Massachusetts 7 - 2020 Edition

2.03 Order of operations with rational numbers

Lesson

We've already learned about the order of operations, which tells us the steps to evaluating expressions with multiple operations.

Remember!

- Evaluate operations inside grouping symbols such as parentheses (...) or absolute value |...|.
- Evaluate exponents such as squares, cubes, or square roots.
- Evaluate multiplication and division going from left to right.
- Evaluate addition and subtraction going from left to right.

We use the same order of operations for rational numbers as we do for integers.

Let's look through some examples of questions involving rational numbers and the order of operations.

Evaluate the expression: $8.5+7.2+\left(-1.3\right)$8.5+7.2+(−1.3)

**Think**: Because this expression only contains addition we can skip to that step in the order of operations. Remember with addition we work from left to right.

**Do**:

$8.5+7.2+\left(-1.3\right)$8.5+7.2+(−1.3) | $=$= | $15.7+\left(-1.3\right)$15.7+(−1.3) | Add $8.5$8.5 and $7.2$7.2 |

$=$= | $15.7+\left(-1.3\right)$15.7+(−1.3) | Adding $-1.3$−1.3 can be rewritten as subtracting positive $1.3$1.3 | |

$=$= | $15.7-1.3$15.7−1.3 | Subtract | |

$=$= | $14.4$14.4 |

Now, let's give these a try.

Calculate $86+\frac{3}{10}\times\left(-2\right)$86+310×(−2).

Conversion of temperature from Fahrenheit to Celsius is defined by the formula $C=\frac{5}{9}\left(F-32\right)$`C`=59(`F`−32), where $F$`F` is the temperature in degrees Fahrenheit and $C$`C` is the equivalent temperature in degrees Celsius. Given that $F=-4$`F`=−4, calculate $C$`C`.

David buys $3$3 shirts at $\$19.90$$19.90 each, and a pair of jeans for $\$20.50$$20.50. The shop has a sale on, and so he receives a $\$8.02$$8.02 discount.

Write and solve a numerical expression for how much he spends in total.

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.