Lesson 2 of 1524
Signed numbers and order of operations
The sign and the order both change the answer.
Practice this chapterAdding a negative is subtraction: −5 + 8 = 3. Subtracting a negative is addition: 5 − (−2) = 7.
A negative times a negative is positive. (−4)(−3) = 12. A negative times a positive is negative.
Do parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.
A square and a sign
−a² = −(a²), while (−a)² = a²
The parentheses decide whether the sign is inside the square.
Worked example
Simplify 2 + 3² × 2.
- 1There are no parentheses. Do the exponent first, then multiplication, then addition.
- 23² means 3 × 3, which is 9. The expression is now 2 + 9 × 2.
- 3Multiply before you add: 9 × 2 = 18. The expression is now 2 + 18.
- 4Add last: 2 + 18 = 20.
- 5The wrong order, (2 + 3)² × 2 or (2 + 9) × 2, is a different expression. This one never groups the 2 with the 3.
Result: 20
Why. The exponent acts only on the 3, the multiplication uses that 9, and the leading 2 is added after both of those. That order is why the result is 20 rather than 14 or 50.
3 + 4 × 2 is 11, not 14. And −3² is −9, while (−3)² is 9.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.