# 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.

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.

## Rules

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

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:

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:

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

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

### 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

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

When represented on a number line, we get

### 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

### Multiplying and Dividing Integers

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

For example,

(-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

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

Solution:

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)

Solution:

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