Negative Numbers

A negative number is a number whose value is always less than zero and it has a minus (-) sign before it. On a number line, negative numbers are represented on the left side of zero. For example, -6 and -15 are negative numbers. Let us learn more about negative numbers in this lesson.

What are Negative Numbers?

Negative numbers are numbers that have a minus sign as a prefix. They can be integers, decimals, or fractions. For example, -4, -15, -4/5, -0.5 are termed as negative numbers. Observe the figure given below which shows how negative numbers are placed on a number line .

Negative Numbers on a number line

Negative Integers

Negative integers are numbers that have a value less than zero. They do not include fractions or decimals. For example, -7, -10 are negative integers.

Rules for Negative Numbers

When the basic operations of addition, subtraction , multiplication, and division are performed on negative numbers, they follow a certain set of rules.

  • The sum of two negative numbers is a negative number. For example, -5 + (-1) = -6
  • The sum of a positive number and a negative number is the difference between two numbers. The sign of the bigger absolute value is placed before the result. For example, -9 + 3 = -6
  • The product of a negative number and a positive number is a negative number. For example, -9 × 2 = -18
  • The product of two negative numbers is a positive number. For example, -6 × -3 =18
  • While dividing negative numbers, if the signs are the same, the result is positive. For example, -56 ÷ -7 = 8
  • While dividing negative numbers, if the signs are different, the result is negative. For example, -32 ÷ 4 = -8

Adding and Subtracting Negative Numbers

For adding and subtracting negative numbers, we need to remember the following rules.

Addition of Negative Numbers

Case 1: When a negative number is added to a negative number, we add the numbers and use the negative sign in the answer. For example, -7 + (- 4) = -7 - 4 = -11. In other words, the sum of two negative numbers always results in a negative number.

This can be understood with the help of a number line. The number line rule says, " To add a negative number we move to the left on the number line ". Therefore, observe the following number line, and apply the rule on -7 + (- 4). We can see that when we start from -7 and move 4 numbers to the left, it brings us to -11.

Addition of negative numbers

Case 2: When a positive number is added to a negative number, we find their difference and use the sign of the larger absolute value in the answer. For example, -9 + (5) ⇒ - 4. Since we are using the sign of the greater absolute value, the answer is -4.

This can be understood better with the help of a number line. The number line rule says, " To add a positive number we move to the right on the number line ". Observe the following number line and apply the rule on -9 + (+5). We start from -9 and move 5 numbers to the right that brings us to -4.

Addition of negative numbers

Subtraction of Negative Numbers

The subtraction of negative numbers is similar to addition. We just need to remember a rule which says:

Rule of Subtraction: Change the operation from subtraction to addition, and change the sign of the second number that follows.

Case 1: When we need to subtract a positive number from a positive number, we follow the subtraction rule given above. For example, 5 - (+6) becomes 5 + (-6) = 5 - 6 = -1.

Now, if we apply the rule of the number line on 5 + (-6), to add a negative number, we move to the left. Therefore, we start with 5 and move 6 numbers to the left, which brings us to -1.

Subtraction of Negative Numbers

Case 2: When we need to subtract a positive number from a negative number, we will follow the same rule of subtraction which says:

For example, -3 - (+1), will become -3 + (-1). This can be simplified as -3 -1 = -4.

Now, if we apply the rule of the number line on -3 + (-1), to add a negative number we move to the left. Therefore, we start with -3 and move 1 number to the left, which brings us to -4.

Subtraction of Negative Numbers

Case 3: When we need to subtract a negative number from a negative number, we will follow the rule of subtraction:

For example, -9 - (-12) ⇒ -9 + 12 = 3. Here, 12 becomes positive. We use the sign of the bigger absolute value that is 12 and the answer is 3.

Multiplication and Division of Negative Numbers

There are two basic rules related to the multiplication and division of negative numbers.

Multiplying Positive and Negative Numbers

  • Rule 1: When the signs of the numbers are different, the result is negative. (-) × (+) = (-). In other words, when we multiply a negative number with a positive number, the product is always negative. For example, -3 × 6 = -18.
  • Rule 2: When the signs of the numbers are the same, the result is positive. (-) × (-) = (+); (+) × (+) = (+). In other words, when we multiply two negative or two positive numbers, the product is always positive. For example, -3 × - 6 = 18.

Dividing Positive and Negative Numbers

  • Rule 1: When we divide a negative number by a positive number, the result is always negative. (-) ÷ (+) = (-). For example, (-36) ÷ (4) = -9
  • Rule 2: When we divide a negative number by a negative number, the result is always positive. (-) ÷ (-) = (+) For example, (-24) ÷ (-4) = 6

Negative Integers With Exponents

There are two basic rules related to negative integers with exponents:

  • If a negative integer has an even number in the exponent, then the final product will always be a positive integer. For example, -4 6 = -4 × -4 × -4 × -4 × -4 × -4 = 4096
  • If a negative integer has an odd number in the exponent, then the final product will always be a negative integer. For example, -9 3 = -9 × -9 × -9 = -729

☛ Related Topics

  • Positive Rational Numbers
  • Natural Numbers
  • Whole Numbers
  • Real Numbers
  • Rational Numbers
  • Irrational Numbers
  • Counting Numbers

Negative Numbers Examples

Example 1: Add the given negative numbers.

a.) -45 and -78

b.) -90 and -67

a.) Since both -45 and -78 are negative numbers, we will add the negative integers and place a negative sign before the sum.

45 + 78 = 123

Now, we will place a minus sign before the sum. Thus, the answer is -123.

b.) To add -90 and -67, we will add the negative numbers and place a negative sign before the sum.

90 + 67 = 157

Now, we will place a minus sign before the sum. Thus, the answer is -157.

Example 2: Subtract the given negative integers: Subtract -5 from -8

When we need to subtract a negative number from a negative number, we will follow the rule of subtraction, ' Change the operation from subtraction to addition, and change the sign of the second number that follows.'

In this case, -8 - (-5) ⇒ -8 + 5 = -3.

Example 3: Simplify the negative integers:

a.) (-3) × (-2)

b.) -24 ÷ -3

a.) To multiply (-3) × (-2), we will multiply the given negative numbers and the sign of the product will be positive. Therefore, in this case, the product of (-3) × (-2) = 6

b.) In order to divide the negative numbers, (-24) ÷ (-3), we will divide them and the sign of the answer will be positive. In this case, (-24) ÷ (-3) = 8

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Practice Questions on Negative Numbers

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FAQs on Negative Numbers

What are negative numbers in math.

A negative number is a number whose value is always less than zero and it has a minus (-) sign before it. On a number line , negative numbers are shown to the left of zero. For example, - 2, - 3, - 4, - 5 are called negative numbers.

What are the Rules for Negative Numbers?

When the basic operations of addition , subtraction, multiplication , and division are performed on negative numbers, they follow a certain set of rules.

  • The sum of two negative numbers is a negative number. For example, -3 + (-1) = -4
  • The sum of a positive number and a negative number is the difference between the two numbers. The sign of the bigger absolute value is placed before the result. For example, -6 + 3 = -3
  • The product of a negative number and a positive number is always a negative number. For example, -5 × 2 = -10
  • The product of two negative numbers is a positive number. For example, -5 × -3 =15
  • While dividing negative numbers, if the signs are the same, the result is positive. For example, (-28) ÷ (-7) = 4
  • While dividing negative numbers, if the signs are different, the result is negative. For example, (-21) ÷ (3) = -7

What is the Sum of Two Negative Numbers?

The sum of two negative numbers is always a negative number. For example, (-7) + (-2) = -9

What are Negative Numbers used for?

There are situations in real life where we use numbers that are less than zero. Negative numbers are used to measure temperature. For example, the lowest possible temperature is absolute zero which is expressed as -273.15°C on the Celsius scale, and -459.67°F on the Fahrenheit scale. Negative numbers are also used to measure the geographical locations that are below the sea level and which are expressed in negative integers like -100 ft Mean Sea Level.

How to Multiply Negative Numbers?

There are two basic rules related to the multiplication of negative numbers.

  • Rule 1: When the signs of the numbers are different, the result is negative. In other words, when we multiply a negative number with a positive number, the product is always negative. For example, -2 × 6 = -12.
  • Rule 2: When the signs of the numbers are the same, the result is positive. In other words, when we multiply two negative or two positive numbers, the product is always positive. For example, -4 × - 6 = 24.

How to Divide Negative Numbers?

The rules that are applied for the multiplication of numbers are also used in the division of negative numbers.

  • Rule 1: When the signs of the numbers are different, the result is negative. In other words, when we divide a negative number with a positive number, the answer is always negative. For example, -12 ÷ 3 = -4.
  • Rule 2: When the signs of the numbers are the same, the result is positive. In other words, when we divide two negative numbers or two positive numbers, the answer is always positive. For example, -14 ÷ - 2 = 7.

What is the Difference Between Negative Integers and Positive Integers?

The main difference between negative integers and positive integers is that negative integers have a value less than zero and positive integers have a value greater than zero. It should be noted that zero is neither a positive integer nor a negative integer.

How do you Add Two Negative Integers?

Adding two negative integers together is easy because we just add the given numbers and then place a negative sign in front of the sum. For example, (-2) + (-5) = -7

What are the Rules For Subtracting Negative Numbers?

There is a basic rule for subtracting negative numbers. "Change the operation from subtraction to addition, and change the sign of the second number that follows". For example, let us subtract -2 - (-5). In this case, we change the operation from subtraction to addition and change the sign of (-5) to (+5). This makes it -2 + (+5) = -2 + 5 = 3.

How to Subtract Negative Numbers?

When we subtract negative numbers, we just need to remember a rule which says: Change the operation from subtraction to addition, and change the sign of the second number that follows. Now, let us apply this rule, for example, subtract 5 from -8. This means -8 - (5). After applying the rule, -8 - (5) becomes -8 + (-5) = -13.

Less than zero.

(Positive means more than zero. Zero is neither negative nor positive.)

A negative number is written with a minus sign in front

Example: −5 is negative five.

The word "negative" can be shortened to "−ve"

Try it yourself:

  • Negative numbers

When you first encounter negative numbers they can be perplexing. How can a bowl contain less than zero oranges? In fact, the counting numbers cannot be negative for this reason. It makes no sense.

But when we use scalar numbers , we are measuring something like temperature or height, negative values are useful. (See Uses of negative numbers .)

We take a fixed point and call that zero. Measurements one way are positive, and they are negative the other way. Zero is neither positive nor negative.

The  '–'  sign

Negative numbers are indicated by placing a dash ( – ) sign in front, such as –5, –12.77. A negative number such as –6 is spoken as 'negative six' .

It also means 'subtract'

An unfortunate thing in math is that the   ' – '   symbol is used for two different things. It signifies a negative number, as described above, but it also means 'subtract' or 'minus'. For example 5–3 means 'subtract 3 from 5' with a result of 2. Here, the minus-sign means subtraction.

So, when talking about a negative number such as –4, train yourself to say 'negative four'  to avoid the confusion. The same confusion happens with the plus ( + ) sign. See Positive numbers .

See also Doing arithmetic with positive and negative numbers .

--> Comparing numbers

Larger /smaller - watch out.

Avoid the words 'larger', 'bigger' and 'smaller' when comparing numbers. They can fool you.

For example is -1000 larger than -4?   It may look like it, but is not. -1000 is less than -4 because it is to the left on the number line. But when you use the word 'larger' you may think otherwise. Avoid these two words in math. Use 'less than' and 'greater than' instead.

Other number topics

  • Introduction to numbers
  • The number line

Scalar numbers

  • What are scalars?
  • Real numbers
  • Natural Numbers
  • Positive numbers
  • The uses of negative numbers
  • Scientific notation (normal form)
  • Complex numbers
  • Imaginary numbers

Counting numbers

  • Counting numbers (whole numbers)
  • Cardinal numbers
  • Cardinality
  • Ordinal numbers

Numbers that have factors

  • Prime numbers
  • Composite (opposite of prime) numbers
  • Rational numbers
  • Irrational numbers

Special values

Math Skills Overview Guide

Negative numbers, what does it mean,  what does it look like, you'll use it..., video: negative numbers introduction, practice problems.

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  • Introduction to Functions
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Definitions:

From Wolfram MathWorld:

  • Negative From Wolfram MathWorld

A general example to help you recognize patterns and spot the information you're looking for

Negative numbers are used to represent the amount of a loss or absence. For example, a debt that is owed may be thought of as a negative asset, or a decrease in some quantity may be thought of as a negative increase. Negative numbers are used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature.

  • Adding Negative Numbers
  • << Previous: Basic Operations
  • Next: Number Sets >>
  • Last Updated: Jul 7, 2023 12:00 PM
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Algebra Topics  - Negative Numbers

Algebra topics  -, negative numbers, algebra topics negative numbers.

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Algebra Topics: Negative Numbers

Lesson 3: negative numbers.

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What are negative numbers?

A negative number is any number that is less than zero. For instance, -7 is a number that is seven less than 0.

It might seem a little odd to say that a number is less than 0. After all, we often think of zero as meaning nothing . For instance, if you have 0 pieces of chocolate left in your candy bowl, you have no candy. There's nothing left. It's difficult to imagine having less than nothing in this case.

However, there are instances in real life where you use numbers that are less than zero. For example, have you ever been outside on a really cold winter day when the temperature was below zero? Any temperature below zero is a negative number. For instance, the temperature on this thermometer is -20 , or twenty degrees below zero.

negative 20 degrees on a thermometer

You can also use negative numbers for more abstract ideas. For instance, in finances negative numbers can be used to show debt . If I overdraw my account (take out more money than I actually have), my new bank balance will be a negative number . Not only will I have no money in the bank—I'll actually have less than none because I owe the bank money .

Watch the video below to learn more about negative numbers.

Any number without a minus sign in front of it is considered to be a positive number, meaning a number that's greater than zero. So while -7 is negative seven , 7 is positive seven , or simply seven .

Understanding negative numbers

As you might have noticed, you write negative numbers with the same symbol you use in subtraction: the minus sign ( - ). The minus sign doesn't mean you should think of a number like -4 as subtract four . After all, how would you subtract this?

You couldn't—because there's nothing to subtract it from. We can write -4 on its own precisely because it doesn't mean subtract 4 . It means the opposite of four.

Take a look at 4 and -4 on the number line:

negative four and four

You can think of a number line as having three parts: a positive direction, a negative direction, and zero . Everything to the right of zero is positive and everything to the left of zero is negative . We think of positive and negative numbers as being opposites because they are on opposite sides of the number line.

Another important thing to know about negative numbers is that they get smaller the farther they get from 0. On this number line, the farther left a number is, the smaller it is. So 1 is smaller than 3 . -2 is smaller than 1 , and -7 is smaller than -2 .

A number line showing how negative numbers get smaller the farther they get from zero, while positive numbers get larger.

Understanding absolute value

When we talk about the absolute value of a number, we are talking about that number's distance from 0 on the number line. Remember how we said 4 and -4 were the same distance from 0? That means 4 and -4 have the same absolute value. We represent taking the absolute value of a number with two straight vertical lines | | . For example, |-3| = 3 . This is read "the absolute value of negative three is three."

negative four and four have the same absolute value

Something important to remember: even though negative numbers get smaller as they get further from 0, their absolute value gets bigger . For example, -10 is smaller than -6. However, |-10| is bigger than |-6| because -10 has a greater distance from 0 than -6.

Calculating with negative numbers

Using negative numbers in arithmetic is fairly simple. There are just a few special rules to keep in mind.

Adding and subtracting negative numbers

When you're adding and subtracting negative numbers, it helps to think about a number line, at least at first. Let's take a look at this problem: 6 - 7 . Even though 7 is larger than 6, you can subtract it in the exact same way as any other number, as long as you understand there are numbers smaller than 0.

6 minus 7 is - 1

While the number line makes it easy to picture this problem, there's also a trick you could have used to solve it.

First, ignore the negative signs for a moment. Just find the difference between the two numbers. In this case, it means solving for 7 - 6 , which is 1 . Next, look at your original problem. Which number has the highest absolute value ? In this case, it's -7 . Because -7 is a negative number, our answer will be one too: -1 . Because the absolute value of -7 is greater than the distance between 6 and 0 , our answer ends up being less than 0 .

Adding negative numbers

How would you solve this problem?

Believe it or not, this is the exact same problem we just solved!

This is because the plus sign simply lets you know you're combining two numbers. When you combine a negative number with a positive one, the sum will be less than the original number—so you might as well be subtracting . So 6 + -7 is the same thing as 6 - 7 , and they both equal -1 .

6 + -7 = -1

Whenever you see a positive and negative sign next to each other, you should read it as a negative . Just like 6 + -7 is the same as 6 - 7:

  • 10 + -11 is equal to 10 - 11 .
  • 3 + -2 is equal to 3 - 2 .
  • 50 + -100 is equal to 50 -100 .

This is true whenever you're adding a negative number. Adding a negative number is always the same as subtracting that number's absolute value.

Subtracting negative numbers

If adding a negative number is actually equal to subtracting, how do you subtract a negative number? For example, how do you solve this problem?

If you guessed that you add them, you're right. Here's why: Remember how we said a negative number was the opposite of a positive one? We compared them to you and your mirror image. Your mirror image is your opposite, which means your mirror image's opposite is you . In other words, the opposite of your opposite is you .

In the same way, you can simplify these two minus signs by reading them as two negatives. The first minus sign negates —or makes negative—the second. Because the negative—or opposite—of a negative is a positive, you can replace both minus signs with a plus sign. This means you'd solve for this:

This is a lot easier, to solve, right? If it seems confusing, you can just remember this simple trick: When you see two minus signs back to back , replace them with a plus sign .

So 6 minus negative 3 is equal to 6 plus 3 . That's equal to 9 . In other words, 6 - -3 is 9 .

Remembering all of the rules for adding and subtracting numbers can be overwhelming. Watch the video below for a trick to help you.

Multiplying and dividing negative numbers

There are two rules for multiplying and dividing numbers:

  • If you're multiplying or dividing two numbers that are either both positive or both negative, your result will be positive .

negative seven times negative seven equals 49

  • If you're multiplying or dividing a positive number and a negative number, your result will be negative .

negative seven times seven equals negative 49

That's it! You multiply or divide as normal, then use these rules to determine whether the answer is positive or negative. For instance, take this problem, -3 ⋅ -4 . 3 ⋅ 4 is 12 . Because both numbers we multiplied were negative, the answer is positive : 12 .

-3 ⋅ -4 = 12

On the other hand, if we were to multiply 3 ⋅ -4 , we'd get a different answer:

3 ⋅ -4 = -12

Again, 3 ⋅ 4 is 12 . But because one of our multiples is negative and the other is positive , our answer must also be negative : -12 .

It works the same way for division. -40 / -10 is 4 because - 40 and -10 are both negatives . However, -40 / 10 is -4 because one number is negative and the other is positive .

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Mathematics LibreTexts

1.2: Negative Numbers

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  • Page ID 56840

  • Morgan Chase
  • Clackamas Community College via OpenOregon

Negative numbers are a fact of life, from winter temperatures to our bank accounts. Let’s practice evaluating expressions involving negative numbers.

Quality-and-Value.jpg

Absolute Value

The absolute value of a number is its distance from \(0\). You can think of it as the size of a number without identifying it as positive or negative. Numbers with the same absolute value but different signs, such as \(3\) and \(-3\), are called opposites . The absolute value of \(-3\) is \(3\), and the absolute value of \(3\) is also \(3\).

We use a pair of straight vertical bars to indicate absolute value; for example,\(|-3|=3\) and \(|3|=3\).

Exercises \(\PageIndex{1}\)

Evaluate each expression.

1. \(|-5|\)

Adding Negative Numbers

To add two negative numbers, add their absolute values (i.e., ignore the negative signs) and make the final answer negative.

Perform each addition.

3. \(-8+(-7)\)

4. \(-13+(-9)\)

To add a positive number and a negative number, we subtract the smaller absolute value from the larger. If the positive number has the larger absolute value, the final answer is positive. If the negative number has the larger absolute value, the final answer is negative.

5. \(7+(-3)\)

6. \(-7+3\)

7. \(14+(-23)\)

8. \(-14+23\)

9. The temperature at noon on a chilly Monday was \(-7\)°F. By the next day at noon, the temperature had risen \(25\)°F. What was the temperature at noon on Tuesday?

9. \(18\)°F

If an expression consists of only additions, we can break the rules for order of operations and add the numbers in whatever order we choose.

Evaluate each expression using any shortcuts that you notice.

10. \(-10+4+(-4)+3+10\)

11. \(-291+73+(-9)+27\)

Subtracting Negative Numbers

The image below shows part of a paystub in which an $ \(18\) payment needed to be made, but the payroll folks wanted to track the payment in the deductions category. Of course, a positive number in the deductions will subtract money away from the paycheck. Here, though, a deduction of negative \(18\) dollars has the effect of adding \(18\) dollars to the paycheck. Subtracting a negative amount is equivalent to adding a positive amount.

Paystub showing a deduction of negative 18 dollars

To subtract two signed numbers, we add the first number to the opposite of the second number.

Perform each subtraction.

12. \(5-2\)

13. \(2-5\)

14. \(-2-5\)

15. \(-5-2\)

16. \(2-(-5)\)

17. \(5-(-2)\)

18. \(-2-(-5)\)

19. \(-5-(-2)\)

20. One day in February, the temperature in Portland, Oregon is \(43\)°F, and the temperature in Portland, Maine is \(-12\)°F. What is the difference in temperature?

20. \(55\)°F difference

Multiplying Negative Numbers

Suppose you spend \(3\) dollars on a coffee every day. We could represent spending 3 dollars as a negative number, \(-3\) dollars. Over the course of a \(5\)-day work week, you would spend \(15\) dollars, which we could represent as \(-15\) dollars. This shows that \(-3\cdot5=-15\), or \(5\cdot-3=-15\).

LOL-coffee.jpg

If two numbers with opposite signs are multiplied, the product is negative.

Exercise \(\PageIndex{1}\)

Find each product.

21. \(-4\cdot3\)

22. \(5(-8)\)

Going back to our coffee example, we saw that \(5(-3)=-15\). Therefore, the opposite of \(5(-3)\) must be positive \(15\). Because \(-5\) is the opposite of \(5\), this implies that \(-5(-3)=15\).

If two numbers with the same sign are multiplied, the product is positive.

WARNING! These rules are different from the rules for addition; be careful not to mix them up.

23. \(-2(-9)\)

24. \(-3(-7)\)

Recall that an exponent represents a repeated multiplication. Let’s see what happens when we raise a negative number to an exponent.

25. \((-2)^2\)

26. \((-2)^3\)

27. \((-2)^4\)

28. \((-2)^5\)

If a negative number is raised to an odd power, the result is negative. If a negative number is raised to an even power, the result is positive.

Dividing Negative Numbers

Let’s go back to the coffee example we saw earlier: \(-3\cdot5=-15\). We can rewrite this fact using division and see that \(-15\div5=-3\); a negative divided by a positive gives a negative result. Also, \(-15\div-3=5\); a negative divided by a negative gives a positive result. This means that the rules for division work exactly like the rules for multiplication.

If two numbers with opposite signs are divided, the quotient is negative. If two numbers with the same sign are divided, the quotient is positive.

Find each quotient.

29. \(-42\div6\)

30. \(32\div(-8)\)

31. \(-27\div(-3)\)

32. \(0\div4\)

33. \(0\div(-4)\)

34. \(4\div0\)

34. undefined

Go ahead and check those last three exercises with a calculator. Any surprises?

  • 0 divided by another number is 0.
  • A number divided by 0 is undefined, or not a real number.

Here’s a quick explanation of why \(4\div0\) can’t be a real number. Suppose that there is a mystery number, which we’ll call \(n\), such that \(4\div0=n\). Then we can rewrite this division as a related multiplication, \(n\cdot0=4\). But because \(0\) times any number is \(0\), the left side of this equation is \(0\), and we get the result that \(0=4\), which doesn’t make sense. Therefore, there is no such number \(n\), and \(4\div0\) cannot be a real number.

Order of Operations with Negative Numbers

P : Work inside of parentheses or grouping symbols, following the order PEMDAS as necessary.

E : Evaluate exponents .

MD : Perform multiplications and divisions from left to right.

AS : Perform additions and subtractions from left to right.

Let’s finish up this module with some order of operations practice.

Evaluate each expression using the order of operations.

35. \((2-5)^2\cdot2+1\)

36. \(2-5^2\cdot(2+1)\)

37. \([7(-2)+16]\div2\)

38. \(7(-2)+16\div2\)

39. \(\dfrac{1-3^4}{2(5)}\)

40. \(\dfrac{(1-3)^4}{2}\cdot5\)

negative numbers maths definition

What are negative numbers?

A guide for negative numbers and their real-world applications

headshot of author Tess Loucka

Author Tess Loucka

negative numbers maths definition

Published January 22, 2024

negative numbers maths definition

Published Jan 22, 2024

  • Key takeaways
  • A negative number is any number smaller than zero.
  • Two negative signs next to each other can be replaced by one positive sign (+). 
  • When multiplying or dividing two numbers with the same sign, the result is positive. If the numbers have different signs, the result is negative.

Table of contents

Properties of negative numbers

Practice problems.

Have you ever woken up in the morning to see frost covering your window and snow piled high on the ground outside? Or maybe you’ve peeked into your freezer to see icicles hanging from the ceiling, and ice covering bags of frozen peas. In these instances, you may have looked at a thermometer wondering just how cold it is. Sometimes it’s so cold the number on the thermometer is less than 0 and the numbers turn into negatives. But what is a negative number anyways? 

We see numbers every day when reading the forecast, making purchases, or getting a score on a quiz, and they’re not always positive ! In our daily life, and in maths problems, we come across negative numbers all the time. 

So, let’s go over what negative numbers are and how they’re used. 

Negative numbers are any numbers smaller than zero. They are represented with a minus sign (-) followed by a digit, such as -3, -2, -1, etc. 

negative numbers

The highlighted side of the number line above is the negative numbers side. They are to the left of the 0 because they have a smaller value than 0. Those to the right of the 0 are positive numbers. They have a greater value than 0. 

As stated above, a negative number is any number smaller than zero. However, there are a few more properties of negative numbers that you should know. 

  • A negative number does not have to be a round number. Unlike integers which must be round numbers, negative numbers can be decimals or fractions, too.
  • Negative numbers are real numbers. Real numbers in maths include both rational and irrational numbers .
  • Negative numbers are not natural numbers. Natural numbers only refer to positive integers, not including 0.
  • Negative numbers are not whole numbers. Whole numbers only include positive integers and 0.

Examples of negative numbers in real life

We already mentioned that negative numbers appear on thermometers to show us that the temperature is “below zero”, but that’s not the only real-life example of negative numbers. 

Negative numbers are all around us! When we make purchases, the money or credit due is a negative number. Negative numbers also appear on elevation maps to indicate places that are “below sea level”. 

Negative numbers can be used as penalties in games, quizzes, and tests. When you get an answer wrong, you may get -5 points, meaning 5 points are being taken away from your total score. 

In sports, too, negative numbers can be used to denote the scores of teams. One great example is golf. The golfer with the lowest score, which represents the least amount of strokes, wins!

As you can see, there are many real-world applications of negative numbers. They may not be as common as positive numbers, but they’re just as important. 

Now, let’s go over the rules for working with negative numbers. 

Adding and subtracting negative numbers

When working with negative numbers in addition and subtraction problems, there are certain laws that you will find to always be true. Remember these laws to make solving problems with negative numbers in the future easy!

One tip for adding and subtracting negative numbers involves the number signs beside each digit (+ or -):

  • If the signs are the same, you can replace them with a plus sign (+). 
  • If the signs are different, you can replace them with a minus sign ( -).

negative number example

Adding negative numbers

When adding negative numbers , if the signs of the two numbers you are adding are the same, add the numbers together and keep the sign the same. 

-6 + -2 = -8 

Since + and – are next to each other in this problem, you can replace them with one negative sign (-). So, this problem can also be written as -6 – 2 = -8

If the signs of the two numbers are different, keep the sign of the greater absolute value. 

6 + -2 = 4 

Again, you can replace the + and – with one – sign. So, this problem can also be written as 6 – 2 = 4.

Subtracting negative numbers

When subtracting negative numbers , if the signs of the numbers are both negative, switch the two adjacent negative signs to a positive. 

-6 – (-2) = -4 can also be written as -6 + 2 = -4

If the signs of the numbers are different, switch the subtraction sign to an addition sign, and switch the sign of the second number. 

-6 – 2 = -8 becomes -6 + -2 = -8

-2 – 6 = -8 becomes -2 + -6 = -8

Multiplying and dividing negative numbers

The laws to remember when multiplying and dividing negative numbers are actually more straightforward than those for adding and subtracting them. 

All you need to know is that when multiplying or dividing numbers with the same sign, the result will be positive. If the signs are different, the result will be negative.

negative numbers maths definition

Multiplying negative numbers

When multiplying two negative numbers together, the result will be a positive number. 

-6 x -2 = 12 

When multiplying a positive number with a negative number, the result will be a negative number. 

6 x -2 = -12 

Dividing negative numbers

When dividing two negative numbers together, the result is a positive number. 

-6 ÷ -2 = 3

When dividing a positive number and a negative number, the result is a negative number.

6 ÷ -2 = -3 

The more examples of negative number equations you go over, the more comfortable you will be with working with negative numbers. A good maths app can provide you with as many examples as you need, as well as detailed solutions and explanations that make learning maths easy and fun.

Click on the boxes below to see the answers!

When subtracting negative numbers , remember that two negatives equal a positive. Change the two negative signs into a positive. -10 – (-4) becomes -10 + 4. You can use mental math or a number line to get -6 as your answer. 

Multiplying any two numbers with different signs results in a negative number. So, -4 x 5 is -20. 

 To add two negative numbers, add the digits together and keep the sign the same. So, -9 + -3 becomes -12 . You can also rewrite this as -9 – 3.

FAQs about negative numbers

negative numbers maths definition

Yes, negative numbers are real numbers.

Negative round numbers are integers , but any fractions or decimals are not.

No, negative numbers are not whole numbers . Whole numbers are only positive round numbers, including 0.

Most negative numbers are rational numbers . If a number can be written as a fraction, that means it is a rational number.

Group 208

Related Posts

What are Positive Numbers?

number line question

What are Number Lines?

what is a number line?

Even & Odd Numbers

prime numbers

Lesson credits

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Tess Loucka

Tess Loucka discovered her passion for writing in school and hasn't stopped writing since! Combined with her love of numbers, she became a maths and English tutor. Since graduating, her goal has been to use her writing to spread knowledge and the joy of learning to readers of all ages.

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Negative Numbers

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Level: Primary 6 / Grade 6 / PSLE

Here is a simple way that I use to explain Negative Numbers.

Before I introduce negative numbers to my students, I remind them of the number line. Numbers are usually written this way on a number line.

negative numbers maths definition

Things to note:

  • The line starts at 0
  • The numbers increase as you move to the right of the line

Now I show them the number line with negative numbers added to it.

negative numbers maths definition

  • The number line has to beginning and no ending, indicated by the arrow on both ends of the line
  • The negative numbers also increases digitally as you move to the left of the line, but the negative sign means the value of the number actually decreases

To help my students understand better, I tell them to think of negative numbers this way:

  • The negative sign tells you how far away the number is from the zero. 
  • So -3 means you are 3 steps away from 0 and -5 means you are 5 steps away from zero.
  • Therefore, -5 is smaller than -3 because you are further away from zero.

Adding and Subtracting with Negative Numbers

When it comes to using negative numbers in addition and subtraction, using a number line is crucial for understanding how it all works.

The first thing to understand is the difference in the meaning between the subtraction symbol (-) and the negative number symbol (-).  They both look the same but have different meanings. 

The subtraction symbol tells us which direction we want to go along the number line.  The negative symbol applies only to the number it is paired with.

The other thing to note is that the addition symbol (+) tells us to move to the right of the number line while the subtraction symbol (-) tells us to move to the left of the number line.

Let's look at some examples. Here is the number line again.

Let's find the answer to: 1 subtract 3. 

We write it as: 1 - 3.  The subtraction tells us to move to the left on the number line.

Starting at number 1, move 3 steps to the left on the number line. You will end up at negative two.

So,  1 - 3 = -2

Here is another way to look at it.

If I have 1 cookie (1) and I want to give you 3 cookies (-3), that means I owe you 2 cookies (-2).  The negative sign means I owe you.

Let's try another example. 

Find the answer to -1 plus 3. 

We write it as: -1 + 3.  The plus or addition sign tells us to move to the right on the number line.

Starting at -1, move 3 steps to the right on the number line.  You will end up at 2.

So,  -1 + 3 = 2

Here is the alternative explanation.

I owe you 1 cookie (-1).  Someone else gives me 3 cookies (+3).  I have to give you what I owe so I end up with only 2 cookies.

Try a few more yourself.  Remember: To add - move to the right.  To subtract - move to the left.  Or think in terms of giving or receiving cookies.

  •  -2 + 5
  •   3 - 5
  •   0 - 3
  •   -1 - 2

Exceptions to the Rule

When a negative number comes after the addition or subtraction sign, it means you have to reverse the normal direction. 

That is, if a negative number comes after the addition sign, it means you move to the left instead of the right on the number line.

Vice versa, if a negative number comes after the subtraction sign, it means you move to the right instead of to the left on the number line.

Let's look at the example below.

You start at the number 2.  Then you move 2 steps to the left instead of the right and end up at 0.

This means that 2 + (-2) is the same as 2 - 2 which gives the answer 0.

2 + (-2) = 0

Here is another example. Let's find the answer to (-3) - (-1).

Start at -3. Then move 1 step to the right instead of the left. You will end up at -2.

So, -3 - (-1) is the same as -3 + 1  which gives the answer -2

-3 - (-1) = -2

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The term "negative," in a mathematical context, refers to real numbers that are less than zero. Negative numbers are the opposite of positive numbers. For example, if zero were to represent a starting point, traveling towards a destination would represent a positive number, while traveling farther away from the destination would represent a negative number. Another common use of negative numbers can be seen with money. Money paid to you is a positive number while money you pay to someone else would be a negative number.

A negative number is indicated using "-" in front of the number. Positive numbers can technically be indicated using a "+", but by convention, positive numbers are written without the plus sign in front of them. Any number without a minus sign is assumed to be positive. Thus, 5 is positive (plus) five, while -5 is negative (minus) five. Typically, the number 0 is considered neither positive nor negative.

Conceptualizing negative numbers

There a number of ways to think about negative numbers. One such way is using a number line. It may be easier to conceptualize negative numbers by seeing them as the counterpart of positive numbers on the other side of zero on the number line:

negative numbers maths definition

Another way is through using subtraction to get a sense of the relative size of numbers. For example, the problem

tells us that the difference between 12 and 4 is 8. We can then extend this to the problem

and conclude that since the difference between 12 and 4 is 8, the difference should remain the same, but negative, since 12 is larger than 4. Thus,

4 - 12 = -8

negative numbers maths definition

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Negative integers.

Negative integers are numbers having values less than 0 and thus have a negative sign before them. Being an integer, they do not include a fraction or a decimal.

It starts from -1, the largest negative integer, and goes on endlessly. Thus {….- 5, -4, -3, -2, -1} is a set of negative numbers.

negative numbers maths definition

Thus, when represented on a number line, they are usually drawn on the left of zero.

Negative integers are widely used in different fields such as banking and finance for calculating profit and loss, science and medicine for showing temperature, calibrating instruments, and measuring blood pressure, body weight, and medical tests.

They are also used to calculate goal differences in sports such as football, hockey, and basketball.

There are some rules followed while performing basic operations involving negative integers.

Adding Integers

Adding Like Signs

When adding a negative integer with a negative integer, we add the numbers and give the sign of the original values. Thus, we move to the left of the number line.

For example, (-4) + (-2) = -6

When represented on a number line, we get:

negative numbers maths definition

Adding Unlike Signs

When adding a positive and a negative integer, we subtract one number from the other number and provide the sign of the larger absolute value.

For example,

(+4) + (-8) = -4

When represented on a number line, we move to its left:

negative numbers maths definition

Again, (-4) + (+8) = +4

When represented on a number line, we move to its right:

negative numbers maths definition

Subtracting Integers

Subtracting a Positive Number from a Negative Number

When subtracting a positive number, it is the same as adding the negative value of that number.

For example, (-6) – (+4) is equivalent to (-6) + (-4) = -10

When represented on a number line, we get

negative numbers maths definition

Subtracting a Negative Number from a Positive Number

When subtracting a negative number, it is the same as adding the positive of that number.

For example, (+6) – (-4) is equivalent to (+6) + (+4) = +10

negative numbers maths definition

Subtracting a Negative Number from a Negative Number

When subtracting a negative number from a negative number is same as adding a positive number to a negative. It is nothing but subtraction between the two numbers and giving the sign of the greater number.

For example, (-8) – (-2) is equivalent to (-8) + (+2) = -6

negative numbers maths definition

Multiplying and Dividing Integers

Multiplication or division of negative numbers with a like sign gives a result with a positive sign before it.

 (-6) × (-2) = 12

 (-6) ÷ (-2) = 3

The multiplication or division of numbers with unlike signs (positive with a negative number or vice versa) gives a result with a negative sign before it.

(-6) × (+2) = -12

(+6) × (-2) = -12

(-6) ÷ (+2) = -3

(+6) ÷ (-2) = -3

Solved Examples

Add: a) (-20) + (-7) b) (+11) + (-5)   c) (-16) – (+4) d) (-8) – (+10)   e) (+6) – (-4)

a) (-20) + (-7) = -27 b) (+11) + (-5) = +6 c) (-16) – (+4)= -20 d) (-8) – (+10) = (-8) + (-10) = -18 e) (+10) – (-9) =(+10) + (+9) = +19

Simplify: a) (-9) × (-7) b) (-24) ÷ (-3)

a) (-9) × (-7) = +63 b) (-24) ÷ (-3) = +8

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This is a glossary of common mathematical terms used in arithmetic, geometry, algebra, and statistics.

Abacus : An early counting tool used for basic arithmetic.

Absolute Value : Always a positive number, absolute value refers to the distance of a number from 0.

Acute Angle : An angle whose measure is between 0° and 90° or with less than 90° (or pi/2) radians.

Addend : A number involved in an addition problem; numbers being added are called addends.

Algebra : The branch of mathematics that substitutes letters for numbers to solve for unknown values.

Algorithm : A procedure or set of steps used to solve a mathematical computation.

Angle : Two rays sharing the same endpoint (called the angle vertex).

Angle Bisector : The line dividing an angle into two equal angles.

Area : The two-dimensional space taken up by an object or shape, given in square units.

Array : A set of numbers or objects that follow a specific pattern.

Attribute : A characteristic or feature of an object—such as size, shape, color, etc.—that allows it to be grouped.

Average : The average is the same as the mean. Add up a series of numbers and divide the sum by the total number of values to find the average.

Base : The bottom of a shape or three-dimensional object, what an object rests on.

Base 10 : Number system that assigns place value to numbers.

Bar Graph : A graph that represents data visually using bars of different heights or lengths.

BEDMAS or PEMDAS Definition : An acronym used to help people remember the correct order of operations for solving algebraic equations. BEDMAS stands for "Brackets, Exponents, Division, Multiplication, Addition, and Subtraction" and PEMDAS stands for "Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction".

Bell Curve : The bell shape created when a line is plotted using data points for an item that meets the criteria of normal distribution. The center of a bell curve contains the highest value points.

Binomial : A polynomial equation with two terms usually joined by a plus or minus sign.

Box and Whisker Plot/Chart : A graphical representation of data that shows differences in distributions and plots data set ranges.

Calculus : The branch of mathematics involving derivatives and integrals, Calculus is the study of motion in which changing values are studied.

Capacity : The volume of substance that a container will hold.

Centimeter : A metric unit of measurement for length, abbreviated as cm. 2.5 cm is approximately equal to an inch.

Circumference : The complete distance around a circle or a square.

Chord : A segment joining two points on a circle.

Coefficient : A letter or number representing a numerical quantity attached to a term (usually at the beginning). For example, x is the coefficient in the expression x (a + b) and 3 is the coefficient in the term 3 y.

Common Factors : A factor shared by two or more numbers, common factors are numbers that divide exactly into two different numbers.

Complementary Angles: Two angles that together equal 90°.

Composite Number : A positive integer with at least one factor aside from its own. Composite numbers cannot be prime because they can be divided exactly.

Cone : A three-dimensional shape with only one vertex and a circular base.

Conic Section : The section formed by the intersection of a plane and cone.

Constant : A value that does not change.

Coordinate : The ordered pair that gives a precise location or position on a coordinate plane.

Congruent : Objects and figures that have the same size and shape. Congruent shapes can be turned into one another with a flip, rotation, or turn.

Cosine : In a right triangle, cosine is a ratio that represents the length of a side adjacent to an acute angle to the length of the hypotenuse.

Cylinder : A three-dimensional shape featuring two circle bases connected by a curved tube.

Decagon : A polygon/shape with ten angles and ten straight lines.

Decimal : A real number on the base ten standard numbering system.

Denominator : The bottom number of a fraction. The denominator is the total number of equal parts into which the numerator is being divided.

Degree : The unit of an angle's measure represented with the symbol °.

Diagonal : A line segment that connects two vertices in a polygon.

Diameter : A line that passes through the center of a circle and divides it in half.

Difference : The difference is the answer to a subtraction problem, in which one number is taken away from another.

Digit : Digits are the numerals 0-9 found in all numbers. 176 is a 3-digit number featuring the digits 1, 7, and 6.

Dividend : A number being divided into equal parts (inside the bracket in long division).

Divisor : A number that divides another number into equal parts (outside of the bracket in long division).

Edge : A line is where two faces meet in a three-dimensional structure.

Ellipse : An ellipse looks like a slightly flattened circle and is also known as a plane curve. Planetary orbits take the form of ellipses.

End Point : The "point" at which a line or curve ends.

Equilateral : A term used to describe a shape whose sides are all of equal length.

Equation : A statement that shows the equality of two expressions by joining them with an equals sign.

Even Number : A number that can be divided or is divisible by 2.

Event : This term often refers to an outcome of probability; it may answers question about the probability of one scenario happening over another.

Evaluate : This word means "to calculate the numerical value".

Exponent : The number that denotes repeated multiplication of a term, shown as a superscript above that term. The exponent of 3 4 is 4.

Expressions : Symbols that represent numbers or operations between numbers.

Face : The flat surfaces on a three-dimensional object.

Factor : A number that divides into another number exactly. The factors of 10 are 1, 2, 5, and 10 (1 x 10, 2 x 5, 5 x 2, 10 x 1).

Factoring : The process of breaking numbers down into all of their factors.

Factorial Notation : Often used in combinatorics, factorial notations requires that you multiply a number by every number smaller than it. The symbol used in factorial notation is ! When you see x !, the factorial of x is needed.

Factor Tree : A graphical representation showing the factors of a specific number.

Fibonacci Sequence : A sequence beginning with a 0 and 1 whereby each number is the sum of the two numbers preceding it. "0, 1, 1, 2, 3, 5, 8, 13, 21, 34..." is a Fibonacci sequence.

Figure : Two-dimensional shapes.

Finite : Not infinite; has an end.

Flip : A reflection or mirror image of a two-dimensional shape.

Formula : A rule that numerically describes the relationship between two or more variables.

Fraction : A quantity that is not whole that contains a numerator and denominator. The fraction representing half of 1 is written as 1/2.

Frequency : The number of times an event can happen in a given period of time; often used in probability calculations.

Furlong : A unit of measurement representing the side length of one square acre. One furlong is approximately 1/8 of a mile, 201.17 meters, or 220 yards.

Geometry : The study of lines, angles, shapes, and their properties. Geometry studies physical shapes and the object dimensions.

Graphing Calculator : A calculator with an advanced screen capable of showing and drawing graphs and other functions.

Graph Theory : A branch of mathematics focused on the properties of graphs.

Greatest Common Factor : The largest number common to each set of factors that divides both numbers exactly. The greatest common factor of 10 and 20 is 10.

Hexagon : A six-sided and six-angled polygon.

Histogram : A graph that uses bars that equal ranges of values.

Hyperbola : A type of conic section or symmetrical open curve. The hyperbola is the set of all points in a plane, the difference of whose distance from two fixed points in the plane is a positive constant.

Hypotenuse : The longest side of a right-angled triangle, always opposite to the right angle itself.

Identity : An equation that is true for variables of any value.

Improper Fraction : A fraction whose numerator is equal to or greater than the denominator, such as 6/4.

Inequality : A mathematical equation expressing inequality and containing a greater than (>), less than (<), or not equal to (≠) symbol.

Integers : All whole numbers, positive or negative, including zero.

Irrational : A number that cannot be represented as a decimal or fraction. A number like pi is irrational because it contains an infinite number of digits that keep repeating. Many square roots are also irrational numbers.

Isosceles : A polygon with two sides of equal length.

Kilometer : A unit of measure equal to 1000 meters.

Knot : A closed three-dimensional circle that is embedded and cannot be untangled.

Like Terms : Terms with the same variable and same exponents/powers.

Like Fractions : Fractions with the same denominator.

Line : A straight infinite path joining an infinite number of points in both directions.

Line Segment : A straight path that has two endpoints, a beginning and an end.

Linear Equation : An equation that contains two variables and can be plotted on a graph as a straight line.

Line of Symmetry : A line that divides a figure into two equal shapes.

Logic : Sound reasoning and the formal laws of reasoning.

Logarithm : The power to which a base must be raised to produce a given number. If nx = a , the logarithm of a , with n as the base, is x . Logarithm is the opposite of exponentiation.

Mean : The mean is the same as the average. Add up a series of numbers and divide the sum by the total number of values to find the mean.

Median : The median is the "middle value" in a series of numbers ordered from least to greatest. When the total number of values in a list is odd, the median is the middle entry. When the total number of values in a list is even, the median is equal to the sum of the two middle numbers divided by two.

Midpoint : A point that is exactly halfway between two locations.

Mixed Numbers : Mixed numbers refer to whole numbers combined with fractions or decimals. Example 3 1 / 2 or 3.5.

Mode : The mode in a list of numbers are the values that occur most frequently.

Modular Arithmetic : A system of arithmetic for integers where numbers "wrap around" upon reaching a certain value of the modulus.

Monomial : An algebraic expression made up of one term.

Multiple : The multiple of a number is the product of that number and any other whole number. 2, 4, 6, and 8 are multiples of 2.

Multiplication : Multiplication is the repeated addition of the same number denoted with the symbol x. 4 x 3 is equal to 3 + 3 + 3 + 3.

Multiplicand : A quantity multiplied by another. A product is obtained by multiplying two or more multiplicands.

Natural Numbers : Regular counting numbers.

Negative Number : A number less than zero denoted with the symbol -. Negative 3 = -3.

Net : A two-dimensional shape that can be turned into a two-dimensional object by gluing/taping and folding.

Nth Root : The n th root of a number is how many times a number needs to be multiplied by itself to achieve the value specified. Example: the 4th root of 3 is 81 because 3 x 3 x 3 x 3 = 81.

Norm : The mean or average; an established pattern or form.

Normal Distribution : Also known as Gaussian distribution, normal distribution refers to a probability distribution that is reflected across the mean or center of a bell curve.

Numerator : The top number in a fraction. The numerator is divided into equal parts by the denominator.

Number Line : A line whose points correspond to numbers.

Numeral : A written symbol denoting a number value.

Obtuse Angle : An angle measuring between 90° and 180°.

Obtuse Triangle : A triangle with at least one obtuse angle.

Octagon : A polygon with eight sides.

Odds : The ratio/likelihood of a probability event happening. The odds of flipping a coin and having it land on heads are one in two.

Odd Number : A whole number that is not divisible by 2.

Operation : Refers to addition, subtraction, multiplication, or division.

Ordinal : Ordinal numbers give relative position in a set: first, second, third, etc.

Order of Operations : A set of rules used to solve mathematical problems in the correct order. This is often remembered with acronyms BEDMAS and PEMDAS.

Outcome : Used in probability to refer to the result of an event.

Parallelogram : A quadrilateral with two sets of opposite sides that are parallel.

Parabola : An open curve whose points are equidistant from a fixed point called the focus and a fixed straight line called the directrix.

Pentagon : A five-sided polygon. Regular pentagons have five equal sides and five equal angles.

Percent : A ratio or fraction with the denominator 100.

Perimeter : The total distance around the outside of a polygon. This distance is obtained by adding together the units of measure from each side.

Perpendicular : Two lines or line segments intersecting to form a right angle.

Pi : Pi is used to represent the ratio of a circumference of a circle to its diameter, denoted with the Greek symbol π.

Plane : When a set of points join together to form a flat surface that extends in all directions, this is called a plane.

Polynomial : The sum of two or more monomials.

Polygon : Line segments joined together to form a closed figure. Rectangles, squares, and pentagons are just a few examples of polygons.

Prime Numbers : Prime numbers are integers greater than 1 that are only divisible by themselves and 1.

Probability : The likelihood of an event happening.

Product : The sum obtained through multiplication of two or more numbers.

Proper Fraction : A fraction whose denominator is greater than its numerator.

Protractor : A semi-circle device used for measuring angles. The edge of a protractor is subdivided into degrees.

Quadrant : One quarter ( qua) of the plane on the Cartesian coordinate system. The plane is divided into 4 sections, each called a quadrant.

Quadratic Equation : An equation that can be written with one side equal to 0. Quadratic equations ask you to find the quadratic polynomial that is equal to zero.

Quadrilateral : A four-sided polygon.

Quadruple : To multiply or to be multiplied by 4.

Qualitative : Properties that must be described using qualities rather than numbers.

Quartic : A polynomial having a degree of 4.

Quintic : A polynomial having a degree of 5.

Quotient : The solution to a division problem.

Radius : A distance found by measuring a line segment extending from the center of a circle to any point on the circle; the line extending from the center of a sphere to any point on the outside edge of the sphere.

Ratio : The relationship between two quantities. Ratios can be expressed in words, fractions, decimals, or percentages. Example: the ratio given when a team wins 4 out of 6 games is 4/6, 4:6, four out of six, or ~67%.

Ray : A straight line with only one endpoint that extends infinitely.

Range : The difference between the maximum and minimum in a set of data.

Rectangle : A parallelogram with four right angles.

Repeating Decimal : A decimal with endlessly repeating digits. Example: 88 divided by 33 equals 2.6666666666666...("2.6 repeating").

Reflection : The mirror image of a shape or object, obtained from flipping the shape on an axis.

Remainder : The number left over when a quantity cannot be divided evenly. A remainder can be expressed as an integer, fraction, or decimal.

Right Angle : An angle equal to 90°.

Right Triangle : A triangle with one right angle.

Rhombus : A parallelogram with four sides of equal length and no right angles.

Scalene Triangle : A triangle with three unequal sides.

Sector : The area between an arc and two radii of a circle, sometimes referred to as a wedge.

Slope : Slope shows the steepness or incline of a line and is determined by comparing the positions of two points on the line (usually on a graph).

Square Root : A number squared is multiplied by itself; the square root of a number is whatever integer gives the original number when multiplied by itself. For instance, 12 x 12 or 12 squared is 144, so the square root of 144 is 12.

Stem and Leaf : A graphic organizer used to organize and compare data. Similar to a histogram, stem and leaf graphs organize intervals or groups of data.

Subtraction : The operation of finding the difference between two numbers or quantities by "taking away" one from the other.

Supplementary Angles : Two angles are supplementary if their sum is equal to 180°.

Symmetry : Two halves that match perfectly and are identical across an axis.

Tangent : A straight line touching a curve from only one point.

Term : Piece of an algebraic equation; a number in a sequence or series; a product of real numbers and/or variables.

Tessellation : Congruent plane figures/shapes that cover a plane completely without overlapping.

Translation : A translation, also called a slide, is a geometrical movement in which a figure or shape is moved from each of its points the same distance and in the same direction.

Transversal : A line that crosses/intersects two or more lines.

Trapezoid : A quadrilateral with exactly two parallel sides.

Tree Diagram : Used in probability to show all possible outcomes or combinations of an event.

Triangle : A three-sided polygon.

Trinomial : A polynomial with three terms.

Unit : A standard quantity used in measurement. Inches and centimeters are units of length, pounds and kilograms are units of weight, and square meters and acres are units of area.

Uniform : Term meaning "all the same". Uniform can be used to describe size, texture, color, design, and more.

Variable : A letter used to represent a numerical value in equations and expressions. Example: in the expression 3 x + y , both y and x are the variables.

Venn Diagram : A Venn diagram is usually shown as two overlapping circles and is used to compare two sets. The overlapping section contains information that is true of both sides or sets and the non-overlapping portions each represent a set and contain information that is only true of their set.

Volume : A unit of measure describing how much space a substance occupies or the capacity of a container, provided in cubic units.

Vertex : The point of intersection between two or more rays, often called a corner. A vertex is where two-dimensional sides or three-dimensional edges meet.

Weight : The measure of how heavy something is.

Whole Number : A whole number is a positive integer.

X-Axis : The horizontal axis in a coordinate plane.

X-Intercept : The value of x where a line or curve intersects the x-axis.

X : The Roman numeral for 10.

x : A symbol used to represent an unknown quantity in an equation or expression.

Y-Axis : The vertical axis in a coordinate plane.

Y-Intercept : The value of y where a line or curve intersects the y-axis.

Yard : A unit of measure that is equal to approximately 91.5 centimeters or 3 feet.

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IMAGES

  1. Negative Numbers: Definition, Uses, Properties, Operations, Examples

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  2. Negative Numbers

    negative numbers maths definition

  3. Negative Numbers: Definition, Uses, Properties, Operations, Examples

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  4. Negative Numbers

    negative numbers maths definition

  5. Negative Numbers

    negative numbers maths definition

  6. What is a Negative Number- Definition and Examples

    negative numbers maths definition

VIDEO

  1. #std8#part 1#negative numbers #maths #English medium

  2. Adding a Negative Value

  3. Negative Numbers

  4. Positive/ Negative Numbers|Integers|Addition|Subtraction|Multiplication|Division|Maths in Malayalam

  5. multiplication of root negative numbers #mathematics #solving #video

  6. Positive& Negative numbers//Addition& Subtraction of Algebra #trending#viral #algebra

COMMENTS

  1. Negative Numbers

    A negative number is a number whose value is always less than zero and it has a minus (-) sign before it. On a number line, negative numbers are represented on the left side of zero. For example, -6 and -15 are negative numbers. Let us learn more about negative numbers in this lesson. What are Negative Numbers?

  2. Intro to negative numbers (article)

    Negative numbers help us describe values less than zero. Example: When the temperature is 8 ∘ below 0 ∘ , it is less than 0 . We can say the temperature is − 8 ∘ . 0 5 − 5 − 8 ∘ A few more negative situations Problem 2A A bank uses positive numbers to represent deposits and negative numbers to represent withdrawals.

  3. Negative numbers

    Arithmetic (all content) Unit 4: Negative numbers About this unit Learn about numbers below 0 and how they relate to positive numbers. Add, subtract, multiply and divide negative numbers. Intro to negative numbers Learn Intro to negative numbers Intro to negative numbers Practice Interpreting negative numbers 7 questions

  4. Negative Definition (Illustrated Mathematics Dictionary)

    more ... Less than zero. (Positive means more than zero. Zero is neither negative nor positive.) A negative number is written with a minus sign in front Example: −5 is negative five. The word "negative" can be shortened to "−ve" Try it yourself: Adding and Subtracting Positive and Negative Numbers

  5. Negative number definition

    Negative numbers are numbers that are less than zero. When you first encounter negative numbers they can be perplexing. How can a bowl contain less than zero oranges? In fact, the counting numbers cannot be negative for this reason. It makes no sense.

  6. Intro to negative numbers (video)

    11 years ago Is -1 more or less than 0.1 • 2 comments ( 359 votes) Upvote Downvote Flag Infiltration 10 years ago -1 is a negative number, which makes it less than any other positive number. 0.1 is positive, so 0.1 is greater than -1. You can compare then to zero like this: -1 < 0 < 0.1.

  7. Library Guides: Math Skills Overview Guide: Negative Numbers

    What does it look like? A general example to help you recognize patterns and spot the information you're looking for $120 + (−$70) = $50 $ 120 + ( − $ 70) = $ 50 You'll use it... Negative numbers are used to represent the amount of a loss or absence.

  8. Algebra Topics: Negative Numbers

    A negative number is any number that is less than zero. For instance, -7 is a number that is seven less than 0. -7 It might seem a little odd to say that a number is less than 0. After all, we often think of zero as meaning nothing. For instance, if you have 0 pieces of chocolate left in your candy bowl, you have no candy. There's nothing left.

  9. 1.2: Negative Numbers

    Negative numbers are a fact of life, from winter temperatures to our bank accounts. In this module, you will learn how to evaluate expressions involving negative numbers, using the rules of arithmetic and order of operations. This is a basic skill that you will need for many other topics in mathematics and science.

  10. What are negative numbers?

    Negative numbers are any numbers smaller than zero. They are represented with a minus sign (-) followed by a digit, such as -3, -2, -1, etc. The highlighted side of the number line above is the negative numbers side. They are to the left of the 0 because they have a smaller value than 0. Those to the right of the 0 are positive numbers.

  11. Introduction to Negative Numbers

    So, -7 is 7 less than 0. 0 - 7 = -7. Any number with a negative sign in front is a negative number. -10, -20, and -1 are all examples of negative numbers. For every positive number, there is an ...

  12. Negative number

    In mathematics, a negative number represents an opposite. [1] In the real number system, a negative number is a number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset.

  13. Negative Numbers

    The negative sign tells you how far away the number is from the zero. So -3 means you are 3 steps away from 0 and -5 means you are 5 steps away from zero. Therefore, -5 is smaller than -3 because you are further away from zero. Adding and Subtracting with Negative Numbers . When it comes to using negative numbers in addition and subtraction ...

  14. Negative numbers

    Proficient Familiar Attempted Not started Quiz Unit test About this unit Negative numbers are a necessary part of our understanding of mathematics and the world. Negative does not mean "bad." It's just changing the same amount, but in the opposite direction, like getting cooler instead of warmer.

  15. Negative Numbers

    A negative number is one that falls below, or to the left of, 0 on a number line. Negative numbers are used frequently in math and science and therefore being able to add, subtract,...

  16. Negative

    Negative. The term "negative," in a mathematical context, refers to real numbers that are less than zero. Negative numbers are the opposite of positive numbers. For example, if zero were to represent a starting point, traveling towards a destination would represent a positive number, while traveling farther away from the destination would represent a negative number.

  17. negative numbers: Definition, Negative Integers with Exponents and

    What are Negative Numbers? A real quantity with a value less than zero ( < 0 ) is said to be negative. Negative numbers are indicated by a minus sign in front of the corresponding positive number, for example -5, -175. The negative numbers are indicated on the number line to the left of the origin.

  18. What are negative numbers?

    Activity 1 Activity 2 What are negative numbers? Numbers don't just stop at zero. When you count backwards from zero, you go into negative numbers. Positive numbers are more than zero:...

  19. negative number

    Negative - Negative = Negative + Positive. • use the larger number and its sign, subtract. Multiplication (x) Positive x Positive = Positive. Negative x Negative = Positive. Negative x Positive = Negative. Positive x Negative = Negative. • change double negatives to a positive.

  20. Negative Integers

    Negative integers are numbers having values less than 0 and thus have a negative sign before them. Being an integer, they do not include a fraction or a decimal. It starts from -1, the largest negative integer, and goes on endlessly. Thus {….- 5, -4, -3, -2, -1} is a set of negative numbers. Negative Integers (Numbers)

  21. Negative numbers

    The idea of anything "negative" is often seen as "bad." Negative numbers are not only good, but they're fun! Walk through this tutorial with us and we'll show you how they are defined, interpreted, and applied. Absolute value is a type of negative number that is expressed as a positive. Confused? Don't be. We got your back.

  22. Math Glossary: Mathematics Terms and Definitions

    This is a glossary of math definitions for common and important mathematics terms used in arithmetic, geometry, and statistics. ... Integers: All whole numbers, positive or negative, including zero. Irrational: A number that cannot be represented as a decimal or fraction. A number like pi is irrational because it contains an infinite number of ...

  23. Multiplying negative numbers review (article)

    Naga Sadow. Multiplying and dividing negatives are the same because there is no difference between those sides of zero except the side of zero. So, when you multiply or divide negatives, you are basically multiplying positives with minus signs behind them. Don't forget that the product of 2 negative numbers is always a positive.