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Simplifying Expressions Using the Order of Operations

Simplifying Expressions Using the Order of Operations

The order of operations introduced in Mathematics 102 also applies to decimals. Do you remember what the phrase “Please excuse my dear Aunt Sally” stands for?

Example

Simplify the expressions:

  1. \(\phantom{\rule{0.2em}{0ex}}7\left(18.3-21.7\right)\)
  2. \(\phantom{\rule{0.2em}{0ex}}\frac{2}{3}\left(8.3-3.8\right)\)

Solution

  
 \(7\left(18.3-21.7\right)\)
Simplify inside parentheses.\(7\left(-3.4\right)\)
Multiply.\(-23.8\)
  
 \(\frac{2}{3}\left(8.3-3.8\right)\)
Simplify inside parentheses.\(\frac{2}{3}\left(4.5\right)\)
Write \(4.5\) as a fraction.\(\frac{2}{3}\left(\frac{4.5}{1}\right)\)
Multiply.\(\frac{9}{3}\)
Simplify.\(3\)

Example

Simplify each expression:

  1. \(\phantom{\rule{0.2em}{0ex}}6÷0.6+\left(0.2\right)4-{\left(0.1\right)}^{2}\)
  2. \(\phantom{\rule{0.2em}{0ex}}{\left(\frac{1}{10}\right)}^{2}+\left(3.5\right)\left(0.9\right)\)

Solution

  
 \(6÷0.6+\left(0.2\right)4-{\left(0.1\right)}^{2}\)
Simplify exponents.\(6÷0.6+\left(0.2\right)4-0.01\)
Divide.\(10+\left(0.2\right)4-0.01\)
Multiply.\(10+0.8-0.01\)
Add.\(10.8-0.01\)
Subtract.\(10.79\)
  
 \({\left(\frac{1}{10}\right)}^{2}+\left(3.5\right)\left(0.9\right)\)
Simplify exponents.\(\frac{1}{100}+\left(3.5\right)\left(0.9\right)\)
Multiply.\(\frac{1}{100}+3.15\)
Convert \(\frac{1}{100}\) to a decimal.\(0.01+3.15\)
Add.\(3.16\)

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