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# Integers

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### Integers

1. 1. Maths ClubPowerpointpresentation
2. 2. INTEGERSIntroduction:In class VI, we read about integers and various operations on them. We shall review them here and study the various properties satisfied by various operations on them.
3. 3. What are Integers ?All natural numbers, 0 and negatives of counting numbers are called Integers.Thus,…., -4, -3, -2, -1, 0, 1, 2, 3, 4,…., etc, are all integers.
4. 4. Positive Integers:1, 2, 3, 4,…., etc, are all positive integers
5. 5. Negative Integers-1, -2, -3, -4,…., etc, are all negative integers.
6. 6. ZeroZero is an integer which is neither positive nor negative.
7. 7. Addition of IntegersRule 1: If two positive or two negative integers are added, we add their values regardless of their signs and give the sum their common sign.Eg: Add (i) 36 and 27, (ii) -31 and -25Solution we have:(i) +36 +27=+63(ii) -31 -25=-56
8. 8. Rule 2: To add a positive and a negative integer, we find the difference between their numerical values regardless of their signs and give the sign of the integer with the greater value to it.REMARK In order to add two integers of unlike signs, we see which is more and by how much.
9. 9. Eg: Add (i) -47 +18 (ii) - 29 +52Solution: Using the rule for addition of integers with unlike signs, we have: (i) -47 +18 =-29 (ii)-29 +52 =+23
10. 10. Subtraction of IntegersFor any integers a and b, we define, a-b= a+(-b).Eg: Subtract: (i) 8 from 5Solution: we have: (i) 5 – 8= 5 +(negative of 8)=5 +(-8)=-3
11. 11. (ii) -6 from 3Solution: we have:(ii) 3 –(-6)=3+ {negative of (-6)}= 3 + 6= 9(iii) 5 from (-5)Solution: we have:(iii) (-5)-5 =(-5)+(negative of 5) =(-5)+(-5)=-10(iv) -8 from -6Solution: we have:(iv) -6-(-8)=(-6)+(negative of -8)= (-6)+8=2
12. 12. Multiplication of IntegersRule 1: To find the product of two integers with unlike signs, we find the product of their values regardless of their signs and give a minus sign to the product.Eg: (i)6x(-5) (ii)(-7)x9Solution: We have:(i)6x(-5)=-30 (ii) (-7)x9=-63
13. 13. Rule 2: To find the product of two integers with the same signs, we find the product of their values regardless of their signs and give a plus sign to the product.Eg: (i)12x16 (ii)(-25)x(-19)Solution: we have:(i) (12x16)=192 (ii)(-25)x(-19)=475
14. 14. Division of IntegersRule1: For dividing one integers by the others, the two having unlike, we divide their values regardless of their signs and give a minus sign to the quotient.Eg: Evaluate(i) (-48)/12 (ii)144/-16Solution: We have:(i)(-48)/12=-4 (ii)144/-16=-9
15. 15. Rule 2: For dividing one integer by the other having like signs, we divide their values regardless of their signs and give a plus sign to the quotient.Eg: Evaluate(i)98/14 (ii)(-48)/(-16)Solution: we have:(i)98/14=7 (ii)(-48)/(-16)=3
16. 16. Made By- Naman Bisht VII-D