# Subtraction of Common and Mixed Fractions (Example)

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In this review, we will discuss subtraction of common and mixed fractions which will be very useful for those of you who are studying the material. As with addition of fractions, subtraction also requires an understanding of the KPK and GCF.

In addition, you also need to understand the nature of the fraction subtraction operation. To find out more about subtracting ordinary and mixed fractions, you can see the information below.

List of contents

## Fraction History

Before discussing the fraction subtraction formula and how to calculate it, you should know its meaning and history. Fractions in English are called *fraction* which comes from the Latin f*ractio*. The meaning of the word is to break or break.

### 1. Fractions in Ancient Egypt

According to historical records, fractions were known in 1800 BC in Egypt. At that time, the Ancient Egyptians wrote fractions with the idea of a unit fraction number, namely with the numerator of one.

Fractional numbers in the form of hieroglyphs are carved on walls or wood with certain symbols, while the number 2/3 uses special symbols.

### 2. Fractions of the Ancient Babylonians and Greeks

The Babylonians through written stone have recognized and used fractional numbers to take roots, and have applied place values. Meanwhile, for the ancient Greeks, all length measurements could be expressed using whole number ratios.

Read: Online Fraction Calculator

### 3. The Idea of Using Decimal Fractions in the Shang. Dynasty

Around 1800 - 1100 BC the use of decimal fractions was known during the Shang Dynasty. This is as stated in the Juizhang Suanshu which is a book on the art of mathematics.

### 4. First Author Horizontal Sign on Fraction

Before being known as a fraction as it is today, the writing of fractional numbers was in the form of certain symbols. Meanwhile, the writing of the horizontal line between the numerator and denominator was introduced by al-Qalasadi (1412-1486).

While another name, namely al-Hassar in the 12th century, is referred to by Jeff Miller as the first discoverer of horizontal signs in fractions. Meanwhile, al-Kasyi's work, Miftah al-Hisab (Key of Calculation) has discussed the use of decimal fractions and how to calculate them.

Read: Fractions

## How to Subtract Common Fractions (Basic)

If it's your first time learning fractions, maybe you're still a little confused about calculating the subtraction operation. Keep in mind that the main key to subtracting fractions is to make sure both denominators are the same so that you can subtract both numerators.

The calculation method that can be done is to find the LCM (Least Common Multiple) and Reduce Fractions. The following is an example of subtracting fractions:

1/3 – 1/4 = ….

From the problem of subtracting fractions, you have to take several steps as follows:

### 1. Record multiples of each denominator in fractions

You can start looking for the LCM (least common multiple) of the two denominators above until you find the same number. If the example is 1/3 and 1/4, then please record all the multiples of 3 and 4 until you find the same number from the two LCM lists.

- Since multiples of 3 include 3, 6, 9, and 12 while multiples of 4 include 4, 8, 12, we find that the lowest number that 3 and 4 have in common is 12.
- If both denominators already have the same number, then you can easily calculate the subtraction of the two numerators.

### 2. Multiply the numerator and denominator so that the denominators of both fractions are the same

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If you have found the same LCM in both denominators, then the next step is to multiply the fractions so that both denominators are the same as follows:

- Multiply 1/3 by 4 to make the denominator 12.
- Multiply 1/4 by 3 to make the denominator 12.

### 3. Make equivalent fractions on all fractions

It should be noted that adjustments to one fraction must also be followed by converting other fractions to their equivalent. Based on the example questions above, it can be applied as follows:

- The number 1/3 is multiplied by 4 to make 4/12.
- The number 1/4 is multiplied by 3 to make 3/12.

### 4. Subtract the numerator from the fraction and keep the denominator the same

If you subtract fractions from the same denominator, you only need to subtract the numerator to find the result. Meanwhile, if the denominators are the same, there is no need to subtract them.

1/3 – 1/4

= 4/12 – 3/12

= 1/12

So the answer for subtracting fractions from 1/3 to 1/4 is 1/12.

From the results of the subtraction, you need to find out whether it can still be simplified or not, the way is to find the GCF (Largest Common Factor) of the two fractional numbers. For example, if the result of the subtraction is the number 6/12, then the GCF of both is 6.

So you need to divide both fractional numbers by 6, and the result is 6:6 = 1 and 12:6 = 2. Thus, the final result of the subtraction can be written as 1/2 which is a simplification of 6/12.

So for fractional numbers that can still be simplified, it is better to write down the simple numbers. As for the answer to the example question above, which is 1/12, it cannot be simplified anymore.

Read: Fraction Division

## How to Subtract Mixed Fractions

Mixed fraction is a form of integer that has a fraction so to perform calculations you need to convert the integer into a fraction. The calculation method is as follows:

2 3/4 – 1 1/5 = ….

From the problem of subtracting mixed fractions, you need to take several steps as follows:

### 1. Convert mixed numbers to improper fractions

The first step is to convert the mixed number into an improper fraction, where the numerator is greater than the denominator. You do this by multiplying the denominator and the integer and then adding it to the numerator.

- 2 3/4 – 1 1/5
- 4 x 2 + 3 = 11/4
- 5 x 1 + 1 = 6/5

### 2. Equalize the denominator of the two fractions if needed

From the example of subtracting mixed fractions above, it is known that the two fractions have different denominators, so they must be equated by finding the LCM of the two numbers.

- The LCM of the number 4 is 4, 8, 12, 16, 20.
- LCM of the number 5 is 5, 10, 15, 20

- Make equivalent fractions if you change the denominator

Based on the KPK above, it is known that the number 20 is the same LCM of the two denominators, so it is necessary to make an equivalent fraction as follows:

- 11/4 x 5 = 55/20
- 6/5 x 4 = 24/20

### 3. Subtract the numerator of both fractions and the denominator remains the same

If you already know a fraction with the same denominator, then all you have to do is subtract the numerator as follows:

55/20 – 24/20

= 31/20

### 4. Simplify the answer

Based on the calculations above, it was found that the results of the reduction are as follows:

2 3/4 – 1 1/5

= 55/20 – 24/20

= 31/20

= 1 11/20

So the result of subtraction is 1 11/20, where 20 times 1 will get a result that is close to 31, while 11 is the difference.

You can also subtract mixed fractions without converting them to improper fractions, that is, by subtracting whole numbers from the fraction as long as the denominators of the fractions are the same. So to be able to add and subtract fractions is to have the same denominator.

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