The lesson
Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
Think of it as moving on a number line
Adding a positive number moves you right; adding a negative number moves you left. Subtracting flips the direction.
Two rules that make everything easier
- 1Adding a negative is the same as subtracting a positive: 5 + (-3) = 5 - 3 = 2.
- 2Subtracting a negative is the same as adding a positive: 5 - (-3) = 5 + 3 = 8.
Simplify -4 + 9 - (-2).
- 1Rewrite the double negative: -4 + 9 + 2.
- 2Combine left to right: -4 + 9 = 5.
- 3Then 5 + 2 = 7.
Why this matters
Use the number line and two key rules to combine positive and negative numbers.
These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.
Common mistakes to avoid
Rushing to the answer without writing steps. Clear work helps you catch mistakes and shows your reasoning.
Re-reading the question too quickly. Underline what you are solving for before you start calculating.
Key ideas from this lesson
- Think of it as moving on a number line
- Two rules that make everything easier
- Adding a negative is the same as subtracting a positive: 5 + (-3) = 5 - 3 = 2.
- Subtracting a negative is the same as adding a positive: 5 - (-3) = 5 + 3 = 8.
Video walkthroughs
Adding & Subtracting Integers
Two simple rules plus a number-line strategy for every case.
Watch on YouTube
Why a Negative Times a Negative Makes Sense
Build intuition for integer sign rules on a number line.
Watch on YouTube
Multiplying and Dividing Negative Numbers
Interpret signed-number multiplication and division in context.
Watch on YouTubePractice
For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.
Exercise 1
Try it yourselfEvaluate: -9 + 14.
Step-by-step solution
- 1|−9| = 9 and |14| = 14.
- 214 − 9 = 5.
- 3The larger magnitude is positive, so the answer is 5.
Exercise 2
Try it yourselfSimplify: 7 − (−4).
Step-by-step solution
- 1Subtracting a negative is adding a positive.
- 27 + 4 = 11.
Exercise 3
Try it yourselfEvaluate: -12 + 5 − 3.
Step-by-step solution
- 1Combine left to right: -12 + 5 = -7.
- 2-7 − 3 = -10.
Exercise 4
Try it yourselfThe temperature was −6°C in the morning and rose 11°C by noon. What is the noon temperature?
Step-by-step solution
- 1Rising means add: -6 + 11.
- 2Different signs: 11 − 6 = 5.
- 3The result is positive: 5°C.
Exercise 5
Try it yourselfSimplify: -3 + (−8) − (−2).
Step-by-step solution
- 1Rewrite: -3 + (-8) + 2.
- 2-3 + (-8) = -11.
- 3-11 + 2 = -9.
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Adding & Subtracting Integers
Question 1 of 5
What is -7 + 3?