ALGEBRA BASICS 2

REVIEW of PROPERTIES

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

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

COMMUTATIVE PROPERTY 3 X 5 5 X 3

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)

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)

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

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

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. 0 a = 0

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 = 63 _______________ 9 x 8 = 8 x 9 _______________ 0 x b = 0 _______________ 3 x (5 x 7) = (3 x 5) x 7 _______________

Complete or rewrite each equation using the property indicated. IDENTITY 0 + y = __________________ COMMUTATIVE 5 + 4 = _________________ ASSOCIATIVE 6 X (7 X 8) = _________________

Complete or rewrite each equation using the property indicated. ASSOCIATIVE 7 + (b + 9) = _______________ COMMUTATIVE 10 x 3 = _______________ PROPERTY of ZERO 0 x 15 = _______________

ORDER OF OPERATIONS

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

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

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

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

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

Do you remember the ORDER of OPERATIONS? M_________________ Now try one D_________________ 3 x (4 + 5) + 2 x 7 A__________________ S__________________

P E M D A S 3 x (4 + 5) + 2 x 7 Parentheses first ( 9 ) Multiply from Left to Right 3 x 9 = 27 + 2 x 7 = 14 Add from Left to Right 27 + 14 Solve = 41

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)] _____________________________________ _____________________________________ _____________________________________ _____________________________________

Find the value of each expression. 10 - ( 5 + 2 ) 10 - 5 + 2 ( 2 + 3 ) x ( 4 + 5 ) 2 + 3 x 4 + 5 ( 9 x 3 ) + ( 9 x 2 ) [ 9 x ( 6 - 3)] x 2

Find the value of each expression if a = 2 b = 3 (b + 6) x 4 ________

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) __________

Number the ORDER of OPERATIONS 1 - 6 ___DIVIDE ___SUBTRACTION ___MULTIPLICATION ___EXPONENTS ___ADDITION ___PARENTHESES