Final answer:
Tyrel can check his work on the expression 2 1/2−3/4 by back-estimating using known fractional relationships or by creating a common denominator and subtracting the numerators to confirm the reasonableness of his original evaluation.
Step-by-step explanation:
To check his work after evaluating the expression 2 1/2−3/4, Tyrel can use different methods. One method is to consider what he knows about fractions and use that to estimate if his answer is reasonable. For instance, Tyrel might recall that half of one-half is one quarter and since three quarters (3/4) is three times one quarter, subtracting three quarters from two and a half should result in a number that is slightly more than two. Furthermore, he can ensure the reasonableness of his answer by remembering that one half is equivalent to two quarters, and since two and a half is more than two, the final answer should be greater than one and a half after subtracting three quarters. Additionally, creating a common denominator and combining the numerators is another robust method to check his work.
To illustrate, by converting 2 1/2 to 5/2 (since 2 times 2 plus 1 is 5) and keeping 3/4 as is, he could find a common denominator, which would be 4 in this case. Therefore, Tyrel would convert 5/2 into 10/4 before subtracting 3/4, leading to 7/4 or 1 3/4 as the final answer. By using this step-by-step process, he can confirm if his original evaluation is accurate.