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# Pre-Algebra Homework Help

### Pre Algebra Contents

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Online Pre Algebra assignment help Services.

### Pre Algebra Operations

```1)  Parenthesis

2)  Powers

3)  Divisions / Multiplication > (left to right)

4)  Subtraction / Addition > (left to right)

Algebraic expression involving multiplication and division

9xm= 9*m= 9(m)= 9m

7xaxb= 7*a*b= 7(a)(b)= 7ab

y/3= y/3

ex.1) Evaluate m(7+w); m=9

9(7+3); w=3

9(10)

90

ex.2) Evaluate 8+ab/40; a=8

8+8*10

40

8+80

40

8+2

10

ex.3) Evaluate 3y+9 ; y=9

2y

27+9

18

36

18

2

```

Patterns and Variables

### Translating Phrases to Algebraic Expressions

```sum +

difference -

product *

quotient /

Translate to a numerical expression

ex.1) the difference of 10 and 5 = 10-5

ex.1) 4 less than 10 = 10-4

ex.3) the product of 8 and 7 = 8*7

ex.4) 45 divided by 3 = 45/3

ex.5) a number increased by 7 = h+7

ex.6) 5 less than a number = n-5

ex.7) 35 increased by twice a number = 35+2*d

ex.8) 1 less than a number divided by 10 = d/10-1
```

### Properties

```Commutative:

a+b = b+a

a*b = b*a

ex.1) 5*7 = 7*5

ex.2) m+7 = 7+m

Associative:

ex.1) (98+47)+53 = 98+(47+53)

98+100

198

ex.2) 7*(5x) = (7*5)x

35x

Identity:

a+0 = a

a*1 = a

Distributive:

a*(b+c) = a*b+a*c

ex.1) a*(3+5) = 9*3+9*5

27+45

72

ex.2) 6(r+s) = 6r+6*5

6r+30

ex.3) (m+7)4 = 4m+28

ex.4) 86*48+86*52
```

### Simplifying Algebraic Expressions

```Simplify - replace with a simpler equivalent expression

ex.1) Simplify  3(2n)

(3*2)n

6n

ex.2) (x+7)+6

x+(7+6)

x+13

Term - parts of an expression separated by + or -

4m+2n-3

terms

Like terms - terms with the same variable 2n and 3n are like terms,

4m and 2m are unlike terms

ex.3) 2x+3x

(2+3)x

5x

ex.4) 25g+15g

(25+15)g

40g

ex.5) 2m+3m+m

6m

ex.6) 4e+3f+e

5e+3f
```

### Integers

```Integers {.-3,-2,-1,0,1,2,3,.}

Numbers such as 4 and -4 are opposites.

The opposite of -4 is written -(-4) = 4.

Absolute Value - distance from zero

ex.1) | 7 | = 7

ex.2) |-4 | = 4

ex.3) | 0 | = 0

ex.4) Find m if | m | = 8.  m = -8,8

Order from least to greatest

ex.5) -1,-6,4 = -6,-1,4

ex.6) -2,|-3 |, -1,| 4 |

3         4

-2,-1,|-3 |,| 4 |

```

### Adding and Subtraction Integers

```Think about money (+ : \$ you have)

(- : \$ you spent)

ex.1) 3+-2 = 1

ex.2) -3+2 = -1

ex.3) -2+-3 = -5

To subtract, we add the opposite of the second number.

|------|   |------|   |------|

| 9-7  | = | 5-1  | = | 2-3  | =

| 9+-7 | = | 5+-1 | = | 2+-3 | =

|------|   |------|   |------|

NOTE: -5 = -5

ex.4) 3-2 = 1

ex.5) -3-2 = -5

ex.6) 3- -2 = 5

ex.7) -3- -2 = -1

```

### Multiplying and Dividing Integers

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

different the answer is negative.

ex.1) 4*-5 = -20

ex.2) -4*5 = -20

ex.3) -4*-5 = 20

ex.4) (-5)3 = -125

ex.5) 42/-7 = -6

ex.6) -42/7 = -6

ex.7) -42/-7 = 6

If n = + then n5 = +

If n = - then n5 = -

If n = + then n8 = +

If n = - then n8 = -

```

### Factors and Multiples

```
factors        product

7*4      =      28

factors of 8 = 1,2,4,8

factors of 84 = 1,2,3,4,6,7,12,14,21,28,42,84

Divisibility - one number is divisible by another if their quotient

is a whole number (no remainder)

ex.1) Is 11 a factor of 143?

ex.2) Is 9 a factor of 326?

Divisibility rules

2 - even

3 - add digits, test 3

4 - test last 2 digits

5 - end in 0 or 5

Multiples - counting by a number

ex3.) List the multiples of 5

0,5,10,15.

ex.4) List the first 3 nonzero multiples of 11\

11,22,33.

```

### Adding and Subtracting Fractions

```
ex.1) 2/5 + 1/3 = 6/15 + 5/15 = 11/15

ex.2) 3/10 + 6/15 = 9/30 + 12/30 = 21/30 = 7/10

ex.3) -2/5 - 3/6 = -12/30 + -15/30 = -27/30 = -9/10

ex.4) 5/6 - -3/4 = 10/12 + 9/12  = 19/12

Reducing Fractional Expressions

ex.1) 3mb/7mk = 3b/7/k

ex.2) 4ef/12f = 1e/3

ex.3) 15ac2/25a2c   15acc/25aac   15c/25a   3c/5a

Adding and Subtracting Mixed Numbers

ex.1) The west wall measures 60 9/16" and 217 7/8". Find the

total length?

ex.2) 3M stock rose from 50 _ to 51 5/8. What was the increase?

ex.3) GM stock fell from 52 1/8 to 50 3/4

```

### Multiplying Rational Numbers

```

Multiply / Divide rules

+ + = +

+ - = -

- + = -

- - = +

ex.1) 2/5 * 5/12 = 10/60

ex.2) -6/4 * -3/5 = 9/10

ex.3) 1/2 of 3/4 = 3/8

ex.4) 2 2/3 (1 1/5) = 16/5

ex.5) 3 1/12 (-2) = 37/6

ex.6) (5/8)2 = 5/8 * 5/8 = 25/64

```

### Reciprocals and Dividing Rational Numbers

```  - two numbers are reciprocals if their product is 1

ex.1) 2/3 in the reciprocal of 3/2 because 3/2 * 2/3 = 1

ex.2) what is the reciprocal of -2000m/3, _______

how many halves are in 3?

3/ 1/2 = 6

2 1/2 / 1/4 = 10

ex.3) 2/3 / 1/6 = -4

ex.4) -5/24 / 5 = -32/15

ex.5) 8/ (-3 _) = -1/24

ex.6) -3 1/8 / -2 1/12 = 3/2 (1 «)

```

### More About Exponents

```Review: Exponents are used to show how many times the some factor is

repeated.

exponent

43 = 4 x 4 x 4 = 64

base

ex.1) 82 = 8*8 = 64

ex.2) 24 = 2*2*2*2 = 16

ex.3) (-.03)2 = -.03 x -.03 = .0009

Rule: To multiply two powers with the same base, we add the

exponents.

ex.1) 32 * 34 = 36

ex.2) 103 * 102 = 105

ex.3) 24 * 2 = 25

Try the following: 45/42 = 43

This suggests a rule for simplifying expressions in this form.

Rule: To divide two powers with the same base, we subtract the

exponents.

ex.1) 25/23 = 22                       ex.4) x6/x2 = x4

ex.2) (-3)7/ (-3)4                     ex.5) m5/m

ex.3) 104/10                           ex.6) 34/34

you can also use the rule given above to simplify the expression

52/54

52/54 = 1/52                                52/54 = 5-2

This shows that 1/52 is the same as 5-2

ex.1) 3-2 = 1/32 = 1/9      ex.3) (-2)-4 = 1/-2-4 = 1/16

ex.2) 5-3 = 1/53 = 1/125    ex.4) 4-1 = 1/-4

```

### Scientific Notation

```Review

103 = 1000                10-3 = 1/1000 = .001

105 = 100000              10-5 = 1/1000000 = .00001

106 = 1000000             10-6 = 1/10000000 = .000001

Scientific notation is used to simplify work with very small or very

large numbers.

3.45      X       103

A decimal between 1 and 10                a power of 10

Write in standard form.

ex.1) 5.8 x 103 = 5800       ex.2) 6.556 x 102 = 655.6

ex.3) 1.8 x 10-4 = .00018    ex.4) 4 x 10-2 = .04

Write in scientific notation.

ex.1) 4567 = 4.567 x 103       ex.2) 1,234,000 = 1.234 x 106

ex.3) 234,000 = 2.34 x 105     ex.4) 50,000,000 = 5.0 x 107

ex.5) 0.000345 = 3.45 x 10-4   ex.6) 0.0206 = 2.06 x 10-2

ex.7) 0.000008 = 8.0 x 10-6    ex.8) 0.2004 = 2.004 x -10

Why are these not in scientific notation?

ex.1)(10 is less than 12.5) 12.5 x 104     ex.2) 2 x 4-5 (the

base must be 10)

Give two reasons for using scientific notation.

1.)  easier for large numbers

2.)  nicer for comparing

```

### Solving Two Step Equations

```

SOLVE

review:     m-17 = 24       3m = 5

m+5 = 11         m/4 = 9

Rule:  Solving equations with combined operations

A: Identify the order the operations were applied to the variable.

B: Undo the operations in reverse order.

```

### Functions

```

Definition: A function is a special relationship between two

variables.

Domain- number put into the function (input).

Function notation: f(x)

ex.) f(x) = 3 x +4

then f(5) = 3(5)+4

= 15+4

= 19

```

### More Simplifying to Solve Equations

```Like terms- have the same variable and exponent

ex 3m+2m = 5m

Unlike terms- cannot be simplified

ex 3m+2k

3m2+2m

ex.1) 9k+5 (k+7) = -49

ex.2) 2m+3(m-7) = 44

ex.3) 3(5n)+14+6n = 21

ex.4) -2(7c)-12+5c = 51

```

### Solving Equations with Variables on Both Sides

```1: Get the variable on one side

2: Solve as always

ex.1) -4(2m-5) = -4m+10

-8m+20 = -4m+10

+8m         +8m

20 = 4m+10

-10          -10

10 = 4m

4     4

5/2 = m

ex.2) 2(m+2) = 2m+4

ex.3) 2(m-2) = 2(m+1)
```

### Ratio, Rate, Proportion

```
Ratio- a comparison of one number to another.

ex.) 3/5 or 3.5 or 3 to 5

Rate- a ratio that involves two different units.

ex.) 216miles/4hours = 54m/h

Proportion- An equation starting that two ratios are equal.

We can use cross product to solve proportions.

ex.1) 2/3 = 24/n     ex.2) 9/12 = 3/n     ex.3) 9/10 = n/22

ex.4) The lions in the zoo eat 40kg.

Of food every 7 days. How many

kg. do they eat in 30 days?

Kg./days     40/7 = k/30

1200 = 7k

7    7

171 = k
```

### Percent, Decimals, and Fractions

```     Percent means hundredths or "out of 100"

Change to decimal.

1.)  43% = 43/100 = .43

2.)  90% = .9

3.)  2% =

4.)  34.7% = .347

5.)  10 «% =

Change to percent.

1.)  .27 = 27%

2.)  .06

3.)  .7

4.)  .065

5.)  .7/8 = 87.5%

```

### Finding a Percent of a Number

```   Estimating Percents

ex.1) 63%\$ of 61

« of 60 = 30

ex.2) 27% of 79

¬ of 80 = 20

Using Proportions

ex.3) 90% of 25

90/100 = n/25  2250 = 100n

100    100

22.5 = n

Using Decimals

ex.4) 6.5% of \$80

.065 x 80 = 5.20

ex.5) 15% of \$25

.15 x 25 = 3.75

Using a calculator

ex.6) 22% of 150

33

```

### Finding the Percent One

```     Number is of Another

"what percent" … n/100

of _ …

ex.1) 17 is what percent of 25?

n   =  17

100     25

25n   =   1700

25         25

n = 68%

ex.2) What percent is 8 out of 13?

n   =   8

100     13

ex.3) What percent of 72 is 12?

n   =   12

100      72

ex.4) What % of 72 is 90?

n   =   90

100      72

```

### Percent of Increase of Decrease

```
change

original = _ %

ex.1) My weight on January 1st = 140

My weight on February 1st = 144

change

original = 4/140 = .0285 = 3%

ex.2) Jenny runs the mile in 9 minutes

in June. In July she can run it in 8

minutes.

change

original = 1/9 = .111 = 11%

```

### Calculating Simple Interest

```

When you borrow money from a bank, credit union, or loan company

you pay for the use of it.  The amount you pay for the use of money

is called interest.

The amount of interest you pay depends upon the principle (amount

borrowed), the rate (percent of interest) charged, and the length of

time the money is kept (time).

Interest = Principle * Rate * Time

I = P * R * T

ex.1) Calculate the interest         ex.2) Principle = \$80,000

on a \$800 loan at 8% interest              Rate = 8% per year

per year if you paid it back in            Time = 30 years

2 years.

ex.3) You use your credit card       ex.4) Principle = \$5000

to buy \$500 worth of clothes.              Rate = 1.5% per month

You have to pay 15% interest               Time = 2 years

per year. How much interest

would you pay after 1 year?

What did the clothes really cost?

ex.5) You put \$1000 in the bank      ex.6) Principle = \$1000

and leave it in for 3 months at            Rate = 8% per year

2.5% interest per year. How much           Time = 3 months

interest do you make? How much

money do you have now?

ex.7) Principle = \$1,000,000

Rate = 8% per year

Time = 3 months

```

### The Basic Counting Principle

```
To find the total number of choices for an event, multiply the

number of choices for each individual part.

ex.1) How many outcomes are possible if you first toss a coin,

then roll a die?

2 * 6 = 12 outcomes

ex.2) How many different pizza combinations can you make with 2

crusts, 2 sauces, and 4 toppings? (only a one topping pizza)

2 * 2 * 4 = 16

ex.3) How many license plates can be made in Minnesota?

10 * 10 * 10 * 26 * 26 * 26 = 17576000

```

### Permutations and Combinations 14-2

```

An arrangement of a group of objects in a certain order is

called a permutation.

ex.1) Andy, Bob and Chris are to be seated at 3 desks arranged

in a row. How many ways can the 3 students arrange themselves?

3 * 2 * 1 = 6

ex.2) Steve, Rachel, Teddy and Kristin are on our 4x100 relay.

How many running orders are there for this relay?

4 * 3 * 2 * 1 = 24

ex.3) 20 people are running for student council. How many

different permutations are there?

20 * 19 = 380 (president & vice president)

A selection of objects without regard to order is called a

combination.

ex.4) choose 2 of these 4: Art, Band, computer, Drafting.

ex.5) Almond Joy, Butterfinger, Crunch, Dollar Bar; choose 3 of 4.

```

### Probability

```
Probability = ways for an outcome to occur

total outcome

Flipping a coin:

ex.1) P(getting tails) = «

ex.2) P(getting heads) = «

Rolling a Die:

ex.3) P(rolling a 5) = 1/6

ex.4) P(not rolling a 5) =

ex.5) P(rolling a 1 or 5) = 2/6 = 1/3

ex.6) P(rolling a 7) =

ex.7) P(rolling a number <7) = 6/6 = 1

Note: If any outcome is certain to happen then

the probability of that outcome is 1.

If any outcome is impossible then the

probability of that outcome is 0.

ex.8) Find P(winning the daily 3)

1/1000

1/10 * 1/10 * 1/10 = 1/1000

```

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