warm up #2 ch 1: simplify if possible try these 1 2 3 4 5
TRANSCRIPT
Try These
1
2
3
4
5
5
5y
ab
abc
3
9
y
xy
8
6
54
15y
ab
a
3
8
Answers
1
2
3
4
5
5
5y
ab
abc
3
9
y
xy
8
6
54
15y
ab
a
3
8
y
8
3b
3c3
4
x
5
18
y
•We will write equivalent expression using the properties
Vocabulary:Equivalent Expression:Expressions that have equal values for the
same replacement values of their variables
CommutativeCommutative PropertiesMultiplication3 • 8 = 8 • 3We can change the order when multiplying without affecting the product.
Addition7 + 3 = 3 + 7We can change the order when adding without affecting the sum.
CommutativeCommutative PropertiesSubtraction
7 - 3 = 3 – 7 ????
Commutative Property does NOT apply to subtraction.
Division 3 ÷ 8 = 8 ÷ 3 ????
Commutative Property does NOT apply to division.
To commute means to moveThe news talks
about the daily commute on the freeway.
Think about how the cars move this will help you to remember commutative property is when the numbers move!
Commutative PropertyAddition
Multiplication
+
+=
Write an equivalent expression using the commutative prop1. 7 + 11
2. 3 +x
3. 5y
It can help you to do more simple calculations
For Example:
180 64 20
200
264
Mental Math1
9 162 72
8
IdentityIdentity PropertiesAddition
7 + 0 = 7 When zero is added to any number, the sum is the same number.
Multiplication9 • 1 = 9 When any number is multiplied by 1, the product is the same number.
Identity is who you areSame with numbers.
We want to be able to do an operation (such as +0 or mult by 1) and get the same thing back, its identity
(Using the Identity Property of Multiplication)
1.for 5
5 Use"1".by gmultiplyin
by 3
2for expression equivalent an Write
15
10
5
5
3
2
Do you reduce this???
Answer is: NO!!!!Usually we reduce everything!We reduce when the directions say to:
1. Simplify2. Evaluate3. Solve4. Calculate (add, sub, mult, divide)
When the directions say to write an equivalent expression we do not reduce
1.for y
y Use"1".by gmultiplyin
by 2
xfor expression equivalent an Write
y
xy
y
yx
22
The Associative Property
(a + b) + c = a + (b + c)(a + b) + c = a + (b + c)
(5 + 2) + 3 = 5 + (2 + 3)(5 + 2) + 3 = 5 + (2 + 3)
(Parenthesis) around different pairs of numbers
The Associative Property
(a (a •• b) b) •• c = a c = a •• (b (b •• c) c)
(2 (2 •• 3) 3) •• 5 = 2 5 = 2 •• (3 (3 •• 5) 5)
(Parenthesis) around different pairs of numbers
Associative: To associate
( + )+
(+ + )