To determine [tex]\( 75\% \)[/tex] of 36, we can break this into a series of simple steps.
First, let’s understand what [tex]\( 75\% \)[/tex] means. [tex]\( 75\% \)[/tex] is the same as saying [tex]\( \frac{75}{100} \)[/tex] or [tex]\( \frac{3}{4} \)[/tex].
Thus, to find [tex]\( 75\% \)[/tex] of 36, we need to multiply 36 by [tex]\( \frac{3}{4} \)[/tex].
Let's follow these steps clearly:
1. Identify the fraction for [tex]\( 75\% \)[/tex]:
[tex]\[ 75\% = \frac{75}{100} = \frac{3}{4} \][/tex]
2. Multiply 36 by [tex]\( \frac{3}{4} \)[/tex]:
[tex]\[ \left(\frac{3}{4}\right) \times 36 \][/tex]
3. Perform the multiplication:
We can rewrite the multiplication for clarity:
[tex]\[ \left(\frac{3}{4}\right) \times 36 = \frac{3 \times 36}{4} \][/tex]
4. Simplify the expression:
[tex]\[ \frac{3 \times 36}{4} = \frac{108}{4} = 27 \][/tex]
So, [tex]\( 75\% \)[/tex] of 36 is 27.
Next, let's address the changes in Carey’s expression [tex]\(\left(\frac{3}{4}\right)(27)\)[/tex]:
Carey's expression [tex]\(\left(\frac{3}{4}\right)(27)\)[/tex] is incorrect because [tex]\( 75\% \)[/tex] (which is [tex]\(\frac{3}{4}\)[/tex]) should be applied to 36, not 27.
- The 27 should be changed to 36: The original problem asks for [tex]\( 75\% \)[/tex] of 36, not 27. Therefore, the change needed is to replace 27 with 36.
- The [tex]\(\frac{3}{4}\)[/tex] is correct: Since [tex]\( 75\% \)[/tex] corresponds to [tex]\(\frac{3}{4}\)[/tex], the fraction part of the expression is correct.
Thus, the corrected expression should be [tex]\(\left(\frac{3}{4}\right)(36)\)[/tex].
Conclusively, the change in Carey’s expression that will lead to the correct answer is: The 27 should be changed to 36.
Thus, the correct final expression is:
[tex]\[ \left(\frac{3}{4}\right)(36) = 27 \][/tex]
This ensures the accurate calculation of [tex]\( 75\% \)[/tex] of 36, which we have confirmed to be 27.
