SajjadAhmad
Find an expression equivalent to the one below
\(\frac{[0.3667][0.8333][0.3333]}{[0.4444][0.6667][0.125]}=\)
A. 2
B. 2.4
C. 2.45
D. 2.75
E. 2.8
None of the answer choices is "equivalent" to the expression in the question. The expression in the question is equal to 2.7500025, rounded to seven decimal places. If a question is asking for something "equivalent", the answer needs to be exactly equivalent. If it's asking for an approximation, the question needs to say precisely that, so a test taker can know that it's correct to use approximation techniques.
Here, 0.125 = 1/8, and 0.3333/0.4444 is exactly equal to 3/4. So we can precisely rewrite the expression as
(0.3667)(0.8333)(3) / (4)(0.6667)(1/8) = (6)(0.3667)(0.8333)/(0.6667)
We can now approximate the remaining terms. 2/3 = 0.6666...., 5/6 = 0.8333..., and 0.36666... = 0.33333... + 0.03333... = 1/3 + 1/30 = 11/30. So using these fractions as our estimates, the above equals
[(6)(11/30)(5/6)] / (2/3) = (11/6)(3/2) = 11/4 = 2.75
But that's not the exact answer.