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How to do Elementary Algebra?


To understand elementary Algebra we need to understand basic operations on rational number, plotting on graphs, fractions of an expression etc. Now let us see how to do elementary algebra.

Step 1: First of all we need to understand the process of factorizations. Basically factors of a number are smaller parts of that number for an instance we can write a number 36 as 9 * 4. Here 9 and 4 are factors of the number 36. Just like that we can find the factors of 9 and 4 as well. We can write 9 as 3 * 3 and 4 as 2 * 2. We can find the factors of a given number until we get a prime number as fraction number.

Step 2: We need to learn the importance of variable like what a variable is, how does it works etc. Basically a variable is the unknown quantity of an expression or an equation. We are supposed to find the value of variable from the equation. As we place the value of variable in the equation, this will form equality on both sides of equation.

Step 3: Now we have to learn how to maintain the equality of an equation. We need to understand how to manipulate a balanced equation.

Step 4: Now solve a simple linear equation with one variable. For Example: Let us take an equation 5x – 3 = 22. We will find value of 'x' as 5x = 25 => x = 5. On putting value of variable 'x' in this equation, both sides will become equal to each other.

5 * 5 – 3 = 22,
25 – 3 = 22,
22 = 22.

concept of elementary algebra

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Elementary algebra, is a prerequisite for learning advanced algebra, is the most important branch of mathematics, which uses the basic concept of arithmetic and algebra. The concept of arithmetic involves some fixed numbers or known quantities, which are known as constants, but algebra involves some unknown quantities, which are known as variables.
Once we have a proper knowledge about an algebraic expression, we can then continue using it, to study the concept of elementary algebra. The basic problems in elementary algebra include solving algebraic equations, solving inequalities, finding the values of variables, the set of their solutions and many more. Elementary algebra problems can be shown as a combination of the following:
Thus, elementary algebra includes the to differentiate the various components of an algebraic equation, with the correct order of their operations (PEMDAS- First bracket open and then follow division, followed by multiplication and then addition and in the last subtraction).

Elementary algebra gives the knowledge of the basic skills of mathematics (add, subtract, multiply, and divide)

Algebra includes the Distributive, Commutative, Associative and other important properties of real numbers with respect to the 4 operations of mathematics, it also includes an important process of graphing an equation to find out its solution, its axes and plotting the points by making a table of data.
The most important use of algebra is to use any symbols to express any variable of your own, in which the variables are those quantities that can change their values (or the unknown values).

Solve Algebraic equations

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We can use the symbolic algebra to represent the situations and then to solve those problems, especially those that involve the linear relationships, which is the basic purpose of doing elementary algebra.

Thus, elementary algebra is done basically by expressing our verbal problems by creating symbolic expressions like, x + 8 is an expression which is used to represent points earned by a student in a given game. It means that the student had already earned 8 points in the previous game and x shows the number of points that the student will earn for the rest of the coming game.

Algebraic equations can be solved by using below operations:
Square root and many more

While doing mathematical operations on algebraic equations, we should keep in mind, that if we divide, multiply, add or subtract any number form the Left Hand Side of any algebraic equation then the same number will be put on the Right Hand Side of the equation too accordingly, with the same sign ( + , - , * or /).

Elementry Algebra helps in day to day life

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 We use the concept of elementary algebra almost all of the time. We know that life is always full of changes and uncertainty.  And such situations can be represented in form of algebraic equations, because using only numbers cannot represent a situation more accurately. Thus, Algebra, and with the help of algebraic symbols, we can predict the various patterns of change that exist in our every day life.

Elementary algebra also helps us to identify the letters in an equation that means a particular thing and then we can look at the symbols used for variables in comparison with the symbols used for arithmetic operations which we know as (+, -, =, / etc.).

Let us understand the concept with our daily calculation struggle,
Sam has some number of chocolates with her. She has to divide these chocolates among 15 kids, provided that each kid should get exactly 5 chocolates. We have to calculate, how many chocolates does she have?
We can convert this into equation as let x is the total number of chocolates that Sam has, then $\frac{x}{15}$ = 5, which gives x = 15 * 5 = 75.  yay!! we solve this.

Practice Problems

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1)  Solve the following system of equations by the method of graphing:
    y = -2x + 5
    x -3y = 6

2) A basket consists of 125 apples out of which 3 are rotten. Find the number of rotten apples, if we have a basket consisting of 3000 apples?
Answer: 72 apples.

3)    Evaluate: $\frac{2xy}{x-y-y^{2}}$ for x = 5 and y = 1.

4)    Add: (3x2 + 4y2 – 55x – 23y + 22) + (6x2 + 40y2 – 20)

5)   Simplify the following exponents provided the answers should be written in positive exponents only.
a)    3x0
b)    (3x)0
c)    (4xy4)-2)

6) Multiply the following algebraic expressions: 
a)    (5x2) (10x2 – 5x + 2)
b)    (2y + 1) (y - 5)