Private Tutoring Math

Algebra used with the distributive property

2010-02-25T09:23:00.000-08:00

QUESTION:

1 = - (-w + 6)
The Distributive Property is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses. Take a look at the problem below

SOLVE:
1 = - (w + 6)

The minus sign on the outside of the parenthesis means you have to change the sign of everything INSIDE the parenthesis. So, you get this...

1 = w - 6

Because you want the w on one side by itself, you have to get rid of the -6... To make -6 a zero, you have to ADD 6 to it. And what you do to one side of the equal sign, you have to do to the other... So, add 6 to the 1 also. You get this...

7 = w

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Absolute Value in Algebra

2010-02-15T13:52:00.000-08:00

This symbol--> |x| represents the absolute value of x, which is the number without its sign. |+3| = 3. |−3| = 3.

Geometrically, |x| is the distance of x from 0.

Both 3 and −3 are a distance of 3 units from 0. |3| = |−3| = 3. Distance, in mathematics, is never negative.

The absolute value leaves a positive unchanged, and makes a negative positive
An absolute value is written like this: |x|, and is read as "the absolute value of x." Note: In certain places, such as calculator and computer programs, you may see it written as abs(x), which naturally means "the absolute value of x," but |x| is the accepted way to write it on your homework and tests.

To force a number to be negative, you can write -|x|. This takes the number, makes it positive, and then negates it. Remember -- just putting a negative sign in front of a number doesn't make it negative. If the number was already negative then you just made it positive! Using the absolute value guarantees we have a positive value so that the negative sign will definitely make it negative.

EXAMPLE:

Rewrite this expression without using absolute value notation:

1) |x+1|+4|x+3| given that x<-3

If x < –3 then x+ 1< 0 and x+ 3 <0. In general, when a<0 |a| = –a, thus

|x+1|+ 4|x+3| =

–(x+1) – 4(x +3) provided x < –3 or simplifying ...

–x – 1 – 4x – 12 =

–5x – 13 when x < –3

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Ordering fraction from least to greatest

2010-02-10T05:34:00.000-08:00

How do i put fractions in order from least to greatest?

Change the denominators to be common and then convert.
EX. 4/5,5/15, 6/30
Put these in order
you have to see what is the LCM for each of the denominators. Like 30. so 4/5 turns into 24/30. I used 30 as my common denominator and to get the numerator I said how many times does 5 go into 30? 6 times! So 6 times 4 equals 24 which is my new numerator. Do this with all the fractions and then you can just put them in order by the top number.

Mean Median and Mode Range and Outliers

2010-02-09T14:18:00.000-08:00

RANGE DEFINITION:
The difference between the highest and the lowest numbers in a set of numbers.
HOW TO FIND THE RANGE:
Subtract the lowest number from the biggest and you get the range!
FIND THE RANGE
ex. 3,6,3,7,9
9-3=6 6 IS THE RANGE

MEAN DEFINITION:
average of all the numbers
HOW TO FIND THE MEAN
found by dividing the sum of the numbers by the amount of numbers added.
FIND THE MEAN
ex. 3,6,3,7,9
3+6+3+7+9=28
28 divided by 5=5.6 5.6 is your mean

MEDIAN DEFINITION:
The number directly in the middle
HOW TO FIND THE MEDIAN:
List all numbers in order from least to greatest.
You count over to the middle. If there are two numbers in the middle, add them and divide by two.
FIND THE MEDIAN
EX. 3,6,3,7,9
3,3,6,7,9 The middle number is 6. 6 is your median.
MODE DEFINITION:
The mode is the number that you see more than any other number.
The number or numbers that occur most often in a set of numbers.
EX. 3,6,3,7,9
the number that occurs the most is 3. 3 is your mode.

DEFINITION OF OUTLIER:
In statistics, an outlieR is an observation that is numerically distant from the rest of the data. Basically the number that seems to be way off from the other numbers.

EX: 3,6,5,85
The outlier would be 85

Learning Integers & Non Integers

2010-02-08T10:30:00.000-08:00

What is an integer? { ... -3, -2, -1, 0, 1, 2, 3, ... }
Integers are the whole numbers, negative whole numbers, and zero. For example, 43434235, 28, 2, 0, -28, and -3030 are integers, but numbers like 1/2, 4.00032, 2.5, Pi, and -9.90 are not. We can say that an integer is in the set: {...3,-2,-1,0,1,2,3,...} (the three dots mean you keep going in both directions.)

It is often useful to think of the integers as points along a 'number line', like this:

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10_____________________________________________________

Note that zero is neither positive nor negative.

About integers
The terms even and odd only apply to integers; 2.5 is neither even nor odd. Zero, on the other hand, is even since it is 2 times some integer: it's 2 times 0. To check whether a number is odd, see whether it's one more than some even number: 7 is odd since it's one more than 6, which is even.

Another way to say this is that zero is even since it can be written in the form 2*n, where n is an integer. Odd numbers can be written in the form 2*n + 1. Again, this lets us talk about whether negative numbers are even and odd: -9 is odd since it's one more than -10, which is even.

Every positive integer can be factored into the product of prime numbers, and there's only one way to do it for every number. For instance, 280 = 2x2x2x5x7, and there's only one way to factor 280 into prime numbers.

There are also things called non integers....such as fractions,Pi, and repeating decimals.

Example Question:
y is a integer.
-3 < y < 2
what are all the possible values of y?

Answer:
So it would be all the numbers in between -3 and +2
Answer: -2,-1,0,+1

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Substituting equations to solve.

2010-02-07T17:37:00.000-08:00

Example Question:
x= y-7
-y=2x=8

Example to solve substituting equations to solve..

substitute 1st equation into the 2nd one

-y = 2*(y-7) - 8
-y = 2y - 14 - 8
-y = 2y - 22
-y - 2y = -22
-3y = -22
y= 22/3

substitute the value of y in the 1st equation to get x.

Fractions into Decimals into Percents

2010-02-07T17:17:00.000-08:00

directions: write each fraction as a decimal rounded to the nearest hundredth.
a. 3/8

When turning a fraction into a decimal you have to divide the top Number ( numerator) by the bottom number (denominator). So for example you would divide 8 divided by 3. you get the answer 2.6666666. to round to the nearest hundredth you round to the second number after the decimal. so it would round to 2.67 is the first answer.

CHANGING DECIMALS INTO FRACTIONS
Directions:change .10 into a faction

Move the decimal over twice to the right and put the number(10) over 100 and then reduce the fraction. 10/100 reduces to 1/10.

CHANGING A FRACTION INTO A PERCENT
When you are changing a fraction into a percent you have to divide the numerator into the demoninator and this will give you a decimal answer. Move the decimal point in this answer twice to the left and you now have our percent.

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Slope Intercept Form

2010-02-07T16:19:00.000-08:00

Slope–intercept form
Y=Mx+B
where m is the slope of the line and b is the y-intercept, which is the y-coordinate of the point where the line crosses the y axis. This can be seen by letting x = 0, which immediately gives y = b. Vertical lines, having undefined slope, cannot be represented by this form.
[edit] Point–slope form

Point slope Form
Y-y1=m(x-x1)
where m is the slope of the line and (x1,y1) is any point on the line. The point-slope and slope-intercept forms are easily interchangeable.
The point-slope form expresses the fact that the difference in the y coordinate between two points on a line (that is, y − y1) is proportional to the difference in the x coordinate (that is, x − x1). The proportionality constant is m (the slope of the line).
Start with point slope form

y - y1 = m(x - x1)

Distribute the slope m

y - y1 = mx - mx1

Add y1 to both sides

y = mx - mx1 + y1
y = mx + b

Example:
A line has a slope of 4 and passes the point (1,2). Write the equation of the line in slope-intercept form.

y - 2 = 4(x - 1)
y - 2 = 4x - 4
y = 4x-2

Question:
Q: Given the ordered pairs of (4, - 1) (5, - 2), develop an equation in the slope intercept format.

A: to find slope of the order pairs use y2-y1/x2-x1 the slope will come out to be m= -1

use point slope form to develop equation y=m(x+b)
(m =slope)
you will get Y=-1(X-4)-1 --->Y= -X+5

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Begining Algebra & Order of Operations (PEMDAS)

2010-02-05T18:24:00.000-08:00

Here is a Order of Operations question that is using the strategy PEMDAS. It is a way to remember the order. I use the sentence Please Excuse My Dear Aunt Sally.
1st: do all operations in the Parenthesis
2nd: Solve all Exponents
3rd: Solve all Multiplications
4th: Solve all Division
5th: Solve all Addition
6th: Solve all Subtraction

(-4)(8-10)= ?
(-6-12)÷3 to the power of 2= ?

-4 times 8=____ next
take that answer and minus -4 times 10
This will give you the first answer...

first subtract -6 minus 12 ( Think of this like money... if you already owe $6 and borrow another $12 then how much are you negative now?)Next take that answer and divide it by 3.
( remember a negative and a positive make a negative)
Next take that answer and when you make it to the power of two you just multiply oit by itself.
(Ex..3 to the power of 2 would be 9.)

Math Manipulatives

2010-02-05T12:36:00.000-08:00

Math word problems are almost always the type of problems that require an out of the box learning strategy. Some of the most newest on the market manipulative's are great to use such as geoboards to for geometry to CD ROM activity game to walk you through steps of Pre Calculus. And as always you can always use a good pen and paper and write the problem out step by step. These techniques help the student focus visually. Most students qualify under this category of visual learner. This means that the recall and input of information is is pout into a visual concept. When I was in the classroom I always found the one subject that worked best was with manipulative's was math. Even if it didn't seem needed, it always seem to register better in long term memory when i did use them.

Here is a great example of using write it out stratagy.

Question:
Juan has a cell phone that costs $12.95 per month plus $0.25 per minute for each call.
Tiff has a phone that costs $14.95 per month plus $.15 per minute for each call.

For what number of MINUTES do the two plans cost the same?

You can get a feel for this problem by diagramming it out on graph paper. The money is on the left, and the minutes run along the bottom.

Start Juan's diagram at $12.95, and continue slanting it upwards at the rate of $0.25 for each minute.
Start Tiff's diagram at $14.95, and continue slanting it upwards at the rate of $0.15 for each minute.

Where the lines cross is the answer to the problem.

There is an algebraic solution too that I will show you but writing it out would work great if you didnt know the algebraic equation to use.

x = number of minutes

Juan cost = 12.95 + 0.25x

Tiff cost = 14.95 + 0.15x

to cost the same, set the two equations equal to each other

12.95 + 0.25x = 14.95 + 0.15x

combine like terms

0.25x - 0.15x = 14.95 - 12.95

.10x = 2

x = 2/.1

x = 20 minutes

About Private Tutoring Math...

2010-02-05T05:35:00.000-08:00

My name is Diana and I am currently a certified Florida teacher. I own my own tutoring company and come across many students with math homework questions with nowhere to turn for help. I am creating this blog to provide math homework help and new and up to date useful learning strategies and information to help students achieve correct math answers with up to date information on the latest math help manipulative's, new online teaching and learning strategies and information on teaching skills for both teachers and students. I will be covering all topics in math including Algebra, Geometry, Calculus, and Pre Calculus. Also, I will cover all the math equations and simple word problems with addition, multiplication, division,and subtraction. I am trying to reach all ages with math homework help. I have strategies and manipulative suggestions that will help you take math homework questions and soar into new heights with a brightened understanding.

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