# Negative Numbers - Definition, Rules, Examples (2023)

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.

 1 What are Negative Numbers? 2 Rules for Negative Numbers 3 Adding and Subtracting Negative Numbers 4 Multiplication and Division of Negative Numbers 5 FAQs on Negative Numbers

## 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 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.

(Video) Negative Numbers: An Overview

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. 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. ### 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.

(Video) Math Antics - Negative Numbers

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

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

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

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

(Video) Learn The Positive and Negative Numbers – Easy TIP To Remember The Rules!

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, -46 = -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, -93 = -9 × -9 × -9 = -729

☛ Related Topics

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

## 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.

(Video) Understand and Learn the Rules of Positive and Negative Numbers

• 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.

## FAQs

### What are the rules of negative numbers? ›

Negative numbers are written with a minus sign in front, for example,-7 and this would be pronounced either "minus 7" or "negative 7". The negative sign tells you how far away a number is from zero, so -2 is two steps away from zero.

What are negative numbers with examples? ›

From Wolfram MathWorld: A real quantity having a value less than zero ( < 0 ) is said to be negative. Negative numbers are denoted with a minus sign preceding the corresponding positive number, i.e., -2, -100.

What is negative number answer? ›

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.

What are the 4 rules of number? ›

The '4 rules' (addition, subtraction, multiplication and division) are at the heart of calculation and problem solving. Over the years a range of teaching methods has been adopted by schools and it is sometimes the case that parents' experiences are not the same as those of their children.

How do you explain negative numbers to a child? ›

Explain that a negative number is like owing money when you don't have any money at all. It is less than zero. So the bigger the numeral, the smaller or less the value.

What are the rules for adding and subtracting negative numbers? ›

Subtracting a number is the same as adding its opposite. So, subtracting a positive number is like adding a negative; you move to the left on the number line. Subtracting a negative number is like adding a positive; you move to the right on the number line.

What is the rule for adding two negative numbers? ›

How do you know if a number is negative? ›

If a number is greater than zero, it is a positive number. If a number is less than zero, it is a negative number. If a number equals to zero, it is zero.

When were negative numbers defined? ›

Negative numbers were first introduced around 200 BCE in China. They represented the amount of something being purchased or a debt. The first mathematician to mention negative numbers in any mathematics work was Diophantus. He began to look at equations that would result in negative number answers.

How do you write a negative number in words? ›

A negative number is written by putting a minus sign, "−", in front of a positive number. For example, 3 is a positive number, but −3 is a negative number. It is read "negative three" or "minus three"; it means the opposite of 3. Sometimes, for emphasis, we write the pair of opposite numbers as −3 and +3.

### Why do we use negative numbers? ›

Why do we need negative numbers? Negative numbers help us describe values less than zero.

What is the answer of two negative numbers? ›

Explanation: The sum of two negative numbers is always negative, hence, this is the right choice. As for the other choices: The product or quotient of two negative numbers is always positive.

What negative means? ›

Negative means focused on what is bad or lacking. A negative ad tells you bad things about the competition. A negative person loves to complain. In math, a negative number is less than zero.

What are number rules? ›

A simple rule for using numbers in writing is that small numbers ranging from one to ten (or one to nine, depending on the style guide) should generally be spelled out. Larger numbers (i.e., above ten) are written as numerals.

What is the general rule of a number? ›

The general rule tells us about the value of any number of the pattern. So for the pattern 2, 4, 6, 8, … the general rule is twice the number of the term. In this unit, we concentrate on patterns with a relatively simple general rule. This is usually a multiple of a number or the power (square or cube) of a number.

What are the three 3 methods to represent negative numbers? ›

These are: Sign-Magnitude method, 1's Complement method, and 2's complement method. These are explained as follows using examples. Signed Magnitude Method : We only add an extra sign bit to recognize negative and positive numbers.

What is the rule for a negative times a positive? ›

RULE 1: The product of a positive integer and a negative integer is negative. RULE 2: The product of two positive integers is positive. RULE 3: The product of two negative integers is positive. RULE 1: The quotient of a positive integer and a negative integer is negative.

How would you classify a negative number? ›

The integers are ..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ... -- all the whole numbers and their opposites (the positive whole numbers, the negative whole numbers, and zero). Fractions and decimals are not integers.

What are the 3 rules for subtracting integers? ›

Rules for Subtracting Integers
• Positive - positive = positive if the first integer is greater.
• Positive - positive = negative if the second integer is greater.
• Negative - Negative = negative if the first integer is greater.
• Negative - Negative = positive if the second integer is greater.
Dec 6, 2021

Why do 2 negatives make a positive? ›

The fact that the product of two negatives is a positive is therefore related to the fact that the inverse of the inverse of a positive number is that positive number back again.

### Do all negatives make a positive? ›

If two negative numbers are multiplied together or divided, the answer is positive. If a positive and a negative number are multiplied or divided, the answer is negative.

How do you know if the answer is positive or negative? ›

When multiplying (or dividing) two numbers with the same signs, the resulting answer is positive. If one is positive and the other negative, the answer will be negative. When more integers are involved work the calculations from left to right.

How do you read a negative value? ›

Introduction
1. On a number line, numbers always increase (become "more positive") to the right and decrease (become "more negative") to the left.
2. Numbers to the right are greater than numbers to the left and numbers to the left are less than numbers to the right.

What is a fact about negative numbers? ›

A negative number is a number that its value is less than zero. Negative numbers are symbolized by a minus or a dash (-) sign in front of a number. They are represented on the number line to the left of origin. Negative numbers can be either be whole numbers, fractions or decimals.

Is a negative number a real number? ›

The real numbers include the positive and negative integers and the fractions made from those integers (or rational numbers) and also the irrational numbers.

Can age be a negative number? ›

No, age cannot be in minus because we all start growing up from the moment we are born. Minus 87 means the man is 87 years back to his actual age.

How do you write a negative number in math? ›

You cannot multiply a number by itself to get a negative number. To get a negative number, you need one negative and one positive number. The rule works the same way when you have more than two numbers to multiply or divide. An even number of negative numbers will give a positive answer.

How do you write 10 to the negative 2? ›

Given, 10 to the power of negative 2. Basically, any negative exponent represents that how many times the reciprocal of the base can be multiplied. Hence,10 to the power of negative 2 can be written as 10-2.

What are 2 examples of negative numbers in the real world? ›

Negative numbers are used in lots of different situations. You read about negative numbers in weather reports and on food packaging. The temperature -5°C is 'negative five degrees' and it means 5 degrees below zero. Read more about negative numbers on food packaging in the factsheet Storing frozen food.

What is a double negative examples? ›

2 A double negative is a non-standard sentence construction that uses two negative forms. Double negatives are created by adding a negation to the verb and to the modifier of the noun (adjectives, adverbs, etc.) or to the object of the verb. I won't (will not) bake no cake. I can't (cannot) go nowhere tonight.

### How do you use negative in a sentence? ›

1, She answered the question in the negative. 2, The word "cheap" has negative overtones. 3, We received a negative answer to our request. 4, The crisis had a negative effect on trade.

What is negativity simple words? ›

: an attitude in which someone considers only the bad qualities of someone or something.

What is the rule for adding and subtracting positive and negative numbers? ›

Subtracting a number is the same as adding its opposite. So, subtracting a positive number is like adding a negative; you move to the left on the number line. Subtracting a negative number is like adding a positive; you move to the right on the number line.

Do 2 negatives make a positive when adding? ›

When you have two negative signs, one turns over, and they add together to make a positive. If you have a positive and a negative, there is one dash left over, and the answer is negative.

What are the rules for multiplying and dividing negative numbers? ›

Just like you can multiply and divide positive numbers, you can do the same with negative numbers. In order to multiply or divide negative numbers you must remember: If the signs are the same, the answer is positive. If the signs are different, the answer is negative.

When adding a negative and a negative What is the answer? ›

When you are adding a negative number to a negative number, it becomes subtraction, where you start from a negative point on the numbers line and move left. For example, -3 + (-2).

Do you add or subtract when both numbers are negative? ›

Rule 3: Subtracting a negative number from a negative number – a minus sign followed by a negative sign, turns the two signs into a plus sign. So, instead of subtracting a negative, you are adding a positive. Basically, - (-4) becomes +4, and then you add the numbers. For example, say we have the problem -2 - –4.

How do you explain negative numbers to students? ›

Explain that a negative number is like owing money when you don't have any money at all. It is less than zero. So the bigger the numeral, the smaller or less the value.

What are a few ways you can represent a negative number? ›

When the number is negative, the sign is represented by 1 but the rest of the number may be represented in one of three possible ways: Sign-Magnitude method, 1's Complement method, and 2's complement method. These are explained as following below.

Which is the best way to represent negative of a number? ›

The simplest is to simply use the leftmost digit of the number as a special value to represent the sign of the number: 0 = positive, 1 = negative. For example, a value of positive 12 (decimal) would be written as 01100 in binary, but negative 12 (decimal) would be written as 11100.

### What happens if you double a negative? ›

A double negative is a statement which contains two negative words. If two negatives are used in one sentence, the opposite meaning may be conveyed.

Do two negatives cancel each other out? ›

When you multiply two negative numbers together, though, the first one flips the sign from positive to negative, and the second one flips it back. In other words, negative numbers cancel each other out: when you multiply a negative number by a negative number, you get a positive number.

What happens if you subtract a negative number? ›

Solutions. Subtracting a negative number from a positive number result in a positive answer. This problem can also be re-written as 6 + 3 = 9. Subtracting a negative number from a positive number results in a positive answer.

What are the rules for multiplying or dividing positive and negative rational numbers? ›

To multiply rational numbers, remember the rules of multiplying positive and negative numbers:
• If the factors have the same. sign, the product is. positive.
• If the factors have different. signs, the product is. negative.

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