How to Study For Algebra

Algebra is the division of mathematics concerning the revise of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. For example:

x - 6 = 2

x – 6 + 6 = 2 + 6

x + 0 = 8

x = 8 (the answer)

The algebraic statements that explain relationships are expressed using algebraic terms, expressions, or equations. Earlier than we use algebra to find information about these kinds of relationships, it is important to first covers some basic terminology. Please express your views of this topic math answers for pre algebra by commenting on blog.


Algebraic Expressions


An expression is a significant group of numbers, variables, and signs, positive or negative, of operation that must make mathematical with logical sense. Expressions:

• contain any number of algebraic terms

• Use symbols of operation—addition, subtraction, multiplication, with division.

• do not contain an equality sign (=)

Example for an expression is:

–4ax + 5wx^2y

In an expression, the symbols of operation separate it into terms. The symbol also becomes part of the term that it follows. The expression more than contains two terms, the first term is –4ax and the second term is +5wx^2y. The addition sign separates the two terms. For example, in the term given above the plus sign (+) separates the –4ax from 5wx^2y and is also part of the second term. Conditions that do not have a sign listed in front of them are understood to be positive. I have recently faced lot of problem while learning Math Parallel Lines, But thank to online resources of math which helped me to learn myself easily on net.


Terms and Factors


A word in an algebraic expression is an expression concerning letters and/or numbers (called factors), multiplied together.

Example 1:

The algebraic expression

9x

is an example of one single term. It has factors 9 and x.

The 9 is called the coefficient of the expression.

Example 2:

5x + 3y have two conditions.

First term: 5x, has factors 5 and x

Second term: 3y, has factors 3 and y

The 5 and 3 are called the coefficients of the conditions.

Like Terms

"Like terms" are terms that enclose the same variables raised to the same power.

Examples

3x^2 and 7x^2 are like terms.

-8x^2and 5y^2 are not like terms, since the variable is not the similar.

First Quadrant

Definition:

The x- and y- axis divides the coordinate plane into 4 regions. These regions are called the quadrants.

Each quadrant bounded by two half-axes. These are often numbered from first to fourth and denoted by Roman numerals: I (where the signs of the two coordinates are (+,+), II (-,+), III (-,-), and IV (+,-). When the axes are drawn according to the mathematical form, the numbering goes counter-clockwise starting from the upper right ("northeast") quadrant.


Cartesian coordinate system


A Cartesian coordinate system specifies each and every point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length.

Each reference line is called a coordinate axis of the system, and the point where they meet is its origin. The coordinates are also defined as the positions of the perpendicular projections of the point onto the two axes, expressed as a signed distances from the origin.

Cartesian coordinates can be used to point out where you are on a map or graph.

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Examples:


Identify the quadrant in which the points (4, 2) and (3, 8) are located.

Choices:

A. first and second quadrants respectively

B. second and third quadrants respectively

C. second and fourth quadrants respectively

D. only the first quadrant

Correct Answer: D

Solution:

Step 1: Start at the origin.

Step 2: Move 4 units to the right from the y-axis.

Step 3: Then move 2 units above the x-axis.

Step 4: The point (4, 2) is in the first quadrant.

Step 5: Move three units to the right from the origin on the x-axis.

Step 6: Then move 8 units above the x-axis.

Step 7: The point (3, 8) is in the first quadrant

Step 8: The points (4, 2) and (3, 8) are only in the first quadrant respectively.

Product Math Term

Introduction for the term Product in math:

The product is an expression which can be obtained by multiplying two or more numbers or expressions. The commutative law of the multiplication is the order of the complex numbers of the product. In matrices the product has a member of order of factors which has the multiplication as shown in them. We have some of the product of multiplication of numbers which can be shown it below.

Is this topic Product Property of Radicals hard for you? Watch out for my coming posts.

Notation for the term Product in Math :


The followings are some of the notations using in product math terms.

Product notations are dot (.), (*), () (), (x)

These all are symbols are using product of two numbers.

The Dot symbol (•)

The Dot symbol is used to find the product of two variables or numbers.

The Star symbol (*)

The star symbol is used to find the products of the numbers.

The Parentheses symbol ( ) ( )

The parentheses symbol is used to find the multiplication of sign numbers and it is a special symbol use only for signed numbers.

The Cross symbol (x)

The cross symbol product is used in between the two numbers. I have recently faced lot of problem while learning Sum to Product Identities, But thank to online resources of math which helped me to learn myself easily on net.


Example problems for Product Math Term:


Ex 1: Multiply 91 by 13.

Sol:

91 and 13(it is nothing but 13 times of 91.

It can written as like

= Two times of 91+1 times of 91

= 1183

= 1183

Ex 2: (a) Solve:

13 x10= 13 times 10=130

(b) Solve:

4 x 4= 4 times 4 = 16

(c) Solve:

4 x 8 =4 times 8 =32

(d) Solve:

1000 * 14 =1000times 15 = 15000

(e) Solve:

(12) .(12)=12 times 12 = 144

Arithmetic Word Problems:

Ex 3: A cost of one bags is 3 dollars. Find the price of 10 bags?

Sol:

Price of 1 bag = 3 dollars

Price of 10 bags = 10 x 3

Price of 10 bags = $30

Ex 4: There are 20 boys and 16 girls in the class. All boys are having individually 2 pen’s find the total no of pen the boys having?

Sol:

Total Number of boys = 20

Total Number of girls = 16

Each boy having 2 pens

Total no of pens= 20 * 2 = 40.

Math Integers

Introduction:

In arithmetic, an integer valued polynomial P (t) is a polynomial taking an integer value P(n) for every integer n. absolutely every polynomial with integer coefficients is integer-valued. There are simple examples to show that the converse is not true: for example the polynomial. I like to share this Polynomial Regression with you all through my article.


t(t + 1)/2

Giving the triangle information takes on integer values whenever t = n is an integer. That is because one out of n and n + 1 must be an even number.

Source Wikipedia


Integer valued polynomial Explanation:

In this integer valued polynomial express the values are real numbers. For every polynomial are integer coefficients.

Here will explain the indegervalued polynomials in the example

The general formula for the integer valued polynomials is given below use this formula and express the inter even numbers

t (t+1)/2

This formula using to evaluate the real number.

For example t=3 we take to express the equation Answer for this problem.   we sub suite the value in above formula to drive the equations.

The triangle numbers takes on integer values whenever t = n is an integer. That is because one out of n and n + 1 must be an even number.

= 3(3+1)/2

=3(4)/2

=12/2

Answer = 6

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Integer valued polynomial examples:


Example1:

To find the value of the given problem?

If t=6 and find the polynomial

Solution:

The triangle numbers takes on integer values whenever t = n is an integer. That is because one out of n and n + 1 must be an even number.

We use the formula and express the given problem

Formula=t(t+1)/2

=6(6+1)

=6(7)

Answer =42

Each polynomial with numeral coefficients is integer-valued.

Example2:

To find the value of the given problem?

If t=8 and find the polynomial

Solution:

We use the formula and express the given problem

Formula=t(t+1)/2

=8(8+1)

=8(9)

Answer  = 72

Math Ordered Pairs

Introduction to ordered pair learning:

Ordered pair learning is a topic in Algebra, which is a subdivision in mathematics. An ordered pair  represents a location (object or point) in the plane. Ordered pairs contains  two terms ‘x’ and ‘y’, represented in the form (x, y), the position of the terms cannot be interchanged unless the they are equal. Ordered pairs are also called as co-ordinates.

Learning to Find ordered pairs:

Depending upon the number of equations given the procedure to find the ordered pairs learning differs.
1. If only one equation is given,
Convert the given equation into a format,
y = a1x +c,
Then substitute different values for ‘x’ and obtain ‘y’
Form ordered pairs learning (x, y), where ‘x’ is the substituted value and ‘y’ is the obtained value.
Therefore different ordered pairs are obtained for various ‘x’ values.

2. If more than one equation is given,
Solve those equations and find out the values of ‘x’ and ‘y’,
Then (x, y) is the ordered pair

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Learning example problems to find ordered pairs

Problem 1:
Find the ordered pairs of y-2x=1
Solution:
y-2x=1,
Change the above equation into y =1+2x,
Substitute x=0
y =1+2(0),
y =1
Therefore the ordered pair (x, y) is (0, 1).
Substitute x=1
y =1+2(1),
y =3
Therefore the ordered pair (x, y) is (1, 3).
Substitute x=2
y =1+2(2),
y =5
Therefore the ordered pair (x, y) is (2, 5).
Substitute x=3
y =1+2(3),
y =7
Therefore the ordered pair (x, y) is (3, 7).
Substitute x=4
y =1+2(4),
y =9
Therefore the ordered pair (x, y) is (4, 9).

Problem 2:
Find the ordered pair of the equations,
3x+2y=5
4x+6y=3
Solution:
Let's start with 3x+2y = 5 for the variable x.
Move the 2y to the right hand side by subtracting 2y from both sides, like this:
Now, the equation reads:
3x = 5-2y
To isolate the x, we have to divide both sides of the equation by the other variables around the x on the left side of the equation.
The last step is to divide both sides of the equation by 3
The solution to your equation is:
x =5/3-(2/3)y
Next, let's solve 4x+6y = 3 for the variable y.
Move the 4x to the right hand side by subtracting 4x from both sides, like this:
Now, the equation reads:
6y = 3-4x
To isolate the ‘y’, we have to divide both sides of the equation by the other variables around the y on the left side of the equation.
The last step is to divide both sides of the equation by 6,
The solution to your equation is:
y =1/2-(2/3)x
Now, plug the earlier result, x=5/3-(2/3)y, in for x everywhere it occurs in
y=1/2-(2/3)x.
This gives y=1/2-2/3(5/3-(2/3)y). Now all we have to do is solve this for y,to have our first solution.
1/2-2/3*(5/3-(2/3)y) evaluates to ½ - 10/9 + 4y/9
Y - 4y/9 = -11/18
5y/9 =-11/18
The last step is to divide both sides of the equation by 5/9 like this:
y = - 11/18 * 9/5
The solution to the equation is:
y = -11/10
Lastly, to find the solution for x, we plug this answer for y into the earlier result that
x=5/3-(2/3)y.
This gives x=5/3-2/3(-11/10).
On, simplifying.
x= 12/5,
So, the ordered pair to given equations are:
(12/5, -11/10)

Math Solver

Introduction to math solver:
Math is the study numbers.Various branches of math are arithmetic,algebra,geometry,trigonometry,calculus,everyday math.

Math solver is a program that is used to calculate the answers to problems in math.The math solver is used to calculate the given math problems. Math solver is mainly used to find a solution with ease and also to work out the accurate solution for the given problem. I like to share this Easy Math Problems with you all through my article.

We generally input the given values to us and within a fraction of a second the math solver gives us the solution that is correct and easy to understand.It is an easy way of doing problems very quickly.Math solver is software that takes the input of data from us , uses the correct formula and gives the output. The math solver program of algebra solves the problems using the various algebraic formulas.The expansion formulas gives us the expansion of expressions while the factorization math solver gives the factors of expressions.Same way the arithmetic math solver to find the interests on investments gives the interest using that particular formula.For geometry also we can draw graphs using math solver that are neat and very clear.


Math Solver:

Mathematics is defined as the science of the study of quality, structure, space, and change. Mathematician gvies out patterns; establish truth by scrupulous deduction from appropriately chosen axioms and definitions”. Using math solver we can solve the given problems. Math solver helps us to solve problems in specific time. The following are the examples involved in math solver. Having problem with Circumference Calculator keep reading my upcoming posts, i will try to help you.


Solving example problems using math solver:

Ex 1: There are 1030 books in the library. We bought 67 more books for the library. How many books are there in the library now?

Given:

There are 1030 books in the library

67 more books is added to library

Therefore we need to add both 1030 and 67

1030 + 67 = 1097

There are 1097 books in the library now.

Ex 2: Margret sold 1392 meatballs on Friday. She sold 1940 more meatballs on Saturday than on Friday. How many meatballs did she sell on Saturday?

Given: Margret sold 1392 meatballs on Friday

She sold 1940 more meatballs on Saturday than on Friday

Therefore we need to add 1392 and 1940,

1392 + 1940 = 333

She sold 3332 meatballs on Saturday.

Ex 3: Kevin sold 1000 balls on Friday. She sold 1500 more balls on Saturday than on Friday. How many balls did she sell on Saturday?

Given: Margret sold 1000 meatballs on Friday

She sold 2000 more meatballs on Saturday than on Friday

Therefore we need to add 1000 and 2000,

1000 + 2000 = 3000

She sold 3000 meatballs on Saturday.

help with math word problems

Introduction to help with math word problem:

Math word problem is a real life problem put in words which has to be converted into mathematical form to solve it. Math word problems has to be solved by logically translating the problem to mathematical form. It requires understanding the mathematical concepts and its applications. I like to share this math tutoring free online with you all through my article.

To help with math word problems - examples

Math word problems help - example 1:

Jack has 21 bananas and 18 grapes . How many pieces of fruits does he have?

Solution:

We know that the sum of 21 and 18 is equal to the total sum of fruit. The total amount of pieces of fruit is unknown, so we will represent that sum with x.

Let x = Total Amount of Fruit from word given

The sum of 21 bananas plus 18 grapes is equal to the total amount of fruit. This can be used to explain the problem into an equation,

21 + 18 = x

By solving the last step equation.

Let x = Total Pieces of Fruit

Initial Equation     21 + 18 = x

After combining like terms 39 = x

The problems answer is then rewritten as a sentence.

There are 39 Total Pieces of Fruit

Math word problems  help - example 2:

Mike is twice as good as workman as Jones and therefore he is able to finish a job in 40 days less than Jones. Working together, they can do it in:

Solution:-

Given Mike is twice as good as work man as Jones.

Therefore the ratio of work done Mike and Jones is 1: 2

If difference of time is 1 days, Jones takes 2 days.

If difference of time is 40 days, Jones takes (2/1 x 40) = 80 days.

So, Mike takes 40 days to do the work.

so mikes one day work =  1/40

Jones one day work =  1/80

Now (mikes + Jones) one day work = ( 1/40 + 1/80 )

The LCM of 40 and 80 is 80.

Now take LCM and add we get

= 2 / 80 + 1/ 80

= (3)/ 80

Work done in one day=3/80

No. of days required to cover 80 portions of work=80/3

Mike and Jones together can do the work in 80 / 3 = 16.66 days. Understanding The Multiplication Table is always challenging for me but thanks to all math help websites to help me out.


More help with math word problems - practices


1. Math word problem help - practice 1:

Peter has 12 shirts and 7 T-shirts. How many of shirts does he have?

Answer: 19 Total number of shirts.

2. Math word problem help - practice 2:

The sum of thrice a number plus 8 is 62. Find the number.

Answer: The number is 18.

2. Math word problem help - practice 3:

Walker is thrice as good as worker as Kim and therefore he is able to finish a job in 40 days less than Kim. When they working  together, how long they can do it in?

Answer: 15 days.

Two Cents

Cents – Introduction:

In many national currencies, the cent is a monetary unit that equals 1/100 of the basic monetary unit. Etymologically, the word cent derives from the Latin word "centum" meaning hundred. Cent also refers to a coin which is worth one cent. In the America and Canada, the 1 cent coin is usually identified by the pet name penny, alluding to the British coin and unit of surname. In Ireland the 1cent coin is occasionally recognized as a penny in position to the Irish penny, worth 1/100 of the Irish pound swap by the euro.

Formula for converting the cents to dollars

1 U.S. cent = 0.01 U.S. dollars

Two Cents – Examples:

Two cents – Example 1:

Find how many dollars in the 2 cents also convert into the dollars

Solution:

Step 1:

Formula for converting cents to the dollars

X cents = x * 0.01 dollars

Step 2:

2 cents = 2 * 0.01 dollars = 0.02 dollars

Answer:

2 cents = 0.02 dollars

Two cents – Example 2:

Find how many dollars in the 102 cents also convert into the dollars

Solution:

Step 1:

Formula for converting cents to the dollars

X cents = x * 0.01 dollars

Step 2:

102 cents = 102 * 0.01 dollars = 1.02 dollars

Answer:

102 cents = 1.02 dollars

Two cents – Example 3:

Find how many dollars in the 22 cents also convert into the dollars

Solution:

Step 1:

Formula for converting cents to the dollars

X cents = x * 0.01 dollars

Step 2:

22 cents = 22 * 0.01 dollars = 0.22 dollars

Answer:

22 cents = 0.22 dollars

More Examples for Two Cents:

Two cents – Example 1:

Find how many dollars in the 32 cents also convert into the dollars

Solution:

Step 1:

Formula for converting cents to the dollars

X cents = x * 0.01 dollars

Step 2:

32 cents = 32 * 0.01 dollars = 0.32 dollars

Answer:

32 cents = 0.32 dollars

Two cents – Example 2:

Find how many dollars in the 42 cents also convert into the dollars

Solution:

Step 1:

Formula for converting cents to the dollars

X cents = x * 0.01 dollars

Step 2:

42 cents = 42 * 0.01 dollars = 0.42 dollars

Answer:

42 cents = 0.42 dollars

Solve Math Problems Fast

Introduction to solve math problems fast:

In this article we are going to discuss about the solve math problems fast. In the math problems have different types of topics. The level math problems has some of the followings numbers sets, logic, real number systems, functions and their graphs, probability and Statistics and some topics from algebra and geometry. The math  problems is more importance for all topics. Here we will see the example problems for solve math problems fast. Is this topic Conditional Probabilities hard for you? Watch out for my coming posts.

Example Problems for Solve Math Problems Fast:
Solve math problems fast – Example: 1

Solve `\int_1^2\int_1^x xy^2dx dy`

Solution:

`I=\int_1^2 \ [ \int_1^x xy^2 dy \ ]dx`

`\int_1^x xy^2dy=\ [ \frac{xy^3}{3}\ ]_{y=1}^{x}=\frac{x^4}{3}-\frac{x}{3}`

Therefore,`I=\int_1^2 \ [ \frac{x^4}{3}-\frac{x}{3} \ ]dx`

` =\int_1^2\frac{x^4}{3}dx-\int_1^2\frac{x}{3}dx`

`=\ [ \frac{x^5}{15} \ ] _1^2- \ [ \frac{x^2}{6} \ ]_1^2`

`=\ [ \frac{32}{15}-\frac{1}{15} \ ]-\ [\frac{4}{6}-\frac{1}{6}\ ]`

` =\frac{31}{15}-\frac{3}{6}`

` =\frac{31}{15}-\frac{1}{2}`

`=\frac{62-15}{30}=\frac{47}{30}`

Solve math problems fast – Example: 2

Determine the unit vector perpendicular to both the vectors `2\bar{i}+\bar{j}+3\bar{k},\bar{i}-2\bar{j}+\bar{k}`

Solution:

Let a,b be the given vectors `2\bar{i}+\bar{j}+3\bar{k},\bar{i}-2\bar{j}+\bar{k}`

`\bar{a}\times\bar{b} =` `[[i,j,k],[2,1,3],[1,-2,1]]`

which is equal to `\bar{i}(1+6)-\bar{j}(2-3)+\bar{k}(-4-1)=7\bar{i}+\bar{j}-5\bar{k}`

Therefore unit vector perpendicular to both the vectors is `\pm\frac{\bar{a}\times\bar{b}}{|a||b|}=\pm\frac{7\bar{i}+\bar{j}-5\bar{k}}{\sqrt{49+1+25}}=\pm\frac{1}{5\sqrt{3}}(7\bar{i}+\bar{j}-5\bar{k})`

Solve math problems fast – Example: 3

Evaluate `\nabla^2(\frac{x}{r^2})`

Solution:

`\nabla^2(\frac{x}{r^2})=\sum \frac{\partial^2}{\partial x^2}[\frac{x}{r^2}] --(1)`

Now,`\frac{\partial}{\partial x}(\frac{x}{r^2})=\frac{1}{r^2}-\frac{2x}{r^3}\frac{\partial r}{\partial x}=\frac{1}{r^2}-\frac{2x}{r^3}[\frac{x}{r}]=\frac{1}{r^2}-\frac{2x^2}{r^4} --(2) [ r^2=x^2+y^2+z^2 and \frac{\partial r}{\partial x}=\frac{x}{r}]`

Therefore,`\frac{\partial^2}{\partial r^2}=\frac{\partial}{\partial x}[\frac{\partial}{\partial x}(\frac{x}{r^2})]=\frac{\partial}{\partial x}[\frac{1}{r^2}-\frac{2x^2}{r^4}],` by using (2)

`=-\frac{2}{r^3}\frac{\partial r}{\partial x}-[\frac{4x}{r^4}-\frac{8x^2}{r^5}\frac{\partial r}{\partial x}]=-\frac{2}{r^3}(\frac{x}{r})-\frac{4x}{r^4}+\frac{8x^2}{r^5}\frac{x}{r}`

Therefore,`\frac{\partial^2}{\partial x^2}[\frac{x}{r^2}]=\frac{8x^3}{r^6}-\frac{6x}{r^4} --(3)`

Now,`\frac{\partial}{\partial y}(\frac{x}{r^2})=-\frac{2x}{r^3}(\frac{y}{r})`

`\frac{\partial^2}{\partial y^2}=\frac{\partial}{\partial y}[-\frac{2xy}{r^4}]`

`=-2x[\frac{1}{r^4}-\frac{4y}{r^5}\frac{\partial r}{\partial y}]=-2x[\frac{1}{r^4}-\frac{4y^2}{r^6}]=\frac{8xy^2}{r^6}-\frac{2x}{r^4} --(4)`

Similarly,`\frac{\partial^2}{\partial z^2}[\frac{x}{r^2}]=\frac{8xz^2}{r^6}-\frac{2x}{r^4} --(5)`

Adding (3),(4),(5), we have

`\sum \frac{\partial^2}{\partial x^2}=\frac{8x}{r^6}[x^2+y^2+z^2]-\frac{10x}{r^4}=-\frac{2x}{r^4}`

`or \nabla^2[\frac{x}{r^2}]=-\frac{2x}{r^4},` by using (1)


I have recently faced lot of problem while learning Sum of Uniform Random Variables, But thank to online resources of math which helped me to learn myself easily on net.

Practice Problems for Solve Math Problems Fast:

1. Find a vector of the magnitude 3 and that which is the perpendicular to both of the vectors `3\bar{i}+\bar{j}-4\bar{k},6\bar{i}+5\bar{j}-2\bar{k}`

`Answer: \pm (2\bar{i}-2\bar{j}+\bar{k})`

2. Solve `\int_1^2\int_3^4 \frac{1}{(x+y)^2}dx dy`

`Answer: log\frac{25}{24}`