1. ALGEBRA
BASICS 2

2. REVIEW of PROPERTIES

3. COMMUTATIVE PROPERTY of ADDITION
The commutative property of addition states
that the order in which numbers are added
does not change the result.
a + b = b + a

5. COMMUTATIVE PROPERTY of MULTIPLICATION
The commutative property of multiplication states
that the order in which numbers are multiplied
does not change the result.
a x b = b x a

7. COMMUTATIVE PROPERTY
3 X X 3

8. ASSOCIATIVE PROPERTY of ADDITION
The associative property of addition states that
the way in which addends are grouped does not
change the result.
(a + b) + c = a + (b + c)

10. ASSOCIATIVE PROPERTY of MULTIPLICATION
The associative property of multiplication states that
the way in which factors are grouped does not
change the result.
(a x b) x c = a x (b x c)

12. IDENTITY PROPERTY of ADDITION
The identity property of addition states that
the sum of an addend and 0 is the addend.
a = a
= 7

14. IDENTITY PROPERTY of MULTIPLICATION
The identity property of multiplication states that
the product of a factor and 1 is the factor.
a x 1 = a
4 x 1 = 4

16. PROPERTY of ZERO
The property of zero states that the product
of a factor and 0 = 0
a x 0 = 0
The property of zero also states that the quotient
of zero and any non-zero divisor is 0.
a = 0

18. Name the property shown by each statement
Name the property shown by each statement. Push the back button to revisit slides to help you remember.
63 x 1 = _______________
9 x 8 = 8 x _______________
0 x b = _______________
3 x (5 x 7) = (3 x 5) x 7 _______________

19. Complete or rewrite each equation using the property indicated.
IDENTITY y = __________________
COMMUTATIVE = _________________
ASSOCIATIVE X (7 X 8) = _________________

20. Complete or rewrite each equation using the property indicated.
ASSOCIATIVE (b + 9) = _______________
COMMUTATIVE x 3 = _______________
PROPERTY of ZERO x 15 = _______________

21. ORDER OF OPERATIONS

22. ORDER of OPERATIONS
If an expression contains two or more operations, they must be completed in a specified order. This is called the ORDER of OPERATIONS. 1. Do all operations in brackets and/or parentheses first [ ] brackets ( ) parentheses

23. ORDER of OPERATIONS
2. Do any exponents, in order from LEFT to RIGHT. Start LEFT and go RIGHT

24. ORDER of OPERATIONS
3. Do all multiplications and divisions, in order from LEFT to RIGHT. Start LEFT and go RIGHT

25. ORDER of OPERATIONS
4. Do all additions and subtractions, in order from LEFT to RIGHT. Start LEFT and go RIGHT

26. PARENTHESES/BRACKETS
ORDER of OPERATIONS
PARENTHESES/BRACKETS
EXPONENTS
MULTIPLICATION
DIVISION
ADDITION
SUBTRACTION

27. Do you remember the ORDER of OPERATIONS?
M_________________ Now try one
D_________________ x (4 + 5) x 7
A__________________
S__________________

28. P E M D A S 3 x (4 + 5) + 2 x 7 Parentheses first ( 9 )
Multiply from Left to Right x 9 = x 7 = 14
Add from Left to Right
Solve = 41

29. Describe the steps necessary to find the value of this expression
Describe the steps necessary to find the value of this expression. P E M D A S
2[5 + 6 x 2 – (4 + 3)] _____________________________________ _____________________________________ _____________________________________ _____________________________________

30. Find the value of each expression.
( )
( ) x ( ) x
( 9 x 3 ) + ( 9 x 2 )
[ 9 x ( )] x 2

31. Find the value of each expression if a = 2 b = 3
(b + 6) x ________

32. Find the value of each expression if a = 5 b = 2
3a x (b + 1) __________
(9b - 4) x a __________
6 x 3 – (a x b) __________

33. Number the ORDER of OPERATIONS ___DIVIDE ___SUBTRACTION ___MULTIPLICATION ___EXPONENTS ___ADDITION ___PARENTHESES