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Learn Negative Numbers

Below zero made simple, from thermometers to sign rules.

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Negative numbers are values less than zero, like a temperature of -5 degrees, a bank balance that is overdrawn or a depth below sea level. Together with zero and the positive whole numbers they make the integers. The ideas that trip people up are comparing them (-8 is less than -2) and the sign rules: subtracting a negative is the same as adding, and multiplying two negatives gives a positive. A number line, plus everyday examples like temperature and money, makes each rule sensible instead of arbitrary. Learnr builds a negative numbers course for students, adults and parents helping children, and teaches it in short interactive lessons.

How to learn Negative Numbers, step by step

Start with a thermometer and number line. Draw a vertical line from -10 to 10. Show that -8 sits below -2, so it is colder and smaller, even though 8 is bigger than 2.
Add by moving along the line. Start at the first number, move right for a positive and left for a negative. -7 + 3 means start at -7 and move 3 right, landing on -4.
Turn subtraction into adding the opposite. 3 - (-5) becomes 3 + 5, which is 8. A money story helps: removing a $5 debt leaves you $5 better off, which is exactly what subtracting a negative does.
Learn the sign rules for multiplying. Same signs give a positive, different signs give a negative: (-4)(-6) = 24 and (-4)(6) = -24. Show the pattern 3 times -2 = -6, 2 times -2 = -4, continuing down to -1 times -2 = 2.
Practice with mixed problems and contexts. Work problems like a temperature dropping from 4 degrees to -9 degrees, a change of 13 degrees. Mixing addition, subtraction and multiplication prevents applying the wrong rule.
Keep it fresh with short daily practice. Sign errors fade with steady use. A few minutes a day in a Learnr course, kept going by a streak, makes integer rules automatic before algebra arrives.

What you'll learn

Place and compare negative numbers on a number line
Add and subtract integers using movement on the line
Explain why subtracting a negative means adding
Multiply and divide integers using the sign rules
Use negatives in real contexts like temperature, money and elevation

What's inside your Negative Numbers course

A sample path Learnr builds for Negative Numbers. Your real course adapts to your goal and level.

1. Numbers below zero and the number line
2. Comparing and ordering integers
3. Adding integers
4. Subtracting integers
5. Multiplying and dividing integers
6. Absolute value and real-world problems

How long does it take to learn Negative Numbers?

Most students get comfortable with negative numbers in about 2 to 4 weeks of regular practice at 2 to 3 hours a week. Adults reviewing before algebra often need only a week or so.

What you need before you start

Addition, subtraction, multiplication and division with whole numbers, plus familiarity with a number line. No other math is needed.

Common mistakes to avoid

Ordering negatives like positives, so -9 is called bigger than -3. On the number line, the number further left is always smaller.
Applying the "two negatives make a positive" rule to addition. -3 + (-5) is -8, not 8; that rule is only for multiplying and dividing.
Dropping the parentheses around a negative, so 3 - (-5) is copied as 3 - 5 and the sign flip is lost.

How Learnr builds your course

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Negative Numbers questions, answered

Why does a negative times a negative make a positive?

Following the pattern -2 times 3, 2, 1, 0 gives -6, -4, -2, 0, increasing by 2 each step. Continuing to -1 and -2 gives 2 and 4. The rule keeps the distributive property working.

How can I explain negative numbers to a child?

Use a thermometer, an elevator going below the ground floor, or money owed. A number line on the floor that a child can walk along makes adding and subtracting physical and memorable.