1. Properties of Mathematics
Everything you need to know and more

2. Properties of Mathematics
OperationsandProperties
3. Properties of Mathematics
No, not these operations!!!
4. Properties of Mathematics
These operations.of NUMBERS!!!!
Addition
Subtraction
Multiplication
Division
5. Properties of Mathematics
No, not these properties!!!
6. Properties of Mathematics
These properties.of NUMBERS!!!!
Associative Property of Multiplication
Commutative Property of Multiplication
Identity Property of Multiplication
Inverse Property of Multiplication
Multiplicative Property of Zero
Multiplicative Property of-1
Associative Property of Addition
Commutative Property of Addition
Identity Property of Addition
Inverse Property of Addition
Substitution Property Distributive Property
Reflexive Property
Symmetric Property
Transitive Property
Addition Property
Subtraction Property
Multiplication Property
Division Property
7. Properties of Mathematics
Hmmmmm.Whats the
difference between
operations of NUMBERS and
properties of NUMBERS ????
and
OPERATION of numbers.
is the WAYwe calculate numbers
(add, subtract, multiply, & divide)
PROPERTIESof numbers.
are the METHODSwe use to calculatenumbers
WAY
METHODS
8. Properties of Mathematics
So Lets get started.
PROPERTIES
OF
NUMBERS
9. Properties of Mathematics
Addition, Subtraction, Multiplication & Division Properties
10. Properties of Mathematics
When you have each side of an expression equal
to the other side, you can add, subtract, multiply
or divide the SAME number on each side and
not change the equalities.
Addition Property
a = b
a + c = b + c
Subtraction Property
a = b
a - c = b - c
Multiplication Property
a = b
a c = b c
Division Property
a = b, (c 0)
=
11. Properties of Mathematics
Addition Property
Subtraction Property
1 = 1
1 +5= 1 +5
6 = 6
1 = 1
1 - 5= 1 - 5
-4 = -4
Multiplication Property
Division Property
2 = 2
2 5= 2 5
10 = 10
10 = 10
10 5= 10 5
6 = 6
12. Properties of Mathematics
IDENTITY PROPERTIES
13. Properties of Mathematics
The Identity Property
Addition
a + 0 = a
Multiplication
a 1 = a
14. Addition
5 + 0 = 5
Multiplication
5 1 = 5
Properties of Mathematics
The Identity Property
15. Properties of Mathematics
REFLEXIVE PROPERTY
16. Properties of Mathematics
a = a
Reflexive Property
1=1
9x=9x
x + y=x + y
3(x-2)= 3(x-2)
17. Properties of Mathematics
SYMMETRIC PROPERTY
18. The Symmetric property is an equality
relationship that switches one expression on
one side of an equation to the other side.
(note: keep expressions exactly as is .)
a + b = c
c = a + b
Properties of Mathematics
Symmetric Property
9 - 5=4
5=9 - 4
5=9 - 4
9-4=5
19. Properties of Mathematics
COMMUTATIVE PROPERTY
20. The Commutative property of addition or multiplication changes the position of a term on one side of an expression.
AdditionMultiplication
Properties of Mathematics
Commutative Property
a
=
b
b
a
b
+ = +
b
a
a
a
b
b
a
21. ADDITION3 + 8=11
8 + 3=11
11=11
MULTIPLICATION25 4 =40
5 2 4 =40
40=40
Properties of Mathematics
Commutative Property
22. Properties of Mathematics
ASSOCIATIVE PROPERTIES
23. Properties of Mathematics
The Associative property ASSOCIATES (groups)
terms of numbers or variables with other terms
using parentheses. (notice: original term positions never change)
ADDITIONa+(b+ c)=(a+b)+ c
MULTIPLICATION(ab) c =a (b c)
Associative Property
24. Properties of Mathematics
ADDITION
MULTIPLICATION
Associative Property
1+(7+ 5)=( 1+5)+ 7
1+(12)=(6)+ 7
13=13
(17) 5 =1 (7 5)
(7) 5 =1 (35)
35=35
25. Properties of Mathematics
INVERSE PROPERTY
OF ADDITION
26. Properties of Mathematics
The Inverse property of multiplication cancels out a number or variable by the using the inverse or opposite operation of the number or variable.
a + -a = 0
Inverse Property of Addition
= 0
1 +
-1
-7 +
7
27. Properties of Mathematics
INVERSE PROPERTY
OF MULTIPLICATION
28. Properties of Mathematics
The Inverse property of multiplication cancels out
a number or variable by the using the inverse or opposite operation of the number or variable and gives a new value of 1.
Inverse Property of Multiplication
a
= 1
29. Properties of Mathematics
Inverse Property of Multiplication
= = 1
3x
5
= = 1
.52
== 1
== 1
a
= 1
30. Properties of Mathematics
Multiplicative Property of Zero
Multiplicative Property of -1
31. Any number or variable multiplied by zero will become zero.
Any number or variable multiplied by -1 will become the opposite sign of that number or variable.
Properties of Mathematics
Multiplicative Property of Zero
a 0 = 0
7 0 = 0
0 x = 0
0 = 0 5y
Multiplicative Property of -1
a -1 = -a
7 -1 = -7
-5y -1 = 5y
-1 3= -3
32. Properties of Mathematics
DISTRIBUTIVE PROPERTY
33. The distributive property distributes(multiplies) a number or variable among the other terms in the parentheses. (multiply)
a(b + c) = ab + ac
Or reverse..
ab + ac = a(b + c)
Properties of Mathematics
Distributive Property
34. 5(x + 2) = 5(x) + 5(2)
5(x + 2) = 5x + 10
Or reverse..
3x + 3y = 3(x+ y)
Properties of Mathematics
Distributive Property
35. Properties of Mathematics
SUBSTITUTION PROPERTY
36. Properties of Mathematics
The Substitution property takes the place of some number, variable or term for something else in your mathematical expression.
Substitution Property
=b
a
b
+ c = d
a
37. Properties of Mathematics
Substitution Property
x = 4
4
2x + 5 = ?
2
()
4
+ 5 = ?
8 + 5 = ?
13 = 13
38. Properties of Mathematics
TRANSITIVE PROPERTY
39. The Commutative property of addition or multiplication changes the position of a term on one side of an expression.
Properties of Mathematics
Transitive Property
c
a
c
b
a
=
=
=
b
40. Properties of Mathematics
Transitive Property
=
17
8 + y
=
Z - 5
17
8 + y
Z - 5
=
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Properties of Mathematics
Acknowledgements