ADDITION OF FRACTION

Fraction is always a quite hard to deal. Dealing fractions with MDAS (Multiplication Division Addition Subtraction) as basic operation is really a big deal. Students seems to be helpless in solving problems involving fractions. By the use of calculator, fraction can be  done easily without understanding how did the answer arrived.

Fraction by definition is a part of a whole. A piece of something. It is very laborious to add fraction when it is dissimilar. (a fraction with no the same denominator). The process requires finding the LCD (Least Common Denominator). Finding the LCD alone is herculean. If you can not find the LCD, you can not end to the right solution. But there is an alternative way to add fraction the easily There is a formula provided below how to deal addition of fraction without finding the LCD.

In the formula "a and c" are the numerator.The "b and d" are the denominator. In this formula, simply get the product of "a and d" added by the product of "b and c". For the denominator, just multiply "b and d".The result would be the answer if it is reduced to lowest term. We will give a numerical example to better understanding. See the illustration below.

We will substitute each values of the given formula to each numerical proportion. In this illustration "a=2", "b=3", "c=4", and "d=5". We get the product of 2 and 5 which is 10, added to the product of 3 and 4 which is 12. The sum of 2 and 5 which is 10 and 3 and 4 which is 12 as the numerator is divided by the product of 3 and 5 which is 15 as denominator (see illustration). 

Notice that the result is improper fraction(a fraction whose numeration is higher than the denominator). We will convert the result into mixed number (a whole number and a proper fraction). In this illustration, the final result is 1 7/15 as final result (see below).

ADDITIONOFFRACTION

MDAS OPERATION

MDAS OPERATION

In mathematics,logical operation is the most important to consider. It is by its gradual order where the final answer can reliable. Constant daily practice is the most advice by many to master mathematics. By basic operation, it should be the Multiplication should be the first in the series of operation, followed by Division, Addition, and Subtraction. Majority got stuck on this because some do not understand how to handle the operation. Multiplication will be treated at first and should not be intervene by Division at the same time. After treating the Multiplication clearly then that is the time for Division. Again do not manipulate them together. The result of the two gradual operations should be then followed by Addition and Subtraction. Let's check with the given illustration.

Based on the description, Multiplication is the first to operate followed by division, addition and lastly subtraction.

Illustration.

1. 12*3/4 + 5 - 3 = 36/4 +5 -3
                           = 9 + 5 - 3
                           = 14 - 3
                           = 11

From the example above. 12 and 3 should be treated because they have "multiplication" as operator. And 12 of 3 is 36 (see the initial result). After multiplication was completely done, division will be the next, and that is to say 36 divided by 4 which gave us 9. The next thing to do is addition to be followed by subtraction. Hence, our final answer is 11 and that is 36/4 +5 -3 = 9 + 5 - 3 = 11.

2. 4*4 / (2*2) - 2 + 3 = 16 /4 -2 +3
                                 = 4 -2 + 3
                                 = (guess what is the final answer)

Our second example was intentionally made for you to finish. What is the answer to this simple math with MDAS operation? Is it 5? Some say its negative one (-1) So what is then is the final answer?

3. 5 + 4*3 - 6 / 2 * 3 = ? (try to fill out the solution,remember the MDAS rule)

The third example was leaved for you to finish. Follow the simple steps of the operation. Check where is the multiplication as operation located. So it is between 4 and 3. Followed by the division which is 6 and 2 but it is multiplied by 2.  Next is the 5 added to the product of 4 and 3. 

Let us try the other two problems.

4. 15/3 + (4*2)/4 - 16 / 3 * 2 + 1 =

5. 2*3 + 6-2 * 3 + 6/2 - 1 =

MDASOPERATION

QUADRATIC EQUATION

This is the formula for quadratic equation. This equation is only for one variable with second degree of order. The general form of quadratic equation is ax²+ bx + c =0. For a derivation reason we arrived what is in the photos above.This is used usually if factoring seems so not a perfect square to get the value of x.

Sample graph of a quadratic equation:

1. A graph of single quadratic equation.

2. A graph of double quadratic equation.

3. A graph of multiple quadratic equation.

These are the illustrations of different graphs of quadratic equation looks like in different form of quadratic equation, may it be single, double or multiple.

LINEAR EQUATION

This is the form of linear equation in two unknowns. It shows a single straight line. This is different from quadratic equations. The arrow of the line means continuity. Meaning the line is extended infinity. The illustration only shows where the line was made. It is from the origin or center (0,0) of the Cartesian plane. The vertical axis is labeled by y and the horizontal axis was labeled by x. In this photo of linear equation, x was only limited from -1 to 5, and y to -3 and 2. It is not required really to extend those grades of the line to higher number. That only depends on how less or great the given of the equation is presented. The green dot shows the exact location of the point, of a line of course. The green dot above shows the point has the (4,1) vertex and the green dot below shows (0,-2) vertex. There are a lot of linear equation in different form, not only from the photos above.

VENN DIAGRAM

This the Venn diagram presentation. It shows logical presentation of a set(s). The red color in between signifies common parts of two sets. First circle and second circle are two different sets. There are several types of sets. They are one-to-one correspondence as a set, equivalents sets, equal sets, proper subsets,overlapping sets, and disjoint sets.

On set operation, we have unary operation and binary operation.  Unary operation is operation only for one set. And for the binary operation we two or more sets to form another set or sets.

CLASSROOM SET UP

This is the actual set up in the classroom where students are more interested in new mathematical learning. The topic being discussed here is linear programming.