Objective - To simplify expressions using commutative and associative properties.

1
Objective - To simplify expressions using
commutative and associative properties.
Commutative -
Order doesnt matter! You can
flip-flop numbers around an operation.
Commutative Property of Addition
a b b a
5 7 7 5
10 3 3 10
Commutative Property of Multiplication
2
Write an equivalent expression.
1) (6 4)
(4 6)
2)
3)
4) 9 7
7 9
5)
3
Addition and multiplication are commutative.
Difficult to prove true!
Easy to prove false!
Is subtraction commutative?
Counterexample -
An example that proves a statement false.
Counterexample
Therefore, subtraction is not commutative.
4
Give a counterexample that shows division is not
commutative.
Counterexample
Therefore, division is not commutative.
5
State whether each situation below is
commutative or not commutative.
1) Waking up in the morning and going to school.
not commutative
2) Brushing your teeth and combing your hair.
commutative
3) Putting on your socks and putting on
your shoes.
not commutative
4) Eating cereal and drinking orange juice.
commutative
6
Give the property that justifies each step.
Statement
Reasons
16 27 84
Given
16 84 27
Comm. Prop. of Add.
100 27
Simplify
127
Simplify
7
Identities
Identity Property of Addition
x 0 x
Zero is sometimes called the Additive Identity.
Identity Property of Multiplication
One is sometimes called the Multiplicative
Identity.
8
Identify the property shown below.
1) 6 8 8 6
Comm. Prop. of Add.
2)
Comm. Prop. of Mult.
3) (2 10) 3 (10 2) 3
Comm. Prop. of Add.
4)
Comm. Prop. of Mult.
5)
Mult. Prop. of Zero
6) 7 0 7
Identity Prop. of Add.
7)
Identity Prop. of Mult.
9
Identity Property of Multiplication
Many Forms of 1
Consequently, there are an infinite number of
ways to write any fraction.
10
Models of Equivalent Fractions
11
Find 6 equivalent fractions for the fraction
below.
Most simplified
12
Write at least 4 equivalent fractions for the
given one below.
Circle the most simplified form of each value.
13
Simplifying Fractions (Reducing)
14
Identify each fraction below.
Reduce!
15
Identify each fraction below.
Reduce!
16
Simplify the following fractions.
17
Simplify the following fractions.
18
Simplify the variable expressions.