1 / 11

Unit one

Unit one. Adding & Subtracting Integers. 1 st ) Adding two positive integers. Find the result then represent it on the number line 3 + 5 = .. 8 ...... -1* 0* 1* 2* 3* 4* 5* 6* 7* 8* 9* 4 + 3 = ... 7 . ....

egan
Download Presentation

Unit one

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Unit one Adding & Subtracting Integers

  2. 1st ) Adding two positive integers • Find the result then represent it on the number line • 3 + 5 = ..8...... • -1* 0* 1* 2* 3* 4* 5* 6* 7* 8* 9* • 4 + 3 = ...7..... • -1* 0 * 1* 2 * 3* 4* 5* 6* 7* 8* • 2nd) Adding two negative integers • (-5) + (-2) =..-7..... • -8* -7* -6* -5* -4* -3* -2* -1* 0* 1* 2* • (-3) + (-4) = ....-7.. • -8* -7 * -6* -5 * -4 * -3 * -2 * -1 * 0 * 1 * 2 *

  3. 3rd ) Adding (ve+) & (ve-) integers • 6 + ( -4 ) = ....2..... • -1* 0* 1* 2* 3* 4 * 5* 6* 7* 8* • 7 + ( -8 ) = .....-1..... • -2* -1* 0* 1* 2* 3* 4* 5* 6* 7* 8* • (-4 ) + 5 = ...1...... • -5* -4* -3* -2* -1* 0* 1* 2 * 3* 4* 5*

  4. Find the result:- 6 -5 a)4 + 2 = b) (-4) + (-1) = c) -10 + 3= d) 5 – 9 = e) 0 + (-5) = f) -9 – 8 = g) 0 – 7 = h) 0 – (-3) = -7 -4 -5 -17 -7 3

  5. -6 i) -3 – 3 = j) -7 + 4 = k) (-10) + (-10) = l) (-5) – 0 = m) 33 - -13 = n) -14 - -28 = o) -5 + -10 = p) -4 + 0 = -3 -20 -5 20 -14 5 4

  6. Properties of addition in ( Z ) • 1st) Closure property: addition is closed in ( Z ) • Example : 5 ϵ Z & -2 ϵ Z , then 5 + ( -2 ) = 3 ϵ Z • 2nd) Commutative property : if a , b ϵ Z , then a + b = b + a • Example : 9 + (-4 ) = 5 & (-4) + 9 =5 then 9 + (-4) = (-4) + 9 =5 • 3rd) Associative property : if a , b , c ϵ Z then a + b + c = ( a + b )+ c = a + (b +c) • Example : 5 + (-4) + (-3) = ( 5 + (-4) ) +( -3 ) = -2 • = 5 + ( (-4) + (-3) ) = -24th) Additive identity ( neutral) element in (Z) is ( zero ) • Example : * 6 + 0 = 0 + 6 = 6 * -4 + 0 = 0 + (-4) = -4 • 5th) Additive inverse ( opposite ) property: the additive inverse of a is ( -a ) • Where : a + (-a) = 0 example : additive inverse of (3 is -3) for 3 + (-3) = 0 • Note that : 1) the additive inverse of zero is zero because 0 + 0 = 0 • The additive inverse of a is (-a) & the additive inverse of (-a) = a • The additive inverse of (-a) is -(-a) = a

  7. Write the inverse (0pposite) of the numbers:- -10 12 a)10 is b) -12 is c) 0is d) 45 is e) -27 is f) 1 is g)- 36 is h) -30 is i) – 19 is j) - -25 is k) 0 is l) -(-13) is 0 -45 27 -1 36 30 19 25 0 -13

  8. Possibility of Subtraction in (Z) • Subtraction is closed in Z : * 10 – 6 =4 ϵ Z * -5 – 3 = - 8 ϵ Z • Subtraction is not commutative in Z : 4 – 3 = 1 but 3 – 4 = -1 Then 4 – 3 ≠ 3 – 4 • Subtraction is not associative in Z : where the result of 5 – 3 – 1 • ( 5 – 3 ) - 1 =1 but 5 - (3 - 1) = 3 then ( 5 – 3 ) – 1 ≠ 5 – ( 3 – 1 )

  9. Write the Property of each of the following:- • -7 + 5 = 5 + ( -7 ) ( ...commutative......................) • 9 + ( -9 ) = 0 (...additive inverse...................) • 0 + ( -11) = -11 ( ... Additive identity.................) • (-8 + 5 ) + 2 = -8 + ( 5 + 2 ) ( ... Associative .....................) • (14 + 6 ) + 10 = (14 + 10 ) + 6 (..... commutative.................) • –b + b = 0 ( ... additive inverse................)

  10. Use the Property of Addition in (Z) to find the result :- • a)-5 + (-8) + 5 • (-5 + (-8) ) + 5 ( associative ) • (-5 + 5) + (-8) ( commutative& assoc.) • 0 + (-8) (additive inverse) • = -8 ( additive identity)

  11. b)113 – 120 + 17 • ( 113 – 120 ) + 17 ( associative) • 113 + 17 – 120 ( commutative) • (113 + 17 ) – 120 ( associative ) • 130 – 120 = 10

More Related