# Division – Examples, PDF

There are plenty of things that require so much human effort to achieve. With great teamwork and the proper division of labor, these efforts can be achieved with the minimum amount of work needed.

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## What Is Division

The division is a mathematical operation that focuses on the equal splitting of numbers into specified parts. Multiplication and division are often paired together due to the fact that both operations function in the opposite way. The division has plenty of uses like the division of student affairs, the division of student academic services, and the emergency division plan.

## How to Divide Fractions

Fractions are defined as part of a whole. These fractions come in the form of real numbers and rational numbers. The division process of fractions is quite different when compared to the division of whole numbers, but it can be done in 4 simple steps.

### 1.) Write Down the Fractions, and Ensure Both Numbers are Fractions

Begin by writing down both given fractions on a piece of paper or a digital note-taking tool. Ensure that both numbers are in their fraction form, as this will act as a visual guide. Whole numbers can be extended into fractions via x/1, where x is the whole number. For example, if the given numbers are 4/3 and 6, we can rewrite 6 in its fraction form of 6/1.

### 2.) Turn One of the Fractions into A Reciprocal

After you have written down the fraction, you must then turn or convert one of the fractions into a reciprocal. You must swap the dividend with the divisor of one of the fractions. Using the same examples you will rewrite 6/1 to 1/6.

### 3.) Multiply the Fractions

You must then multiply both fractions with their appropriate dividends and divisors. Using the same examples you must multiply the 4 × 1 and 3 × 6, which results in 4/18.

### 4.) Simplify the Fraction

When you have finished multiplying the fractions, you will then simplify the fractions to their simplest form. This means that you must check if both the dividend and divisor share a denominator. Using the example both 4 and 18 have an LCD of 2, allowing you to simplify the example to 2/9.

## What is synthetic division?

Synthetic division is a technique people use to divide polynomial equations. These equations are quite daunting to look at and are harder to divide when compared to other types of equations. Synthetic division is a short-hand technique that allows the person to divide polynomial equations with more ease when compared to the longer and more nuanced technique. This is because synthetic division presents a more simplified and less complicated look when compared to the long polynomial division method, which is achieved by taking out X or any of the variables in the equation and writing the numbers attached to them instead.

## What is a long division?

Long division refers to the simple technique of dividing numbers through the divisor and the dividend. Common examples of equations that utilize long division are x/y, quotient between x and y, and x divided by y where x is the dividend and y is the divisor. This is characterized by the use of the long division symbol (⟌) and with the dividend on the left side while the divisor is sequestered on the right side of the symbol. This is often the go-to method in dividing numbers with high values and is often accompanied by a simplification process (through the usage of the Least Common Denominator or LCD) to help ease up the difficulty of the long division.

## Why is the concept of division very important to learn?

The division allows people to understand the concept of cutting down a specific procedure, product, responsibility, etc. into equal and manageable chunks. This concept allows us to divide specific things and share them with specific people practically. A common real-life example of the application of division is through the division of tasks in specific group work. If the person allocating the task does the dividing properly, each member will have equal amounts of input and responsibility, while dividing up the effort needed to complete said group work. Another real-life example of the practical application of division is observed in the ability to budget and allocate one’s funds for a whole year or month.

The division is a mathematical operation that concerns itself with the cutting or separating of numbers. This operation is the juxtaposition and the inverse of multiplication, similar to the relationship between subtraction and addition. This is an important technique to learn due to its numerous applications in logic and real-life.