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Chapter 5: Problem 103

Perform the indicated operations. If possible, reduce the answer to its lowest terms. \(\frac{1}{4}-6(2+8) \div\left(-\frac{1}{3}\right)\left(-\frac{1}{9}\right)\)

Short Answer

Expert verified
The simplified result of the operation is 21.25.

Step by step solution

01

Identify and Calculate Inside Parentheses

According to BIDMAS/BODMAS/PEMDAS operations rule, operations enclosed in parentheses are performed first. However, in our problem, the parentheses \( (2+8) \) can be simplified to 10. The problem now is \( \frac{1}{4}-6 \cdot 10 \div\left(-\frac{1}{3}\right)\left(-\frac{1}{9}\right)\)
02

Perform Division and Multiplication from Left to Right

Next, according to the BIDMAS/BODMAS/PEMDAS operations rule, multiplication and division operations are performed from left to right. Let's start with multiplication: \(6 \cdot 10 = 60\). Now let's move to the division: \( \frac{60}{-\frac{1}{3}} = 60 \cdot -3 = -180\). This results in: \(\frac{1}{4} + 180 \cdot -\frac{1}{9}\). Then continue with the multiplication: \(180 \cdot -\frac{1}{9} = -20\). This results in: \(\frac{1}{4} -(-20) = \frac{1}{4} + 20\). Finally, continue with the addition: \( \frac{1}{4} + 20 = 5/4 + 80/4 = 85/4 = 21.25 \). Thus, the solution is 21.25.
03

Check the Solution

After the arithmetic manipulations, the final answer is 21.25. In this step, review the calculation to ensure that all arithmetic operations are conducted correctly according to the order of operations.

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