TennesseeAdult Education

Algebra

Lesson 5

This curriculum was written with funding of the Tennessee Department of Labor and Workforce Development and may not be reproduced in any way without written permission. ©

What is Algebra?

A clown was carrying a handful of balloons. Along came the wind and blew 8 away, leaving him only with 9. How many did he start with?

Algebra takes real life problems and puts them into math so we can solve them.

x-8 = 9

The goal in Algebra is to find out the unknown!

20 pennies

6 pennies

+ ? pennies

20 = 6 + x

A scale has 20 pennies on one side . On the other side is 6 pennies and an unknown amount of pennies. Both sides equal the same weight.

x-8 = 9

x-8 9

+8 +8x = 17

What is Algebra?

A clown had 17 balloons. Along came the wind and blew 8 away, leaving him only with 9.

The goal in Algebra is to find out the

unknown!

-3 + 7 =

- - - +++ +++ +

4

-Different signs subtract numbers

-Always keep the sign of the larger number when subtracting and adding

-2 + 9 =

- - +++ +++ +++

7

-4 + 2 =

- - - - ++

-2

-7 + 5 =

- - - - - - - +++ ++

-2

-3 + 16 =

- - - +++ ++++ +++ +++ +++

13

-5 + -5 =- - - - -- - - - -

-10

-if both negatives, add together- keep the negative sign

-8 + -4 =

- - - - - - - -- - - -

-12

In math 2 negatives (-)(-)

equal a positive (+)

-4 – (-3) =

- - - -+++

-1-4 + 3 =

-8 – (-4) =

- - - - - - - -+++ +

-4-8 + 4 =

-6 – (-8) =

- - - - - -+++ +++ ++

2-6 + 8 =

-2 – (-7) =

- -+++ +++ +

5-2 + 7 =

-9 – (-3) =

- - - - - - - - -+++ +++

-6-9 + 3 =

Rule Add/Subtract

Same signs -add numbers

1 + 3 = 4-1 - 3 = -4

Different signs -subtract numbers

-3 + 4 = 14 – 3 = 1

Keep sign of the largest number

Rule Add/Subtract

++- -

4 + (-2) = 4 – 2 = 2

+ -- +

-3 – (-4) = -3 + 4 = 1

Guided Practice

1. +8 – 14 = ______

2. -2 + 11 = ______

3. -33 - 22 = ______

4. (-7) + (-3) = ______

5. (-10) + (16) = ______

6. -4 – (-4) = ______

7. 5 x -3 = ______

8. -6 x 2 = ______

9. -4 x -8 = ______

10. 42 ÷ -7= ______

11. -3 x -9 = ______

12. -20 ÷-2 = ______

Order of OperationsPlease Excuse My Dear Aunt Sally

1. Parenthesis (4-2)

2. Exponent 4³

3. Multiply 4(3) or 4x3

4. Divide 4÷2 or 4/2

5. Add 4+2

6. Subtract 4-2

(6-4)² - 2 =

(2) ²- 2 =

4 – 2 =

2

(6x2)(8÷2) ² =

(12)(4) ² =

(12)(16) =

192

2(3 + 2 x 6 -1)² =

2(3 + 12 – 1) ² =

2(15 – 1) ² =

2(14) ² =

2(196) =

392

3 x 4 + 6 ÷ 2 + 5 - 1

12 + 6 ÷ 2 + 5 – 1

12 + 3 + 5 – 1

15 + 5 – 1

20 – 1

19

Key Terms

• product

• squared

• sum

• difference

• half

• quotient

• decreased

multiply

times itself

add

subtract

divide by 2 or ½

divide

subtract

Guided Practice

six more than the square of four is twenty two=

4² + 6 = 22

5x – 1 = 7

one less than five times a number equals seven

the quotient of a twelve and four plus a number

12 ÷ 4 + n

Algebra Rules

1. What you do to one side you must do to the other. This keeps them equal.

2. You must get the variable by itself to find out what number value it equals.

Guided Practice

-4 = x + 2

-2 - 2

x = -6

3 + 2n = 43

-3 -3

2n = 40

2 2

n = 20

½ n -4 = 9-2

½ n -4 = 7

+4 +4

½ n = 11

2( ½ n) = 11(2)

n = 22

Substitution

– you put the number where the letter was

what is:x-2

if x = 6

6 -2 = 4

Guided Practice

3(n) – 2(4) + 16 / x if x = 4

3(4) – 2(4) + 16 / 4

12 – 8 + 16 / 4

12 – 8 + 4

12 – 12

0

Guided Practice

b³c + bc + 2b² if b = 3; c = 4

(3) ³(4) + (3)(4) + 2(3) ²

9(4) + (3)(4) + 2(9)

36 + 12 + 18

66

Key Terms

• expression– a way to represent spoken information about an

unknown number:

“a number plus 3” = n + 3

• equation– shows that two quantities are equal

• inequality– uses symbols < and > to show “greater than” and

“less than”