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?
2/3 * 9/4 results in a product greater than 1.
When multiplying fractions, if the numerator of one fraction is larger than the denominator of the other, the product can exceed 1. In this case, multiplying 2/3 by 9/4 yields a value greater than 1, demonstrating that the student's claim is incorrect.
This multiplication results in 1/4, which is indeed less than 1. Both fractions have numerators smaller than their respective denominators, leading to a product that confirms the student's claim.
The product of these fractions is 6/25, which is also less than 1. Similar to the previous choices, both numerators are smaller than their denominators, supporting the student's assertion instead of disproving it.
The result of this multiplication is 5/8, which is again less than 1. The fraction 1/2 has a numerator smaller than its denominator, and while 5/4 is greater than 1, its effect still results in a product below 1.
This results in 10/12, which simplifies to 5/6, still less than 1. Here, although one of the fractions is greater than 1, the other is not sufficient to bring the product above 1.
This multiplication yields 18/12, which simplifies to 3/2, a number greater than 1. This outcome illustrates that it is possible for the product of two fractions to exceed 1, directly contradicting the student's claim.
The student's assertion that multiplying any two fractions results in a product less than 1 is disproven by the example of 2/3 multiplied by 9/4, which yields a result greater than 1. The other options illustrate cases where the product remains less than 1, but they do not represent the general rule. Thus, the existence of fractions that, when multiplied, exceed 1 illustrates the variability of outcomes in fraction multiplication depending on the values involved.
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