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Evaluate expressions involving directed rational numbers

We've already learnt about the order of operations, which tells us the steps to solving equations with multiple operations.

Step 1: Do operations inside grouping symbols such as parentheses (...), brackets [...] and braces {...}.

Step 2: Do multiplication and division going from left to right.

Step 3: Do addition and subtraction going from left to right.

We use the same order of operations for questions with negative rational numbers. We just need to remember the rules for working with negative numbers. Make sure you're familiar with how to add, subtract, multiply and divide negative terms.

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


Question 1

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

Think: Working from left to right we first want to add $8.5$8.5 and $7.2$7.2. Next we are adding a negative number, which is the same as subtracting the absolute value.


$8.5+7.2+\left(-1.3\right)$8.5+7.2+(1.3) $=$= $15.7+\left(-1.3\right)$15.7+(1.3)
  $=$= $15.7-1.3$15.71.3
  $=$= $14.4$14.4


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 $F=113$F=113, calculate $C$C.

Question 4

David buys $3$3 shirts at $\$19.90$$19.90 each. For also buying a pair of jeans for $\$20.50$$20.50, he receives a $\$4.20$$4.20 discount. 
Write and solve a numerical expression for how much he spends.

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