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Chapter 5: Problem 104

Perform the indicated operations. If possible, reduce the answer to its lowest terms. \(\frac{3}{4}-4(2+7) \div\left(-\frac{1}{2}\right)\left(-\frac{1}{6}\right)\)

Short Answer

Expert verified
The answer is \(-\frac{1725}{4}\)

Step by step solution

01

Simplification within brackets

Firstly, simplify what's inside the brackets which is \(4(2+7)\). Multiply 4 with the result of the operation in brackets (2+7=9), which results in \(36\). So, the expression becomes \(\frac{3}{4}-36 \div \left(-\frac{1}{2}\right)\left(-\frac{1}{6}\right)\)
02

Multiplication and Division

Then, perform multiplication and division, from left to right. The multiplication of \(\left(-\frac{1}{2}\right)\) and \(\left(-\frac{1}{6}\right)\) will be positive \(\frac{1}{12}\). This results in the expression \(\frac{3}{4}-36 \div \frac{1}{12}\). The division of 36 by \(\frac{1}{12}\) results in 432. So the expression now is \(\frac{3}{4}-432\).
03

Subtraction

Lastly, perform the subtraction. Convert 432 to fraction with denominator 4 to perform subtraction from \(\frac{3}{4}\). Hence, 432 is \(1728/4\). Now, the expression is \(\frac{3}{4}-\frac{1728}{4}\). Subtracting, we get \(-\frac{1725}{4}\).
04

Simplification

\(-\frac{1725}{4}\) is the simplest form of the fraction, hence cannot be simplified further. Therefore, the answer is \(-\frac{1725}{4}\).

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Most popular questions from this chapter

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(\sqrt{3}, 3,3 \sqrt{3}, 9, \ldots\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=10, r=-4\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(\frac{2}{3}, 1, \frac{4}{3}, \frac{5}{3}, \ldots\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{100}\), when \(a_{1}=50, r=1\).

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{6}\), when \(a_{1}=18, r=-\frac{1}{3}\).
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