When adding and subtracting negative numbers comes into play in middle school, students often lose the confidence they once had with standard positive numbers.
We notice this same hesitation very often at Mathnasium. This confusion simply stems from a change in math intuition.
Up to this point, students rely on concrete counting, like adding three items to two items builds a larger pile. Negative numbers break those physical rules. Addition no longer guarantees a larger total, subtraction no longer guarantees a smaller one, and abstract values become hard to picture.
However, this roadblock does not have to stay in your way. Our tutors prepared this guide to outline the core rules for adding and subtracting negative numbers, explain why those rules work, and share visual techniques that make every step make sense.
A negative number is simply any number with a value less than zero. We write negative numbers with a minus sign in front of them, such as –5, –12, or –100.
We can also think of a negative number as the mathematical opposite of a positive number. It sits the exact same distance from zero, just in the opposite direction.
If this idea feels a little abstract at first, we can just picture negative numbers in everyday situations:
Temperature: On a bitter cold winter day, we record a temperature like –5° because it sits five degrees below zero.
Money: If we owe a friend five dollars, we track that balance as –$5 because our account sits five dollars below zero.
Sports & Games: When our team loses ten yards in football or drops ten points in a video game, we write that change as –10.
Elevation: When a submarine travels 50 feet below sea level, we mark its depth at –50 feet.
Addition combines values, and subtraction is just adding the opposite.
When we add a positive number, our value increases (it climbs toward or further into positive territory):
–5 + 3 =2
–4 + 9 =5
When we add a negative number, our value decreases (it pulls us toward or deeper into negative territory).
–5 + (–3) = –8
5 + (–3) = 2
When we subtract a positive number, it is just adding a negative number in disguise (our value decreases):
–5 – 3 -> –5 + (–3) = –8
5-8 -> 5 + (–8) = –3
When we subtract a negative number, it is just adding a positive number in disguise (our value increases):
–5 - (–3) = –5 + 3 = –2
2- (–5) = 2 + 5 = 7
When two signs sit right next to each other, we can simplify them instantly:
Two different signs (+ – or – +) become a minus (value decreases).
Two same signs (+ + or – –) become a plus (value increases).
If sign changes feel a little abstract, number lines come to our rescue. Instead of memorizing rules, we can use them as a visual map to solve any problem:
Our starting number is where we stand on the number line.
The direction we move depends on whether our total value increases or decreases:
Step right to increase value (adding a positive or subtracting a negative).
Step left to decrease value (adding a negative or subtracting a positive).
Shall we try that out with a couple of examples?
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Let’s solve –5 + 6 on a number line.
We begin at –5.
Since we are adding a positive number, step 6 units to the right
We cross zero and end up at 1.
So, –5 + 6 = 1.
This time, we want to solve 4 + (–6) on the number line:
Our starting position is +4.
Since we are adding a negative number, we step 6 units to the left.
We cross zero and end up at –2.
4 + (–6) = 2
Let’s show what 9 − 13 looks like on the number line:
We stand at 9.
Subtracting a positive number decreases our value, so step 13 units to the left.
We cross zero and end up at –4.
We found that 9 - 13 = –4.
Lastly, let's see what 4 – (–6) looks like on the number line:
We start at 4.
Subtracting a negative number is taking away a debt, which increases our value, so step 6 units to the right.
We land at 10.
So, 4 – (–6) = 10.
And that’s how we do it. Not so difficult, right?
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You’ve seen the rules that govern adding and subtracting negative numbers. You’ve also seen how a number line makes the whole process easier. Now, let’s put those skills to a challenge with a nice mix of practice problems.
Using the core rules of signed numbers, work out these:
–14 + 25
–12 + – 15
11 - 28
–9 - 30
Using the number line, find the answers for each:
–4 + 7
3 + (–8)
5 - 9
–2 - 6
When you finish, check your answers at the bottom of our guide.
At Mathnasium, we use personalized learning plans and interactive teaching techniques to make concepts like negative numbers make sense.
Mathnasium is a math-only learning center dedicated to helping K–12 students of all skill levels excel in math.
We believe mastering math requires more than memorization and repetitive drills. Because every child learns differently, we tailor each student's journey to match their pace and style.
We make this possible through the Mathnasium Method™, our proprietary approach designed around individual students’ needs and learning styles.
Here’s how it works:
Assessment and Personalized Learning Plans: Each student begins their Mathnasium journey with a diagnostic assessment that identifies current skills, strengths, and gaps. From those findings, we build a personalized learning plan tailored to their goals, whether that means closing foundational gaps, deepening conceptual understanding, or building the mathematical reasoning competitive coursework requires.
Teaching for Understanding: Our specially trained instructors use natural, everyday language and a mix of verbal, visual, mental, tactile, and written techniques so each concept lands before we move forward.
Problem-Solving and Critical Thinking: We give students time to work through problems independently. That productive struggle helps them learn to trust their own reasoning. When we do step in, we explain both the how and the why behind each answer, so students build problem-solving and critical thinking skills they can use in math and beyond.
An Engaging and Fun Learning Environment: Sessions include games, earned rewards, and consistent celebration of progress. Students build confidence alongside fluency, and many develop a more positive relationship with math over time.
The impact extends beyond the classroom:
94% of parents report improvement in their child's math skills and understanding
93% of parents report an improved attitude toward math after attending Mathnasium
90% of students saw improvement in their school grades
With over 1,100 learning centers across North America, there is likely a Mathnasium close to you.
If you’re located in or near Redondo Beach, you can find us at Mathnasium of Redondo Beach, a trusted local center with years of experience building confident math thinkers.
Whether your child is looking to catch up, keep up, or get ahead in math, our team is happy to assist.
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📅 Schedule a Free Assessment at Mathnasium of Redondo Beach
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If you’ve given our exercises a try, check how you did below.
–14 + 25 = 11
–12 + (–15) = –27
11 -28 = –17
–9 -(–30) = 21
A. –4 + 7
B. 3 +(–8) = –5
C. 5 -9 = –4
D. –2 - (–6) = 4
Mathnasium of Redondo Beach is a math-only learning center for K-12 students in Redondo Beach, CA. Trusted by over a million parents, Mathnasium uses personalized learning plans and the proprietary Mathnasium Method™ to help students catch up, keep up, and get ahead on their math journey.
Our specially trained tutors deliver face-to-face instruction in a supportive and fun small-group environment, working with students to develop a deep understanding of math, build confidence, and improve academic performance.
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