Order of Operations with Negative Numbers
Integer practice with signed numbers written clearly, such as 5 − (−3) and (−2)³.
What changes with negative numbers
Nothing in the order: it is still grouping, exponents, multiplication and division, then addition and subtraction. What changes is the sign rules inside each step: subtracting a negative adds, and a product or quotient of two negatives is positive.
The answer key shows each signed operation on its own line, such as “Subtract: 5 − (−3) = 8”, so students can see where a sign changed.
Worked examples
- [(53 − (−1)) × 4] − 8 = 496
- Parentheses, exponents: 5³ = 125[(125 − (−1)) × 4] − 8
- Parentheses: 125 − (−1) = 126[126 × 4] − 8
- Parentheses: 126 × 4 = 504504 − 8
- Subtract: 504 − 8 = 496496
- (33 − (−18)) ÷ (13 − (−2)) = 3
- Parentheses, exponents: 3³ = 27(27 − (−18)) ÷ (13 − (−2))
- Parentheses: 27 − (−18) = 4545 ÷ (13 − (−2))
- Parentheses: 13 − (−2) = 1545 ÷ 15
- Divide: 45 ÷ 15 = 33
Two more, answers only
- 72 − (−20 + 7 + (−13)) = 75
- 33 + 17 + [4 − (9 − (−20))] = 19
More worksheets
Questions
How are negative numbers written on the sheets?
A negative number after an operation sign is put in parentheses, for example 5 − (−3) or 4 × (−6). A negative number may stand bare at the start of an expression or just after an opening bracket, for example −8 + 3.
Is −2² on these sheets?
Never. A negative base always gets parentheses: (−2)². That keeps every problem unambiguous.
What can I do for free?
Make 3 new worksheets a day with up to 20 problems each, print them, save them as PDF or download them as HTML. Free sheets carry a small footer line, and the answer key shows every final answer plus step-by-step work for the first 3 problems. No account is needed.
Contact
A wrong answer, a missing topic, a question? Write a line; we read every message.