Directed Numbers

 What are Directed Numbers?

we can count things like stones,dogs,trees..etc ,for counting these objects we use natural numbers 1,2,3,4,5.... but sometimes we want to count numbers with a direction 

Ex-

 lets imagine about a River which remain water constant for a long period, But One day it's water level dropped so we need to express this situation with numbers. in here we can apply directed numbers. But how?          

   If water lavel drop we can call it as a negative Value. like (-1.5)meters

   When water level Rise We can Represent it as a positive value like (+2) meters 

So when we have two direction Value change we can use Directed Numbers

Ex-Temperature 

      water Level

      financial Situations

      for a Motion of an Object

examples for Directed Numbers(Integers)

+1,+2,+5,+6,+7.. -1,-2,-3....

Def for Directed Numbers
"All the numbers that are written with a positive or negative sign to indicate not only their magnitude but also one of two directions which are opposite to each other are defined as directed numbers."

How to Identify the sign of a Directed Number

when someone didn't mention about sign of a number we consider it as a positive number.

sign is always placed in left side of the number

ex- -4,+3,-7.5

     +3-4+12  (in this expression -sign for 4 and               7.5,+sign for 3 )

Addition and subtraction of Directed Numbers

rule 1

when we have Addition or subtration 

If

signs are eqal add the numbers without considering their signs and put answer. the sign of the answer should remain same.

                   ex- (1)  +13+2

                                 = +15

                         (2)  -10-5

                                = -15

                         (3)  12+8

                                = +20

rule 2

when we have Addition or subtration 

If

signs are not  eqal subtract the numbers without considering their signs and put answer.the sign of the answer should be the sign of Largest number

                   ex- (1)  +13-2

                                 = +11(largest number is 13 it's                                             sign is +)

                         (2)  -10+5(largest number is 10 it's                                             sign is -)

                                  = -5

                         (3)  12-8(largest number is 12 it's                                             sign is +)

                                = +4

Photo by Tyler Easton on Unsplash