Component 2
The Language of Algebra
2 Language of Algebra
“Rules of
Algebra”
Stage 1
Stage 2
Stage 3
2 Language of Algebra
PE
ADM
S
Exponents
Parenthesis (and other grouping symbols)
Multiply and divide from left to right
Add and subtract from left to right
ally
ear
unt
y
xcuse
lease
PE
ADM
S
xcuse Exponents
lease Parenthesis (and other grouping symbols)
y
ear
unt
ally
Order of
Operations
Tool
Please Parenthesis (and other grouping symbols)
( ) [ ]
/{ }√
(12÷3) +1
4+1
5
Grouping Symbols
2 Language of Algebra
Add and subtract from left to right
Multiply and divide from left to right
PE
ADM
S
xcuse Exponents
lease Parenthesis (and other grouping symbols)
y
ear
unt
ally
Order of
Operations
Tool
E xcuse Exponents
53 means you are to use 5 as a factor
3 times
5•5•5
125
42 – (8•2)
42 – 16
16 – 16
0
2 Language of Algebra
Multiply and divide from left to right
Add and subtract from left to right
PE
ADM
S
xcuse Exponents
lease Parenthesis (and other grouping symbols)
y
ear
unt
ally
Order of
Operations
Tool
M
16 divided by
8 • 2 – 7
16 divided by 8 is 2
2 • 2 – 7
2 • 2 is 4
4 – 7 = -3Dear
Caution
!
2 Language of Algebra
Multiply and divide from left to right
y
Multiply and divide from left to right
Add and subtract from left to right
16 ÷ 8 • 2 – 7
16 ÷ 16 – 7
1 – 7
-6
Remember that
there are several
ways to show
multiplication in
algebra such as 3y
or (3)(y) or 3 • y.
There are also
several ways to
show division
including 20 ÷ y,
20/y, or 20/y.
2 Language of Algebra
PE
ADM
S
xcuse Exponents
lease Parenthesis (and other grouping symbols)
y
ear
unt
ally
Order of
Operations
Tool
Aunt
SAdd and subtract from left to right
12 – 4 • 2 + 2
4 • 2
12 – 8 + 2
4 + 2 = 6
2 Language of Algebra
Multiply and divide from left to right
ally
Add and subtract from left to right
PE
ADM
S
xcuse Exponents
lease Parenthesis (and other grouping symbols)
y
ear
unt ally
60 ÷(3 + 1) – 2 • 2
2
9+1 = 10
60÷10 = 6
2 • 2 = 4
6-4 = 2
2 Language of Algebra
Multiply and divide from left to right
Add and subtract from left to right
Use PEMDAS to find the value or
evaluate an algebraic
expression.
You will be given an expression that contains
variables and a value to use for
the variable.
Substitute the number value for
the variable.
24 ÷ (x + 2)
for x = 1
24 ÷ (1 + 2)
2 Language of Algebra
PE
ADM
S
xcuse Exponents
lease Parenthesis (and other grouping symbols)
y
ear
unt ally
Multiply and divide from left to right
Add and subtract from left to right
24 ÷ (x + 2) for x = 1
24 ÷ (1 + 2)
24 ÷ 3
8
2 Language of Algebra
PE
ADM
S
xcuse Exponents
lease Parenthesis (and other grouping symbols)
y
ear
unt ally
Multiply and divide from left to right
Add and subtract from left to right
x (3 + 2) – 50/x
for x = 2
2 (3 + 2) – 50/2
3+2 = 5
5 = 25
2
2
22 (25) – 50/2
2• 25 = 50
50 ÷ 2 = 25
50-25 = 25
2 Language of Algebra
PE
ADM
S
xcuse Exponents
lease Parenthesis (and other grouping symbols)
y
ear
unt ally
Multiply and divide from left to right
Add and subtract from left to right
Practice on your Own!
PROPERTIES
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Now that you remember how to simplify and evaluate numerical and algebraic expressions, we are ready to use these skills to solve equations.
2 Language of Algebra
PE
ADM
S
xcuse Exponents
lease Parenthesis (and other grouping symbols)
y Multiply and divide from left to right
ear
unt Add and subtract from left to rightally
Distributive Property
(x + 2)
5
2 Language of Algebra
(x + 2)
5
A = 5 (x+2)
5
x 2
A = 5(x) + 5(2)
5(x + 2) = 5(x) + 5(2)
or
5(x + 2) = 5x +10
2 Language of Algebra
Solve for x.
x = 2(y+2)+2y
Copy this equation on your paper and
solve for x.
2 Language of Algebra
Check your Work
Did you find that x = 4y +
4?
x = 2y + 4 +2y
In this example, how would you solve for
x if y = 3?
Distributive
Property-
a property indicating a way
in which multiplication is
applied to addition of two
or more numbers in which
each term inside a set of
parentheses can be
multiplied by a factor
outside the parentheses,
such as a(b + c) = ab + ac
2 Language of Algebra
Continue
Did you find that x = 16?
Substitute 3 for y.
Substitute 16 for x.
16 = 2(3) + 4 +2(3)
Distributive
Property-
a property indicating a way
in which multiplication is
applied to addition of two
or more numbers in which
each term inside a set of
parentheses can be
multiplied by a factor
outside the parentheses,
such as a(b + c) = ab + ac
2 Language of Algebra
Check your Work
Sometimes, the variable you are solving for is isolated on one or the
other side of the = sign.
More often, it is not. Two guidelines will help you when you meet an
equation such as 5x + 3(x + 4) = 28.
First, simplify both sides of the equation
(if needed) then, use inverse operations to isolate the variable.
2 Language of Algebra
Use what you have learned so far to solve the equation for x.
Copy the equation onto your paper and solve.
Check your thinking with the following.
5x + 3(x+4) = 28
2 Language of Algebra
Check your Work
Distributive
Property-
a property indicating a
way in which
multiplication is applied
to addition of two or
more numbers in which
each term inside a set
of parentheses can be
multiplied by a factor
outside the
parentheses, such as
a(b + c) = ab + ac
5x + 3(x+4) = 288x + 12 = 28
First, use the distributive property and combine like terms to simplify the left side of the equation.
Subtract 12 from both sides to isolate the variable term. Finally, divide both sides by the coefficient of the variable to isolate the variable and solve the equation.
8x = 16x = ?
Coefficient-
a number or
quantity placed
(generally) before
and multiplying
another quantity, as
3 in the expression
3x.
2 Language of Algebra
Check your Work
Solving for m
PROPERTIES
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¼ (12 +16) = 10-3( -2)
2 2¼ (12 +16) = 10-3( -2)
mm
2 Language of Algebra
Component 2 Quiz
PROPERTIES
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2 Language of Algebra
Component 1
This concludes Component 2.
1 2 3 4Linear Algebra
Rules of Algebra
Using Technology
Patterns of Change