Fractions

Subtracting Fractions

Fractions ﹣ Subtract Fractions

Here we introduce you to subtracting fractions, that is, subtracting one fraction from another. We start with the simple subtraction of fractions with the same name. Afterwards, you will get all the information on subtracting fractions with different names and on subtracting mixed fractions. A video on subtracting fractions concludes the topic. With the calculator for subtracting fractions, you can perform any calculations here.

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On the parent page on fractions you will find a lot of general information about fractions and their transformations. If you want to learn how to do the other arithmetic operations on fractions, visit our guides on Adding fractions, Multiplying fractions or Dividing fractions.

Contents on the topic "Subtracting fractions"

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How do you subtract fractions?

Fractions are subtracted by first making them equal and then subtracting the numerators, i.e. subtracting them from each other. Each fraction is thus first expanded so that all the fractions to be subtracted thereby have the same denominator. The numerators of the fractions with the same name are then subtracted, while the common denominator remains the same.

In the following, we will show step by step, using examples, first the subtraction of fractions with the same name, then the subtraction of fractions with different names and finally the subtraction of mixed fractions.

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How do you subtract fractions with the same name?

If the fractions to be subtracted already have the same name - they all have the same denominator - you can simply subtract the numerators of the fractions to be subtracted from each other. The common denominator remains the same. In this way, you finally get the difference of the fractions.

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Example: Subtraction of fractions with the same name
2414 = 2 − 14 = 14

In this example, both fractions have the same denominator, i.e. both have the same number below the fraction bar. They therefore have the same name. To subtract the two fractions, only the two numbers, i.e., the two numerators above the fraction bar, have to be subtracted from each other.

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How to subtract unequal-named fractions?

Fractions are unequal-named exactly when the respective numbers below the fraction bar, i.e. the two denominators of the fractions to be subtracted, are different. For subtraction, unequal-named fractions must first be made equal-named, just as in the addition of fractions. If they then have the same name, i.e. the same denominator, only the numerators above the fraction must be subtracted from each other, while the common denominator remains.

Example: Subtraction of unequal-named fractions
1314 = 412312 = 4 − 312 = 112

The two fractions to be subtracted from each other here initially have the two denominators 3 and 4. For subtraction, they must first be made equal. To do this, both fractions are transformed so that they have the same denominator, i.e. a common denominator. The fractions are always transformed in such a way that their value, i.e. the fraction number, does not change. There are basically several ways of transforming fractions, which are described on the parent page on the topic Fractions.

Make fractions have the same name

Two fractions can be made equal by expanding one fraction with the denominator of the other. So you multiply both the numerator and the denominator of one fraction by the denominator of the other fraction.

Expand

Extending a fraction is a transformation in which the value of the fraction, i.e. the fraction number, is not changed. This is because the fraction represented by the fraction is only divided into smaller sections, i.e. the fraction or the division is refined.

Fractions are expanded by multiplying both the numerator and the denominator by the same number.

Making the same name using the example

We can thus make the two fractions from the above example have the same name as follows.

The left fraction is expanded with the denominator 4 of the right fraction. Expanding by 4 means multiplying the numerator and denominator of the left-hand fraction by 4.

13 = 1 × 43 × 4 = 412

The right-hand fraction is expanded with the denominator 3 of the left-hand fraction. Expanding by 3 means multiplying the numerator and denominator of the right-hand fraction by 3.

14 = 1 × 34 × 3 = 312

Now the two fractions with the same name can be subtracted, as in the example:

412312 = 4 − 312 = 112

Note

The described equal-named making is based on expanding the two fractions in such a way that the two different denominators are finally multiplied together. However, this often leads to the fact that the values of the expanded fractions can become very large, which makes the subsequent calculations more time-consuming. Therefore, to make them equal, the smallest common denominator (main denominator) of the fractions should be determined. The main denominator is the smallest common multiple (kgV) of the denominators and thus often smaller than the multiplication of the two denominators. You can read more about the lowest common denominator at fraction-calculator.

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How to subtract mixed fractions?

Mixed fractions are composed of an integer and an ordinary fraction. They are also called mixed numbers. To subtract mixed fractions, the whole number of each fraction is first converted into the corresponding fraction so that the two fractions can then be subtracted from each other. For this purpose, as with every subtraction of fractions, they must be made equal if necessary, so that finally the numerators can be subtracted with the denominator remaining the same.

Example: Subtraction of Mixed Fractions
223 − 213 = 8373 = 13

The integer part of the two mixed fractions, i.e. the two in each case, was converted here into 6 thirds each and added to the associated fraction. The two mixed fractions were thus converted into improper fractions. Fractions are called improper if the numerator is greater than the denominator.

Conversion of mixed fractions into improper fractions

You convert a mixed fraction or mixed number into a non-genuine fraction by multiplying the integer part by the denominator and then adding the numerator to it. The denominator remains unchanged.

Conversion using the example

The two mixed fractions from the above example are thus converted into improper fractions as follows.

The left mixed number is transformed as follows: The integer 2 is multiplied by the denominator 3 and added to the previous numerator 2.

223 = 2 × 3 + 23 = 83

The right mixed number is transformed as follows: The integer 2 is multiplied by the denominator 3 and added to the previous numerator 1.

213 = 2 × 3 + 13 = 73

Subtraction of the two fractions

Since the two transformed fractions already have the same name, they can now be subtracted from each other.

8373 = 8 − 73 = 13
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Video on subtracting fractions

Finally, a video on the subject of subtracting fractions by Math Antics. After an introduction, the video first explains how to subtract fractions with the same name. Math Antics explains how to expand fractions to obtain the common denominator for subtracting two fractions. Later shortening for the common denominator is described. Finally, the subtraction of mixed fractions is described.

Source information

As source for the information in the 'Fractions' category, we have used in particular:

Last update on November 22, 2022

The last changes in the 'Fractions' category were implemented by Michael Mühl on November 22, 2022. The main changes were:

  • 22.11.2022: Publication of the topic Fraction together with the corresponding texts.
  • Editorial revision of all texts in this category