What are Negative Numbers?

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Welcome to our What are Negative Numbers support page.

Hopefully all (or nearly all) your questions about negative numbers will be answered here!

We have also included an interactive app produced by PhET to help you understand this concept.

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What are Negative Numbers?

A negative number is a number that has a value of less than zero..
You can find negative numbers in different measurements, such as temperature, as well as money.
Fractions, decimals, percentages and just about any types of number can be negative.
-5 can be read as 'minus 5' or 'negative 5'. It means 5 below zero.

Examples of negative numbers

Here are some examples of negative numbers:

-5, -1.8, -200, - 2 ½ , -29, -0.327 are all negative numbers.

Negative Numbers in Real-life

Negative numbers can be quite tricky to understand, and in many contexts, they do not really make much sense.

For example, I can have 5 pencils in my hand, but can I hold -3 pencils? No that is not possible.

Likewise, I can count 12 ducks swimming in a pond, but can I count -7 ducks? No.

We have given some examples below of when negative numbers are used in real-life to help you understand what are negative numbers and why we need them.

TEMPERATURES

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If you are measuring temperatures in Celsius, then 0°C is the freezing point of water, and if the temperature falls below that then it is negative.

Temperatures in Fahrenheit can also be negative for very cold places such as the Arctic, Greenland, parts of Russia and Alaska.

The higher the negative value, the colder the temperature is, so -10°F is colder than -2°F, or -14°C is colder than -9°C.

MONEY

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If your bank account is in credit, it means that you have money in the bank that is yours.

If your bank account is in debit, or you are overdrawn, it means that you owe the bank money - this is a negative bank balance.

Example - if you have $100 of credit at the bank, but you also have a $500 loan then your balance is $100 - $500 = -$400. You owe the bank $400.

HEIGHT ABOVE SEA LEVEL

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We tend to measure the height of geographical features such as hills and mountains in terms of their height above sea level, which is 0.

Mount Everest is 29,031 ft (8849 m) above sea level.

The Dead Sea Depression in Israel is a land area which sits at 1355 ft (413 m) below sea level, so its height above sea level would be -1355 ft.

There are at least 33 other countries that have areas of land that lie below the height of the sea level.

POINT DIFFERENTIAL

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In many sports, we can look at the number of points a team has scored against the number of points a team has allowed. This gives us the point differential (or goal difference in soccer).

For example, San Francisco 49ers 55 - 10 win over Denver Broncos during Super Bowl XXIV on January 28, 1990. 45 point difference. The Denver Broncos would gain a -45 point difference from this match.

One of the worst point differentials in football history was in 1976, when Tampa Bay Buccaneers had a differential of -287, an average deficit of over 20 points per game!

What are Negative Numbers Explorer

This is a Integer Number Explorer app created by:

PhET Interactive Simulations University of Colorado Boulder https://phet.colorado.edu

It is a great app for exploring negative numbers and especially for comparing positive and negative numbers.

You can either choose 'Explorer' Mode for a real-life example of negative numbers relating to height above sea level, or you can go to 'Generic' Mode which involves comparing and sequencing positive and negative numbers on a number line.

Other Recommended Worksheets

Here are some of our other related worksheets you might want to look at.

Comparing negative numbers

How to compare negative numbers

When you are comparing with negative numbers, everything swaps around and becomes a little more complicated!

With negative numbers, the more negative the number is, the lower its value.

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As you go right along the number line, the values are increasing.

As you go left along the number line, the values are decreasing.

This means that any positive number (or even zero) will always be greater than any negative number.

Examples

0 > -3 this means 0 is greater than -3
-8 < -5 this means -8 is less than -5
-27 > -30 this means -27 is greater than -30
-26 < 2 this means -26 is less than 2

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Ordering Negative Numbers -10 to 10

Negative Number Lines

We have a selection of number lines, both filled and blank that have been designed to support learning and understanding with negative numbers.

One of our pages contains just negative number lines, the other page contains both positive and negative numbers.

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Number Lines with Negative and Positive Numbers

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Number Line Negative Numbers only

Randomly Generated Negative Number Worksheets

Our random worksheet generator will create a range of worksheets with values of your choice.

You can create your own unique worksheets complete with answers in seconds!

You can then choose to print or save your sheets for another time.

Adding Negative Numbers

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Adding Positive and Negative Numbers (randomly generated)

Subtracting Negative Numbers

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Subtracting Positive and Negative Numbers (randomly generated)

Adding & Subtracting Negative Numbers

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Adding and Subtracting Negative Numbers (randomly generated)

Multiplying Negative Numbers

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Negative Number Multiplication (randomly generated)

Dividing Negative Numbers

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Dividing Negative Numbers (randomly generated)

Multiplying & Dividing Negative Numbers

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Multiply and Divide Negative Numbers (randomly generated)

Negative Numbers Games

Take a look at our collection of negative numbers games.

We have a range of games of varying levels of difficulty.

Our games include:

counting backwards along a number line (easiest)
comparing and sequencing negative numbers
subtracting with negative answers
using all 4 operations to get a negative target number (hardest)

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Negative Numbers Games

Absolute Value and Opposite Numbers Worksheets

We have a selection of worksheets designed to help students learn about asbolute value.

Topics covered include:

absolute value and opposite numbers
comparing absolute values
absolute value arithmetic
solving absolute value equations

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Absolute Value Worksheets

We hope you have found this page useful, and helped you to understand and learn what are negative numbers. Please feel free to leave us any feedback using the Facebook comments below.

How to Print or Save these sheets

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