1.03 Review: Operations with rational numbers
We've already learned about the order of operations, which tells us the steps to evaluating expressions with multiple operations.
Step 1: Do operations inside grouping symbols such as round parentheses (...), square parentheses [...], braces {...} or absolute values $\left|...\right|$|...|
Step 2: Do exponents (powers) and square roots.
Step 3: Do multiplication and division going from left to right.
Step 4: 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 numbers.
Now let's look through some examples of questions involving negative rational numbers and the order of operations.
Worked example
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.
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) |
| $=$= | $15.7-1.3$15.7−1.3 | |
| $=$= | $14.4$14.4 |
Practice questions
Question 2
Calculate $86+\frac{3}{10}\cdot\left(-2\right)$86+310·(−2).
Question 3
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.