1. A student claimed that multiplying any two fractions will always result in a number that is less than 1. Which of the following shows that the student's claim is NOT correct?
Answer: E
2/3 * 9/4 shows that the student's claim is NOT correct.
Multiplying the fractions 2/3 and 9/4 results in a product greater than 1, specifically 3/2 or 1.5, which contradicts the student's assertion that the product of any two fractions is always less than 1.
A) 1/3 * 3/4
Multiplying 1/3 and 3/4 results in 1/4, which is less than 1. This supports the student's claim rather than disproving it, as both fractions are less than 1, and their product remains less than 1.
B) 2/5 * 3/5
The product of 2/5 and 3/5 is 6/25, which is also less than 1. Similar to Option A, this outcome reinforces the student's claim since both fractions are less than 1, leading to a product that is still below 1.
C) 1/2 * 5/4
The multiplication of 1/2 by 5/4 yields 5/8, which is less than 1. This option does not contradict the student's assertion, as the product remains below 1, thereby supporting the claim.
D) 2/3 * 5/4
Calculating 2/3 times 5/4 gives 10/12 or 5/6, which is again less than 1. This option does not disprove the student's statement since the product is less than 1, aligning with the claim.
E) 2/3 * 9/4
This multiplication results in 18/12, which simplifies to 3/2 or 1.5, clearly demonstrating that the product can exceed 1. This directly contradicts the student's claim, proving it to be incorrect.
Conclusion
The correct answer, 2/3 * 9/4, clearly illustrates that multiplying two fractions can yield a result greater than 1, thereby disproving the student's claim. All other options result in products that are less than 1, supporting the student's assertion rather than challenging it. Thus, the student's claim is not universally valid.