Download presentation

Presentation is loading. Please wait.

Published byBartholomew Miles Modified over 9 years ago

1
Unit one Adding & Subtracting Integers

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

5
i) -3 – 3 = j) -7 + 4 = k) (-10) + (-10) = l) (-5) – 0 = m) 33 - -13 = n) -14 - -28 = o) -5 + -10 = p) -4 + 0 = -6 -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) ) = -2 4th) 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:- 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 -10 12 0 -45 27 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

Similar presentations

© 2024 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google