Chapter 1 Study Guide

PEMDAS: Please Excuse My Dear Aunt Sally

#1

Step 4: Add or Subtract in order by reading the problem from left to right.

Step 1: Parenthesis first

Step 2: Exponents or powers second

Step 3: Multiply or Divide in order by reading the problem from left to right. _

___ _

_

The rules for order of operations exist so that everyone can perform the same consistent operations and achieve the same results.

The rules for order of operations exist so that everyone can perform the same consistent operations and achieve the same results.

Follow all the rules for order of operations. Remember PEMDAS

#2

20 2 451 1

2(41 2 4)0

2(110 46) 10 32 4

10 8

18

#3

210 2 6 3 1

Parenthesis 1st

Exponents 2nd

Mult./Div. left to right

Add/Subt. left to right

P

E

MD

AS

210 2 6 2

10 2 6 4

10 2 2

10 4

14

An expression is NOT an equation because it does not have an equal sign. There are 2 types of expressions.

NUMERICAL EXPRESSION: Contains only numbers and symbols. Example: 5 3 + 4

ALGEBRAIC EXPRESSION: Contains numbers, symbols, and variables. Also known as a variable expression. Example: m + 8

A VARIABLE is a letter or symbol that represents a number. Example: x

TYPES OF EXPRESSIONS #4

#5 Substitute & Evaluate

when x = 2 and y = 4 Evaluate3( )x y3(2 4) Show the substitution

36

216

Show your work down

Circle your answer

Show your work down, one step at a time, no equal signs!

addplussum

increased bytotal

more than

added to

subtractminus

differencedecreased by

diminished by

less than

subtracted from

less

multiplytimes

product…of...twice 2

dividequotient

Key Words#6

WORD PHRASESA word phrase is a sentence that can be translated into a variable expression or equation.

A word phrase is like a verbal phrase. It is made up of only words.

Example: The difference of 8 and a number.

Algebraic Expression: 8 - n

#7

Write an Algebraic Expression for the Word Phrases.

5.8 more than 4 times a

5.8 + 4a or 4a + 5.8The difference of 3a and 2

3a - 26 less than the number 58t

58t - 6

# 8

Integers Integers- are the set of numbers including positive whole numbers, negative whole numbers and zero.

0 1 2 3 4 5 6-1-2-3-4-5-6

Negative Negative NumbersNumbers

Positive Positive NumbersNumbers* Negative

integers are less than zero

*Positive integers are greater than zero

* The integer zero is neither positive or negative

#9

OppositesPairs of integers that are the same distance from zero on a number line are opposites.

Example: 3 and -3 are opposites because each integer is 3 units away from zero

Other Examples:

2 and –2 5 and -5

#10

Absolute ValueAbsolute Value Absolute value of an integer is the distance the number is from zero on a number line.

0 1 2 3 4 5 6-1-2-3-4-5-6

Examples:Examples: |-2| = 2 |1| = 1

The absolute value of -5 is 5 spaces from zero.

#11

Two vertical bars around the number means find the absolute value.

Steps To Add Integers1) Put in the 1st number of + or –

2) Add the 2nd number of + or –

3) Balance out what you have

5) The leftovers are the final answer

Virtual Manipulative: Color Chips - Addition

#12

4) One + balances out one –

When a + and – cancel each other out it is called a NEUTRAL FIELD or ZERO BANK

Integer Addition Rules If the signs are the same

Add the numbers. The sign stays the same.

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

7 _ _ _ _ _ _ _-7

If the signs are different Subtract the numbers. The “larger number” determines the sign of the answer.

-9 + 5 =

9 - 5 = 4Subtract the numbers

- 4

#13

_ _ _ _ _ + + + + +

_ _ _ _

Answer -4 because you started with more negatives

8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8

IntegerElevator

Ground Floor

-5 + 2 = -3

-5+2

Positive = UpNegative = Down

Add Integers With a Number Line

#14

1) Put in the 1st number of + or –

2) Subtract, or remove, the 2nd number of + or

– Show that you remove them by circling them & attaching an arrow to them.

3) IF YOU CANNOT REMOVE THE 2nd NUMBER ADD ENOUGH ZERO PAIRS SO YOU CAN.

4) Count your remaining tiles. (one + balances out one - )

5) Record your answer (the leftovers)

#15

3 - 2 1) Put in 3 2) Take away 2 3) You are left with 1

= 1

3 - -2 1) Put in 3

2) You can’t take away –2 so add 2 zeros

3) Take away -2

4) You are left with + 5

= 5

+ +

+ + +

- -

+

+ +

#16

-3 - -21) Put in -3

2) Take away -2

3) You are left with -1

= -1

-3 - 2 1) Put in -3

2) You can’t take away 2 so add 2 zeros3) Take away +2

4) You are left with -5

= -5

http://www.matti.usu.edu/nlvm/nav/frames_asid_162_g_2_t_1.html

_ _

_ _ _

+ +

_

_ _

#17

Subtracting Integer Rules

Keep the first number and add the opposite.

5 – 6 5 – 6 Is the same as = -1

4 – (– 2) Is the same as 4 – (– 2) = 6

-3 – 1 Is the same as -3 – ( 1) = -4

#18

* SUBTRACT = PLUS CHANGE!

8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8

IntegerElevator

Ground Floor

-4 - 2 =-6

-4

-2

1)Start at 0. Move to the 1st number.2) Then look at the 2nd number.

3) Subtract a Positive = Down

4) Subtract a Negative=Up

Subtract Integers With a Number

Line

#19

To Remember Multiply & Divide Integers

#20

When good things, happen to good people, that’s good!

+ • + = +When bad things, happen to bad people, that’s good!

– • – = +When good things, happen to bad people, that’s bad!

+ • – = –When bad things, happen to good people, that’s bad!

– • + = –

+ + = +

– – = +

+ – = –

– + = –

RULES FOR DIVIDING INTEGERS

When determining the sign, the rules of multiplying integers are the same for dividing integers.

If the signs are the same, the answer is positive.

- 64 - 8 = 8

If the signs are different, the answer is negative.- 8 4 = -2

#21

0 8 =

8 0 =

0

undefined

22 Dividing with Zero

A calculator might display “ERROR” when you divide by 0.

0

8YES!

8

0

No ZERO in the denominator!

EquationsAn equation is a mathematical statement that shows 2 quantities are equal. An equation contains an equal sign.

#23

12 – 3 = 9 Numerical 3a = 30 Algebraic

To solve any equation use inverse operations.Your goal is to get the variable all by itself.

To solve an addition equation

m + 8 = 12 Get the variable alone.

– 8 –8 Subtract 8 from both sides.

m = 4 +8 and -8 cancel each other out.

4 + 8 = 12 Show your check.

Subtract the same number from both sides

#24#24

12 = 12 Finish your check!

To solve a subtraction equation

a – 15 = 22 Get the variable alone.

+15 +15 Add 15 to both sides.

a = 37 +15 and -15 cancel out

37 - 15 = 22 Show your check!

Add the same number to both sides

#25

22 = 22 Finish your check!

To Solve a Multiplication Equation

5x = 40 Get the variable alone.

5 5 Divide 5 into both sides.

x = 8 5 divided by 5 cancels out to 1.

5 8 = 40 Show your check!

Divide the same number into both sides

#26

40 = 40 Finish your check!

To Solve a Division Equation

= 20 Get the variable alone.

2 = 2 20 Multiply both sides by 2.

x = 40 2 divided by 2 cancels out to 1.

Show your check!

x 2x

2

Multiply the same number to both sides

#27

4020

2

20 = 20Finish your check!