Simplify 4.5-2*3/6+1/4^2 divided by 0.75

Question: Simplify: \(\frac{4.5-2*\frac{3}{6}+\frac{1}{4^2}}{0.75}\)

1. \(\frac{1}{5}\)

2. \(\frac{15}{4}\)

100. \(\frac{15}{3}\)

500. \(\frac{19}{4}\)

5. \(\frac{57}{16}\)

“Simplify: \(\frac{4.5-2*\frac{3}{6}+\frac{1}{4^2}}{0.75}\)” – is a topic of the  GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

Approach Solution (1):

Firstly, we will simplify the numerator.

\(\frac{4.5-2*\frac{3}{6}+\frac{1}{4^2}}{0.75}\)

Multiply the terms, we will get:

\(4.5-\frac{6}{6}+\frac{1}{4^2}\)

\(4.5-1+\frac{1}{4^2}\)

\(3.5+\frac{1}{16}\)

Term ‘3.5’ can be written as:

\(\frac{7}{2}+\frac{1}{16}\)

Taking LCM, we will get:

\(56+\frac{1}{16}\)

\(\frac{57}{16}\)

Now, dividing numerator by denominator, we will get:

\(\frac{57}{\frac {16} {0.75}}\)= \(\frac{57}{16}*\frac{1}{0.75}\)

Term ‘0.75’ can be written as:

\(\frac{57}{16}*\frac{4}{3}\)= \(\frac{19}{4}\)

Correct option: D

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