Algebraic Expressions
and Properties
3.1
Algebraic Expressions
3.2
Writing Expressions
3.3
Properties of Addition and Multiplication
3.4
The Distributive Property
5
6
4
3
2
1
10
12
8
6
4
2
15
18
12
9
6
3
20 24
16
12
8
4
25 30
20
15
10
5
30 36
24
18
12
6
1
2
3
4
5
6
5
6
4
3
2
1
5
6
4
3
2
1
10
12
8
6
4
2
15
18
12
9
6
3
20 24
16
12
8
4
25 30
20
15
10
5
30 36
24
18
12
6
1
2
3
4
5
6
5
6
4
3
2
1
“Did you know that 5
3
6
5
6
3
5,
but 5
4
6
Þ
6
4
5?”
“Only certain operations like addition
and multiplication preserve equality
when you switch the numbers around.”
“Descartes, evaluate this expression
when
x
5
2 to determine the number of
cat treats you are going to eat today.”
“Remember that you evaluate an
algebraic expression by substituting
the value of
x
into the expression.”
3.1
Algeb
3
l
b
3

Interpreting Numerical
Expressions
Example 1
Write a sentence interpreting the expression 3
×
(19,762
+
418).
3
×
(19,762
+
418) is 3 times as large as 19,762
+
418.
Example 2
Write a sentence interpreting the expression (316
+
43,449)
+
5.
(316
+
43,449)
+
5 is 5 more than 316
+
43,449.
Example 3
Write a sentence interpreting the expression (20,008
−
752)
÷
2.
(20,008
−
752)
÷
2 is half as large as 20,008
−
752.
Write a sentence interpreting the expression.
1.
3
×
(372
+
20,967)
2.
2
×
(432
+
346,322)
3.
4
×
(6722
+
4086)
4.
(115
+
36,372)
+
6
5.
(392
+
75,325)
+
78
6.
(352
+
46,795)
+
100
7.
(30,929
+
425)
÷
2
8.
(58,742
−
721)
÷
2
9.
(96,792
+
564)
÷
3
Example 4
Simplify 4
2
÷
2
+
3(9
−
5).
First:
P
arentheses
4
2
÷
2
+
3(9
−
5)
=
4
2
÷
2
+
3
⋅
4
Second:
E
xponents
=
16
÷
2
+
3
⋅
4
Third:
M
ultiplication and
D
ivision (from left to right)
=
8
+
12
Fourth:
A
ddition and
S
ubtraction (from left to right)
=
20
Simplify the expression.
10.
3
2
+
5(4
−
2)
11.
3
+
4
÷
2
12.
10
÷
5
⋅
3
13.
4(3
3
−
8)
÷
2
14.
3
⋅
6
−
4
÷
2
15.
12
+
7
⋅
3
−
24
i
3
(19 762
418)
x
0
1
2
4
4 +
x
5
6
“Great! You’re up to
x
= 2.
Let’s keep going.”
What You
Learned Before