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-world 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. Assess the reasonableness of answers using mental computation and estimation strategies.