1. Real Number

3. Real Numbers Natural Number Integer 1, 2, 3, … Whole Number
T.So
Whole Number
Real
Numbers
Natural Number
Irrational Number
0, 1, 2, 3, …
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

4. Property of Equality

6. Transitive Property Transitive Property
Reflexive Property
Reflexive Property
Symmetric Property
Symmetric Property
Transitive Property
Transitive Property

7. Addition Property
Addition Property
Multiplication Property
Multiplication Property

8. Property of Equality Reflexive Property EX. 7 = 7 5 = 5 10 = 10 = 4
7 = 7
5 = 5
10 = 10
= 4
9 = 9
Reflexive Property is A = A
when A is Real number.
Symmetric Property
If 9 = then = 9
If 6 = then = 6
If 7 = then = 7
If = then = 12
Symmetric Property is if A = B, then A = B when A and B is Real number.

9. Transitive Property If 32 = 9 and 9 = 6 + 3 then 32 = 6 + 3
If = and = M then = M + 3
Transitive Property is if A = B and B = C, then A = C when A ,B and C are Real number.

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

11. 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.

13. Additional Property

14. Associativity Closure Property Additive identity Inverse property
Commutative Property
Associativity
Closure Property
Additive identity
Inverse property

15. Closure Property
If 4, -3  R then 4 + (-3)  R
If 20, 34  R then  R
If -45, -9  R then (-9)  R
Closure Property is if a, b  R Then a + b  R Ex. 3, 6  R then  R

16. Commutative Property of Addition=
(-56) = 4 + (-56)
(-56) + (-99) = (-99) + (-56)
Commutative Property of Addition is a + b = b + a ex =

17. (-99) + ((-2) + 8) = ((-99)+ (-2)) + 8
Associativity
10 + (2 + 8) = (10 + 2) + 8
26 + ( ) = (26+ 13) + 34
(-99) + ((-2) + 8) = ((-99)+ (-2)) + 8
Associativity a + (b + c) = (a + b) + c ex (7 + 2) = (6 + 7) + 2

18. Additive identity Additive identity is 0 + a = a = a + 0
= =
= =
0 + (-9) = = (-9) + 0
Additive identity is
0 + a = a = a + 0

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

20. 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 =

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

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

23. 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 =

24. positive numbers
two positive numbers

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

26. 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

27. 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

28. 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

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

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

31. 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

32. 12. rectangle is 4 m longer than it is wide, its area is 192 m2
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