- Add and subtract integers

adding and subtracting integer

* adding two like signs integers is adding their distances from zero and preserving their sign

2 + 5 = 7 and (-3) + (-10) = -13

* adding two inlike signs integers is subtracting their distances from zero and preserving the sign of the one which has the great distance

(- 4) + 10 = 10 - 4 = 6 and 15 + ( - 20 ) = - ( 20 - 15 ) = - 5

* the addition of two opposite number is equal to zero

( - 6) + 6 = O

* to subtract two integers we add to the first the opposit of the second

(-6 ) - 8 = (-6) + (-8) = - 14

examle1

5+(-2) =

(-5) +2 =

5+2 =

(-5)+(-2) =

► answer

example

(-5) +8

► answer

exercise1

(-6) - (-4)=

(-5) + 3=

12 )- (-8)=)

-15 - (5)= )

(-2) + (-7)=

4 – 7=

answer ►

adding and subtracting with branckets

rule

* you can remove the bracket after the sign (+) in condition to change all signs of numbers inside the bracket

* you can remove the bracket after the sign (-) without changing the signs of numbers inside the bracket

rules

a - ( b + c ) = a - b - c

a - ( b - c ) = a - b + c

a + ( b + c ) = a + b + c

a + ( b - c ) = a + b - c

examples

−(−x + y)

x − y.

−(x − y)

−x + y.

. −(x + y − 2)

−x − y + 2.

a − [b − (c − d + e)]	=	a − [b − c + d − e]

	=	a − b + c − d + e.

exercises

remove the brackets then simplify

(x − 3) − (y − 4)	=

(x + 2) + (y + 8)	=

(x + 2) − (y + 8)	=

. (x − 2) + (y + 8)		=

. (x − 2) − (y + 8)		=

. (x − 2) − (y − 8)=

. (x − 2) + (y − 8)=

. (a − 2) + (b + 3) − (c − 7)=

(a − 5) − (b + 6) − (c − 9)		=

(a + 2) − (b − 3) + (c − 8) − (d + 1)=

answer