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2.03 Order of operations with rational numbers

We've already learned about the order of operations, which tells us the steps to evaluating expressions with multiple operations.
  1. Evaluate operations inside grouping symbols such as parentheses (...) or absolute value |...|.
  2. Evaluate exponents such as squares, cubes, or square roots.
  3. Evaluate multiplication and division going from left to right.
  4. 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.

Worked example

Question 1

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.


$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$15.71.3 Subtract
  $=$= $14.4$14.4  


Now, let's give these a try.

Practice questions

Question 2

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


Question 3

Conversion of temperature from Fahrenheit to Celsius is defined by the formula $C=\frac{5}{9}\left(F-32\right)$C=59(F32), 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.

Question 4

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 multistep real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals) by applying properties of operations as strategies to calculate with numbers, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies.

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