Component 2 The Language of Algebra. 2 Language of Algebra “Rules of Algebra” Stage 1 Stage 2...

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

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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