Basics of Algebra

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Algebra Mathematics

Basic algebra is that domain of math that is one step more conceptual than arithmetic. Know that arithmetic is the molding of numbers through basic mathematical operations. Algebra institutes a variable, which represents an unknown number or can be alternated for a whole group of numbers. 

Basic arithmetic questions pose numerical problems such as 3 + 6 = ? Algebraic concepts, on contrary, ask basic algebra questions like: If x + 6 = 9, find the value of x? Instead of instantly identifying a basic sum, we have to perform additional work to solve for an unknown.


Basic Algebra Rules  

Once you master the basic rules of mathematics, you'll have the technique to tackle higher levels of mathematics. 


Following Are the Rules Commonly Performed in Algebra

  1. Adding And Subtracting Like Terms

For the purpose of adding or subtracting any terms in algebra, your terms should be like terms, which have a similar variable and are raised to the same power. If your data consists of like terms, you add or subtract the numbers linked to the variable, known as the coefficients. The variable itself is consistent i.e. does not change. Let's take a look at an example:

-2x + 5y + 4x – 2y

(-2x + 4x) + (5y – 2y)

(-2 + 4)x + (5 – 2)y

2x + 3y


Application and Process of Adding and Subtracting Like Terms

We need to follow the below stated step-by-step procedure:-

  • Reorder our terms to group them by like terms.

  • Rewrite the like terms to only have the coefficients inside and the variable outside of parentheses.

Note: Although rewriting is not mandatory, it helps showing the Math we completed in the final step to arrive at the correct answer of 2x + 3y.

This type of math is called simplifying expressions. When you are to solve an algebraic equation like this, it is very important to keenly consider + and - signs as affixed to a term. Take into account the following:

-5a + 6b = 3a - 2b

-2a + 4b


Important Point to Remember while Adding and Subtracting Terms

Remember that we can only add or subtract like terms.


Reason Behind Adding and Subtracting Only Like Terms

Let’s make you easily understand this using an example. Suppose that, in a kitchen shelf we have 4 plates and 2 bowls. We will not be able to add the 4 plates to the 2 bowls – since they are not similar types of object.

We go get another 6 pencils and 6 books. Altogether we now have 10 plates and 8 bowls. We are unable to combine these quantities, seeing that these are different types of objects.

Likewise, in algebra, we can only add (or subtract) the same "objects", or those with the similar letter raised to the same power. For example:


Example:

Simplify 9x + 5y − 6x + 7b

Solution:

Given: 9x + 5y − 6x + 7b

The only like terms in this expression are 9x and -6x

We are unable to do anything with the 5y and 7b

Thus, we will only group the terms (like) we can subtract, and leave the remaining as it is:

(9x − 6x) + 5y + 7b

= 3x + 5y + 7b

= 7b + 3x+ 5y (We generally display our variables in alphabetical order, but it is not mandatory).


  1. Multiplying and Dividing Like Terms

In order to multiply or divide terms, we need not require consisting of like terms. This algebraic rule is different from addition and subtraction, so be cautious! Let’s consider an example of a basic multiplication with a variable:

Example: Multiply x2(x7 + 5a)

Solution: We do the expansion applying the distributive law:

X2(x7 + 3a)

= x9 + 3ax2

We are unable to simplify this answer further.


How to Combine Like Terms?

Let’s take an example. Alisha’s mother bought home 6 peaches, 3 apples and a melon and put them in the fruit basket. Father came home with 2 peaches and an apple and put them in the basket. Write an algebraic equation for what mother bought and what father bought home.

Use ‘p’ for peaches, ‘a’ for apples, and ‘m’ for melon. Then add up the two expressions and write an equation for what is ultimately in the bowl.

Let’s combine the like terms:

Mother: 6p + 3a + m

Father: 2p + a

Total: 6p + 3a + m + 2p + a = 8p + 4a + m

= 4a + m + 8p

FAQ (Frequently Asked Questions)

1. What is meant by algebra?

Algebra is the stepping stone for all higher levels of mathematics. For the purpose of understanding any mathematical field, you require to be able to speak algebra, which involves elements such as solving an algebraic equation, simplifying the expression and segregating the variable.

2. What is the use of algebra?

Algebra is a powerful means for problem solving in different fields of life like finance, business, architecture, science, economics, engineering, ship-building and day-to-day tasks.

3. What do we understand by terms and factors?

While going through basic algebra lessons, you will frequently come across the mathematical words—terms and factors. That said, a term in an algebraic expression that involves letters and/or numbers (known as factors), multiplied together.

4. How can we write algebraic equations for everyday life?

We often get confused with variables and symbols presented in algebra. However, these elements usually represent normal quantities and we intuitively do algebra all the time. Following can be an everyday situation to write corresponding algebraic equations.

A cake having 12 pieces is to be divided between 4 people. Let ‘a’ be the slices and ‘m’ be the people and piece per person be ‘p’. Write an expression for how many pieces each person gets.

Algebraically, applying the division rule – 12a/4m = 3p