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# Negative|Definition & Meaning

## Definition

A number is considered **negative** if its value is always **below zero** and it is preceded by the symbol for the negative sign **(-) symbol**.

## What Are Negative Numbers?

A **minus sign** serves as a prefix for a number to indicate that it is a negative number. They may be written in **integer, decimal, or even fractional forms**. As an illustration, the digits –**4, -15, -4/5, and -0.5 **are examples of what are known as negative numbers.

**What Are Negative Integers?**

Numbers that have a value that is less than zero are considered to be **negative integers**. They do not contain any fractions or decimals in their totals. Negative integers include the numbers **-7 and -10**, for instance.

**Formulas and Guidelines for Negative Numbers**

When performing the four fundamental **arithmetic computations** of addition, subtraction, multiplication, and division on negative numbers, one must adhere to a predetermined set of guidelines.

- A negative number is obtained by
**adding two other negative numbers**. For instance, -5 plus (-1) equals -6. - The difference between two numbers can be calculated by
**adding positive and negative numbers**. The sign of the absolute value with the greater magnitude comes before the outcome. For instance, -9 plus 3 equals -6. - When a ‘-‘ number is multiplied by a positive one, you get another
**negative one**. For instance, -9 multiplied by 2 equals -18. - A positive number is produced when
**two negative numbers are multiplied**For instance, -6 over -3 equals 18 - When
**splitting negative numbers**, the result is positive if the signs of the numbers being divided are the same. For instance, -56 divided by -7 equals 8. - If you
**divide negative integers**and the results are still negative, check to be sure that the signs are the same. For instance, -32 divided by 4 equals -8.

**Calculating Negative Numbers by Adding and Subtracting**

We must commit the following rules to memory to successfully add and subtract negative numbers.

### Addition of Numbers With a Negative Sign

**Case 1**

When adding a negative number to another negative number, we must add the two numbers together and include the negative sign in the solution. For instance, **-7 plus (- 4) equals -7 minus 4, which equals -11.** To put it another way, whenever you add two negative integers, you get another negative number.

**Case 2**

When adding a positive number to a negative number, we calculate the difference between the two numbers. Then we utilise the sign of the more excellent absolute value in the response. For instance, **-9 plus (5) equals -4.** The** answer is -4** since the sign of the more excellent absolute value is being used in this calculation.

A number line is a helpful tool to grasp this concept better. The rule for using the number line states that when adding a positive number, one must travel to the right along the line.

**Subtracting Negative Numbers**

The process of subtracting negative numbers from positive numbers is similar to addition. Said, we need to keep in mind a rule that states:

The **Subtraction Rule** Is as Follows: Alter the sign of the second number that follows and the operation, which should be changed from subtraction to addition.

**Case 1 **

When we have to subtract a positive number from another positive integer, we use the formula for subtraction that was presented earlier in this paragraph. For instance**, 5 – (+6) becomes 5 + (-6), 5 – 6, which equals -1.**

**Case 2**

When we have to subtract a positive number from a negative number, we will stick to the same rule of subtraction that we used in the previous example, which states:

The Subtraction Rule Is As Follows: Alter the sign of the second number that follows and the operation, which should be changed from subtraction to addition. For instance, the expression -3 minus (+1) will yield -3 plus (-1). It can be concluded by saying that **-3 minus -1 equals -4.**

**Case 3 **

The following rule of subtraction will guide us when we need to subtract a ‘-‘ number from another negative number:

The Subtraction Rule Is As Follows: Alter the sign of the second number that follows and the operation, which should be changed from subtraction to addition.

For instance**, -9 minus (-12) multiplied by -9 plus 12 is 3.** Because of this, 12 is now in the positive. We use the sign of the **absolute value** with the greater magnitude of 12, even if the answer is 3.

**Performing Multiplications Using Positive and Negative Numbers**

Rule 1 states that the outcome will be negative whenever the signs of the numbers being added together are different. **(-) Ã— (+) = (-) . (-).** When we ‘x’ a negative number by a positive one, the result is always negative. In other words, the product is always a negative number. Consider the following: -3 times 6 is -18.

Rule 2 states that the result will be positive whenever the signs of the numbers are the same. **(-) Ã— (-) = (+); (+) Ã— (+) = (+).** To put it another way, regardless of whether the numbers being multiplied are positive or negative, the product of such a multiplication is always positive. For instance, **-3 multiplied by -6 equals 18.**

**Calculating Differences Between Positive and Negative Numbers**

**Rule 1** states that the outcome of dividing a – number by a number is always going to be a negative number. **(-) Ã· (+) = (-). **For instance, (-36) divided by (4) equals (-9).

**Rule 2** states that the answer to dividing a negative number by another negative number will always be positive. **(-) Ã· (-) = (+)**. (-24) divided by (-4), for instance, equals 6.

**Example 1**

What is the sum of the following equation:

(-2) + (-3) + (-1) = ?

**Solution **

We know that when negative numbers are added, we get a negative number. So,

(-2) + (-3) + (-1) = -6

**Example 2**

What is the product of -5 and -6?

**Solution **

We know that the product of two negative numbers is a positive number. So,

-5 * -6 = 30

*All images/graphs are created using GeoGebra.*