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:
- \(\phantom{\rule{0.2em}{0ex}}7\left(18.3-21.7\right)\)
- \(\phantom{\rule{0.2em}{0ex}}\frac{2}{3}\left(8.3-3.8\right)\)
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:
- \(\phantom{\rule{0.2em}{0ex}}6÷0.6+\left(0.2\right)4-{\left(0.1\right)}^{2}\)
- \(\phantom{\rule{0.2em}{0ex}}{\left(\frac{1}{10}\right)}^{2}+\left(3.5\right)\left(0.9\right)\)
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. | \(3.16\) |
This lesson is part of:
Introducing Decimals
View Full Tutorial