Adding Common and Mixed Fractions (Discussion)

One of the basic sciences of mathematics is about fractions. Basically, fractions are divided into 3 types, namely common fractions, pure fractions, and mixed numbers. In this case, the topic that we will cover is the addition of common and mixed fractions.

You need to know that the difference between these two types of fractions will lie in the numerator and denominator. If an ordinary fraction is a fraction whose numerator and denominator are integers, the mixed number will consist of a whole number and a pure fraction.

Fraction History

To start a discussion regarding this, let's first discuss the history of the fractional number itself. Basically, fractions like this were first discovered around 1600.

Each resident in this world will have different perceptions regarding fractions, and if these perceptions are summarized, it will be explained as follows:

Read: Online Fraction Calculator

1. Ancient Egyptians

Fractional numbers were first discovered in an ancient Egyptian relic, or commonly known as the Egyptian Papyrus. What is unique about this history is, at that time the ancient Egyptians were not familiar with this type of fractional number in depth.

They only know the type of unit fraction calculation or unit fraction, which is expressed as 1/n where n is a positive integer. At that time, the inhabitants of ancient Egypt used a different method of writing numbers with the method of writing numbers today

In the past, fractional numbers were symbolized by 3 horizontal lines. Since then, the inhabitants of ancient Egypt began to increasingly recognize fractional numbers.

2. Ancient Romans

Meanwhile, the ancient Romans themselves used a unit of weight called the axle, and one of the units of weight used was 12 uncia.

What is meant by 12 uncia in this case is one twelfth of a certain number. Later, there will be other terms used by the ancient Romans in understanding this fractional number, and these terms are:

• 1/12 is called uncia
• 6/12 is called semis
• 1/24 is called semuncia
• 1/144 is called scripulum

Read: Roman numerals

3. Babylonians

Just like the understanding of fractions from other parts of the world, the Babylonians also developed a fractional number system in a way that was not easy to write down.

In the past, the Babylonians used inscribed stones or tablets to show the use of fractions or even the calculation of taking the root of a certain number. In addition, at that time the Babylonians also used place values ​​in writing fractions like this.

4. Indian Nation

After time continues to run with the use of different fractions in each region, new then around the year 500 AD, the Indians began to develop a number system called Brahmi.

Basically, in this brahmi number there will be 9 symbols and the number 0. Then, time was running again and the trade process started by the Indians and Arabs.

Since then, the scattered numerals in this regard have begun to use some new symbols that are still unknown to many people. However, this numeration quickly spread to the Arab world, so that more and more people recognized it well.

Read: Linear Equations and Inequality

How to Add Common Fractions (Basic)

There are several ways you can do to perform the process of adding ordinary fractions, which has become a basic science in the world of mathematics. In this case, the methods are:

1. Find the Least Common Multiple for the Denominator

You need to do this step because to add common fractions like this, you need to equate the two denominators first. Thus, you need to find the Least Common Multiple (LCM) of the existing denominators.

If you have done these steps, now you need to choose the smallest Least Common Multiple (KPK).

2. Multiply the numerator by the denominator

After doing the steps above, now you need to multiply the numerator by the denominator. This needs to be done to get the proper denominator. Because by multiplying these two parts, the smallest LCM number will appear as before.

3. Convert Other Fractions to Equivalent Fractions

In this case, when you want to adjust the first fraction, then you need to make the other fractions into equivalent fractions first.

4. Add the Two Numers

If the denominators of both fractions are the same, now you need to add the parts to the numerator. This needs to be done without changing the denominator. That way, the results of the addition of these fractions will be more visible and correct.

5. Simplify Results If Needed

Even though this stage has actually been completed, if the result of the addition is still too large, then you can simplify the numbers again.

In addition, if the numerator part of the fraction is still larger than the denominator, then the step you need to take is to convert it to a mixed number. In this case, you can divide the numerator and denominator so that you get an integer.

Read: One Variable Linear Absolute Value Equation

How to Add Mixed Fractions

To add mixed numbers, you will also need some special steps that will be different from the previous method. Needless to say, here's the right way to add mixed fractions, namely:

1. Convert Mixed Fractions to Common Fractions

To start the process of adding mixed fractions, you first need to convert them to common fractions. So, if the number obtained in the fraction is a whole number, then the number must be changed first.

Once converted into a common fraction, this can cause the numerator part to be greater in value than the denominator part. That way, these fractions will be easier to add up.

2. Find Least Common Multiple (LCM) If Needed

You can do this step if the denominators of the two fractions are not the same. Later, you have to write down the multiples of each denominator, so that you can find 1 certain multiple of the same number.

Read: Two-variable Quadratic Linear Equation System

3. Convert the Fraction to an Equivalent Fraction

If in the previous step you needed to change the denominator, then you also need to convert the fraction into an equivalent type of fraction.

Basically, you have to change all the parts of the denominator first to get the smallest LCM. Then, you can multiply all fractions by an existing number, to change the denominator of the fraction into the appropriate LCM number.

4. Add the two parts of the numerator

Before going to the last step, you need to add up the two existing numerators, without changing the denominator, after the denominator has been equated. When the two numerators have been added, then you can immediately write the answer at the top of the denominator.

5. Simplify the result of the sum

If the numerator part of the result is still larger than the denominator, then you need to simplify again. The trick, you can divide the part until you get the appropriate integer number.

Actually, this method of adding ordinary and mixed fractions can be done easily by anyone. Most importantly, you already know how to do it properly and correctly, so you can practice it directly with ease.