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PLEASE HAVE OUT:
1.
PENCIL and PAPER
(Possibly Eraser and Calculator)
2.
Yesterday’s HOMEWORK.
PLEASE
BE QUIET
after the bell rings!
Yesterday’s Homework
Assignment -- Tuesday (10/5)
Pgs.
29-31: 10, 12, 16, 18,
32.
10. Number of football games and
number of years. $530,000
12. Irrelevant: grades student are
in. Needed: number of adults.
Pgs. 29-31: 10, 12, 16, 18, 32.
16.
Multiply preceding number by
3; 162, 486, 1,458
18. Subtract 3, then 4, then 5 and
so on; 45, 38, 30
32.
Clear-Off-Desk
except for:
PENCIL
and PAPER!
Possibly Eraser
and Calculator
Focus on
Lesson!
1.7 “The Commutative and
Associative Properties”
Goal
1 - You will simplify
expressions by applying the
associative and
commutative properties.
 The
operations of addition and
multiplication have special
properties.
PROPERTIES OF ADDITION AND
MULTIPLICATION
Commutative
Property of
Addition
 In
Words
 In Algebra
 In
Arithmetic
Commutative
Property of
Multiplication
In a sum, you can  In a product, you
add terms in any
can multiply
order.
factors in any
order.
 a + b = b + a  ab = ba

6
+9=9+6
6
x9=9x6
PROPERTIES OF ADDITION AND
MULTIPLICATION
Commutative
Property
Commute means
to change
locations.
In just addition or just multiplication,
changing positions does NOT change
the answer.
PROPERTIES OF ADDITION AND
MULTIPLICATION
Associative
Associative
Changing the
grouping of terms
will NOT change
the sum.
Changing the
grouping of factors
will NOT change the
product.
Property of
Addition
 In
Words

Property of
Multiplication

(a
+
b)
+
c
=
 In Algebra
(ab)c
=
a(bc)
a + (b + c)
 In
(6 + 9) + 2 =
Arithmetic
6 + (9 + 2) (6 x 9)2 = 6(9 x 2)
PROPERTIES OF ADDITION AND
MULTIPLICATION
Associative
Associate means
Property
to join or group
together.
In just addition or just multiplication
changing grouping symbols does
NOT change the answer.
Example 1
– Using Commutative Property
 Explain why
it does
NOT matter which of
the two numbers you
use as the length
when you find the
area of a rectangle.
17 ft
by
23 ft
Example 1
– Using Commutative Property
 Solution
 The
area A of a rectangle is
17
ft
the product of its length l and
by
width w.
 Using the commutative
23 ft
property of multiplication you
can write:
 A = lw = 23 x 17 = 17 x 23.
 The choice of l does NOT matter.
Example 1
– Using Commutative Property
abba

622 6
While multiplication is
commutative (order does NOT
matter), division is NOT
commutative and order does
matter.
However,
Example 2
– Using Associative Property
 Show that:
 (13 + 8) + 25 = 13 + (8 + 25)
 Solution
 Evaluate each expression separately.
+ 8) + 25 =  13 + (8 + 25) =
 13 + 33 =
21 + 25 =

46
46
 (13


Example 2
– Using Associative Property
However, (a – b) – c  a
 (8 – 5) – 2  8 – (5
– (b – c)
– 2)
 While addition is
associative
(grouping symbols do NOT matter),
subtraction is NOT associative
and grouping symbols do
matter.
(8
– 5) – 2 = 1
8 – (5 – 2) = 5
1.7 “The Commutative and
Associative Properties”
 Are
there any questions
about The Commutative
and Associative Properties
of Addition and
Multiplication?
1.7 “The Commutative and
Associative Properties”
Goal
2 - You will justify the
process used to
simplify expressions.
 Knowing the
properties of numbers can
help you use mental math to evaluate
expressions.
 When you use a property of numbers to
explain why a step of your answer is
valid, you are justifying the step.
Example 3
Justifying an Answer



Use mental math to evaluate:
43 + (68 + 57). Justify each step.
Solution
To evaluate 43 + (68 + 57) using
mental math, look for numbers that are
easy to add first. Notice that the ones’
digits in 43 and 57 are easy to add. So, it
is easier to add 43 and 57 than 68 and 57.
Example 3
Justifying an Answer







Use mental math to evaluate:
43 + (68 + 57). Justify each step.
Solution
43 + (68 + 57)
Wrote original problem
= 43 + (57 + 68) Commutative Property
= (43 + 57) + 68 Associative Property
= (100) + 68
Added 43 and 57
= 168
Added 100 and 68
1.7 “The Commutative and
Associative Properties”
 Are
there any questions
about Justifying Steps?
 Classwork
 1.7
Pgs. 34 - 35: 1-8 and 26-28
Make sure you have the
proper heading and format.



930
Danny Dana
10/1
Math 7 - Dequer
1.7 Pg.34-35: 1-8 & 26-28
Please work Quietly and OnYour-Own for 10-15 min.
1.
Have out your Dana Planner
turned to the Assignment Sheet
for Week 5.
Make sure you have the
proper heading and format.



1.
930
Danny Dana
10/6
Math 7 - Dequer
1.7 Pg.34-35: 1-8 & 26-28
You may now get help from and
give help to near neighbors. When
your done, check odd numbered
problems in the back of the book on
SA-2.
1.7 “Guided Practice”
Pgs. 34 - 35: 1-8 and 26-28
1. Associative
Property - Multiplication
2. Commutative Property - Multiplication
3. Commutative Property – Addition
4. Associative Property – Addition
5.
C

26. C
6. B
27. J
7. D
28. B
8. A
Make-Up Tests
 Math 7
Make-Up Quizzes
are available Tomorrow,
Thursday (10/7/03), at 7:45 a.m.,
12:40 p.m. (during lunch) and/or
3:05 p.m. in Room 29.
 If it is a retest bring the original Blue
Scantron Form and colored quiz (if
possible) with you.
Class/Homework Assignment -Wednesday (10/6)
Pgs.
34-35: 10, 12, 14,
18, 22.
on 1st Quarter Project
or Assigned Replacement!
Work