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# Integers

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### Integers

1. 1. INTEGERS
2. 2. RULES FOR INTEGER
3. 3. ADDITION RULE1)When the signs are same, ADD and keep the sign. (-2) + (-4) = (-6)2)When the signs are different , SUBTRACT and use the sign of the larger number. (-2) + 4 = 2 2 + (-4) = (-2)
4. 4. SUBTRACTION RULEWhen subtracting , change the subtraction toadding the opposite and then follow youraddition rule.Example 1) -4 – (-7) - 4 +(+7) Different sign---subtract and use larger sign 3Example 2) -3 -7 -3 + (-7) Same sign --- Add and keep the sign. (-10)
5. 5. The additive inverses (oropposites) of two numbers addto equal zero.Example: The additive inverseof 3 is -3 Proof: 3 + (-3) = 0 We will use the additive inverses for subtraction problems.
6. 6. • Multiplying a positive integer anda negative integer , we multiplythem as whole numbers and put aminus sign(-) before the product.We thus get a negative integer. 3 x (-4) = (-12)
7. 7. Product of two negativeintegers is a positiveinteger. We multiply thetwo negative integers as awhole numbers and put thepositive sign(+) before theproduct. (-31) x (-10) = +310
8. 8. If the number of negative integers in aproduct is even , then the product is apositive integer; if the number ofnegative integers in a product isodd, then the product is a negativeinteger.(-9) x (-5) x (-6) x (-3) = 45 x 18 = 810(-9) x (-5) x 6 x (-3) = 45 x (-18) = (-810)
9. 9. 1 is the MULTIPLICATIVE IDENTITY forintegers.For an integer ’ a’ we have, ax1 = aMULTIPLICATION BY ZEROProduct of an integer and a zero is zero. For an integer a , a x 0 = 0
10. 10. DIVISION RULE• When we divide a negative integerby a positive integer or vice versa, wedivide them as whole number andthen put a minus sign(-) before thequotient. We, thus get a negativeinteger. 72 (-8) = (-9)
11. 11. •Division of a negativeinteger by anothernegative integer gives apositive integer asquotient. (-45) (-9) = 5
12. 12. PROPERTIES UNDER ADDITION AND SUBTRACTION1)Integers are closed for addition and subtraction both. That is, a+b and a-b are again integers, where a and b are any integers. 7+3 =10 and 7-3 =42) Addition is commutative for integers, i.e., a+b = b+a for all integers a and b. 4+5 = 5+4 = 9
13. 13. 3) Addition is associative for integers, i.e.,(a+b)+c=a+(b+c) for all integers a,b and c. (2+3)+4 = 2+(3+4) = 94) Integer 0 is the identity under addition. That is , a+0=0+a = a for every integer a. 3+0 = 0+3 = 3
14. 14. PROPERTIES UNDER MULTIPLICATIONa)Integers are closed under multiplication i.e., a x b is an integer for any two integers a and b. 3x4=12, which is an integer.b)Multiplication is commutative for integers i.e. axb=bxa for any integers a and b. 2x4 = 4x2 = 8 2x(-4) = (-4)x2 = (-8)
15. 15. c)The integer 1 is the identity under multiplication, i.e. 1xa = ax1 = a for any integer a .d)Multiplication is associative for integers, i.e.(axb)xc = ax(bxc) for any three integers a,b and c. 1x(3x5) = (1x3)x5 = 15