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# Real Number

Real Number. 1, 2, 3, …. T.So. Whole Number. Real Numbers. Irrational Number. Natural Number. 0, 1, 2, 3, …. 0.5254578. Rational Number. Integer. Positive (more than 0). Negative (less than 0). Number divide 0 is 0. Zero. Divide all number is no answer. Multiply all number is 0.

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## Real Number

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1. Real Number

2. 1, 2, 3, … T.So Whole Number Real Numbers Irrational Number Natural Number 0, 1, 2, 3, … 0.5254578 Rational Number Integer Positive (more than 0) Negative (less than 0) Number divide 0 is 0 Zero Divide all number is no answer Multiply all number is 0 Plus all number is all number Minus all number is all number

3. Property of Equality

4. Reflexive Property Reflexive Property Symmetric Property Symmetric Property Transitive Property Transitive Property

6. Property of Equality Reflexive Property EX. 7 = 7 5 = 5 10 = 10 • = 4 9 = 9 Reflexive Property is A = A when A is Real number. Symmetric Property If9 = 6+ 3 then 6+ 3 = 9 If6 = 4 + 2 then4 + 2 = 6 If7 = 4 + 3 then4 + 3 = 7 If12 = 10 + 2 then10 + 2 = 12 Symmetric Property is if A = B, then A = B when A and B is Real number.

7. Transitive Property If 32 = 9 and9 = 6 + 3 then32 = 6 + 3 If 52= 25 and25 = 21 + 4 then52= 21 + 4 If 42= 16 and16 = 6 + 10 then62= 6 + 10 If 132= 169 and169 = M + 3 then32 = M + 3 Transitive Property is if A = B and B = C, then A = C when A ,B and C are Real number.

8. Addition Property If 4  3 = 12 and c = 2 then(4  3) + 2 = 12 + 2 If 5  2= 10 and c = 5 then(5  2 ) + 5 = 10 + 5 If 7 8 = 56 and c = 9 then(8 7) + 9 = 56 + 9 If 8  4 = 32 and c = 3 then(8 4) + 3 = 32 + 3 Addition Property is if A = B, then A + C = B + C when A ,B and C is Real number.

9. Multiplication Property If 4 x 8 = 32 and c = 5 then (4 x 8 )x 5 = 32 x 5 If 9 x 6 = 54 and c = 8 then (9 x 6 )x 8 = 54 x 8 If 12 x 8 = 96 and c = 9 then (12 x 8 )x 9 = 96 x 9 Multiplication Property is if A = B, then A × C = B ×C when A ,B and C is Real number.

11. Commutative Property Associativity Closure Property Additive identity Inverse property

12. Closure Property If4, -3  R then4 + (-3) R If20, 34  R then20 + 34  R If-45, -9  R then45 + (-9)  R Closure Property is ifa, b  R Thena + b  R Ex.3, 6  R then3 + 6  R

13. Commutative Propertyof Addition 6 + 3 = 3 + 6 (-56) + 4 = 4 + (-56) (-56) + (-99) = (-99)+ (-56) Commutative Property of Addition is a + b = b + a ex.2 + 4 = 4 + 2

14. Associativity 10 + (2 + 8) = (10 + 2) + 8 26 + (13 + 34) = (26+ 13) + 34 (-99) + ((-2) + 8) = ((-99)+ (-2)) + 8 Associativity a + (b + c) = (a + b) + c ex.6 + (7 + 2) = (6 + 7) + 2

15. Additive identity 0 + 8 = 8 = 8 + 0 0 + 10 = 10 = 10 + 0 0 + (-9) = -9 = (-9)+ 0 Additive identityis 0 + a = a = a + 0

16. inverse property of addition (-15) + 15 = 0 = 15 + (-15) (-47) + 47 = 0 = 47 + (-47) (-99) + 99 = 0 = 99 + (-99) (-65) + 65 = 0 = 65 + (-65) Inverse property of additionFor real number a will have-a is (-a) + a = 0 = a + (-a) ex.(-5) + 5 = 0 = 5 + (-5)

17. 1. When the square of a certain number is diminished by 9 times the number the result is 36. Find the number. square of a certain number = 9 times the number =

18. 2. A certain number added to its square is 30. Find the number. A certain number = its square =

19. 3. The square of a number exceeds the number by 72. Find the number. a number = square of a number =

20. 4. Find two positive numbers whose ratio is 2:3 and whose product is 600. First numbers = numbers whose ratio is 2:3 = 2x:3x product is 600 =

21. positive numbers two positive numbers

22. 5. The product of two consecutive odd integers is 99. Find the integers. odd integers = consecutive odd integers = If x = 9 consecutive odd integers = 9+2=11 If x = -11 consecutive odd integers = -11+2=-9

23. 6. Find two consecutive positive integers such that the square of the first is decreased by 17 equals 4 times the second. First number = Second number = First number = 7 Second number = 7+1=8

24. 7. The ages of three family children can be expressed as consecutive integers. The square of the age of the youngest child is 4 more than eight times the age of the oldest child. Find the ages of the three children. youngest child = oldest child = The ages of three family children = 10,11,12 year old

25. 8. Find three consecutive odd integers such that the square of the first increased the product of the other two is 224. three consecutive odd integers = 9,10,11

26. 9. The sum of the squares of two consecutive integers is 113. Find the integers. If x= 7 two consecutive integers is 7 and 8 If x= -8 two consecutive integers is -8 and -7

27. 10. The sum of the squares of three consecutive integers is 302. Find the integers. If x= -11 three consecutive integers is -11,-10,-9 If x= 9 three consecutive integers is 9,10,11

28. 11. Two integers differ by 8 and the sum of their squares is 130. If integers is -3 two integers is -3 and -11 If integers is 11 two integers is 11 and 3

29. 12. rectangle is 4 m longer than it is wide, its area is 192 m2. Find the dimensions of the rectangle. Dimensions of the rectangle = 12 x 16 = 192

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