Chapter 2—Integers
2-10 Order of Operations for Integers
When you complete the work for this section, you should be able to: - Simplify signed-integer expressions that include any combination of addition, subtraction, multiplication, and division.
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Remember When solving combinations of addition, subtraction, multiplication, and division in the same expression: - Do the multiplication and division first, from left to right.
- Do the addition and subtraction last, from left to right.
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Here is an expression that includes both addition and multiplication:
4 + 2 x 6
"Solving" the expression by simply performing operations from left to right, we get:
( +4 ) + 2 x (+ 6) = 6 x 6
6 x 6 = 36 |  |
But the correct procedure calls for doing the multiplication operation first, and then the addition:
4 + 2 x 6 = 4 + 12
4 + 12 = 16 |  |
There is a HUGE difference between 36 and 16. Always multiply before adding.
Here is an example of an expression that combines addition and division:
6 ÷ 2 + 4
Doing the division first:
6 ÷ 2 + 4 = 3 + 4
3 + 4 = 7 |  |
But doing the addition first:
6 ÷ 2 + 4 = 6 ÷ 6
6 ÷ 6 = 1 |  |
Examples 1
Endless Examples & Exercises 1
Now consider an example that has more than two operations:
Problem 2 + 3 x 4 – 5 = _____ | |
| Procedure | |
- Do the multiplication first
| 2 + 3 x 4 – 5 = 2 + 12 – 5 |
- Do the addition/subtraction from left to right
| 2 + 12 – 5 = 9 |
Solution 2 + 3 x 4 – 5 = 9 | |
Here is an example that includes all four basic arithmetic operations. There are a lot of ways to do this wrong ... and only one way to do it right:
Problem 2 + 3 x 2 – 16 ÷ 4 = _____ | |
| Procedure | |
- Do the multiplication and division first, from left to right:
| 2 + 3 x 2 – 16 ÷ 4 = 2 + 6 – 16 ÷ 4
2 + 6 – 16 ÷ 4 = 2 + 6 – 4 |
- Then do the addition and subtraction, also from left to right:
| 2 + 6 – 4 = 8 – 4
8 – 4 = 4 |
Solution 2 + 3 x 2 – 16 ÷ 4 = | |
Examples 2
Endless Examples & Exercises 2
