1.02 Mixed operations with integers
We know how to follow the order of operations when evaluating expressions involving more than one operation.
The order is as follows:
- Evaluate whatever is contained in brackets.
- Evaluate any powers.
- Evaluate any multiplication or division, reading from left to right.
- Evaluate any addition or subtraction, reading from left to right.
If we have negative integers in our expression, we still follow the exact same rules; we just need to be careful when evaluating the terms involving negatives.
Worked example
Find the value of $34-8\times7\div\left(-2\right)$34−8×7÷(−2).
Think: What operations are used in the expression? Are there any powers?
Do: Referring back to the order of operations, we see that brackets are evaluated first. There are brackets around $-2$−2, but these are used to indicate that we are dividing by $-2$−2, there is no operation to perform inside the brackets. Next we evaluate any powers. There are no powers so we can ignore this step.
Multiplication and division come after, both are in this expression so we work from left to right
| $34-8\times7\div\left(-2\right)$34−8×7÷(−2) | $=$= | $34-56\div\left(-2\right)$34−56÷(−2) |
Evaluating the product $8\times7$8×7 |
| $=$= | $34-\left(-28\right)$34−(−28) |
Evaluating the quotient $56\div\left(-2\right)$56÷(−2) |
|
| $=$= | $34+28$34+28 |
Simplifying the subtraction of a negative |
|
| $=$= | $62$62 |
Evaluating the addition |
Reflect: By following the order of operations, taking care when the operations involve negative integers, we can solve complex looking expressions by dealing with them in a systematic way, and breaking them into small easy to solve calculations.
Practice questions
Question 1
Evaluate $5+9\times\left(-6\right)$5+9×(−6).
Question 2
Evaluate $\left(7-8\right)\times\left(-5\right)$(7−8)×(−5).
Question 3
Evaluate $21\div\left(-7\right)\times2$21÷(−7)×2.