Unit 2 (Algebra)

In unit 2 we learned about algebra.

-Terminologies in algebra:

• Variables - the letters such as a,b,c,x,y
• Coefficient - number in front of the variable
• Constant - number without variable
• Monomials - Algebraic expression containing one term
• Binomials - Algebraic expression containing two terms
• Trinomials - Algebraic expression consist of three terms
• Polynomials - Algebraic expression which have two or more terms
• Like terms - have the same pro-numerals/variable/letter
• Unlike terms - have different pro-numerals/variable/letter

   *In algebra,term of the same kind is called like terms can be combined into a single terms.

Algebraic operations:

- Addition and subtraction of like terms.
With like terms we can just immediately add or subtract a pro-numeral with another pro-numeral

Example: 9a+12a = 21a         10a-29a = -19a

 But if they are unlike terms you should simplify them first. 

Example:

12X + 5Y + 2X + 76B = 76B +14X+ 5Y

The way simplify the equations is by using like terms operations. 
Like so

- Multiplication of pro-numerals. 
For multiplication of pro-numerals we need to do it separately between the coefficient and the variable.

Example: 16x X 5y=
                16 X 5    = 80
                 x X y     = xy
                 answer= 14 ab
-Division of pro-numerals. 
To do division between pro-numerals we can convert it into a fraction and do it separately between coefficient and variables. Using that way, we can simply divide the pro-numerals.

Example: 20x/ 5x = 4( we can cancel the variables by crossing them)

Using algebra

-Using algebra we can use algebra to solve problems like the ones below

When a pro-numeral is multiplied by itself, we can express them using index notation.

example: a x a x a x a x a x a x a x a = a

Worked example:

Not only that, in algebra there are equations and in-equations.

Equations

Algebra equation = Algebraic expression that use equal sign

Example of algebraic equation = 3x + 7 =  4x + 4

To solve the problem above we need to group them (monomials with monomials and the constant with the other constant). To group them we should change the sign.We change sign only if the numbers move above the equal sign.

*the sign in front of the numbers stay with the numbers

After the process, the algebra will look like this =
 3x-4x =7+4
-x =11
x = -11

In Equations

In Equation = Algebraic expression that dont use equal sign.

Inequalty sign :

Example:

Note= the way use the changing sign concepts/magic door.

When multiplying/dividing an inequation by a negative number, the sign must be change.  

                  
Worked example:

The way above is using another method which is balancing methods. To answer the inequation problem you must answer it in a curly bracket or number line.

We also learned about algebraic fractions.

To solve algebraic fractions, you just need to apply the same concept of fraction. For addition and subtraction we need the same denominator. In multiplying and dividing, we need to do it separately between variables and the coefficients.
Worked example for addition and subtraction:

Worked example for multiplication and division: