).
- Since \( \frac{195}{24} > \frac{60}{24} \), the statement is **true**.
**Conclusion**: The only true statement is:
**4. \( \frac{15}{6} \cdot 3 \frac{1}{4} > \frac{15}{6} \)**.