# Why do we use false fractions

## Fractional calculation: different types of fractions

### Mixed fractions

Mixed fractions are a combination of an integer and a fraction. Mixed fractions are an alternative way of writing improper fractions.

$ \ frac {7} {3} = \ frac {6} {3} + \ frac {1} {3} = 2 \ frac {1} {3} $

This notation is often misunderstood when calculating fractions and interpreted as a multiplication, although it is actually an addition:

$ 2 \ frac {1} {3} = 2 \ cdot \ frac {1} {3} ~~~~~~~~~~ \ textcolor {red} {FALSE} $

$ 2 \ frac {1} {3} = 2 + \ frac {1} {3} ~~~~~~~ \ textcolor {green} {CORRECT} $

**Mixed** Fractions consist of one **whole number** and one **fracture**. All improper fractions can be converted into **mixed fractions** convert.

$ \ frac {7} {2} = 3 \ frac {1} {2} $

$ \ frac {17} {3} = 5 \ frac {2} {3} $

$ \ frac {27} {5} = 5 \ frac {2} {5} $

### Multiple fractions

Fractions in which the numerator and / or the denominator are also a fraction are called multiple fractions. To simplify multiple fractions, you need the calculation rules for dividing fractions.

First, let's consider the case where only the numerator is a fraction. A break on the counter **or** Denominator is a fraction is also called **Double fraction**.

$ \ large {\ frac {\ frac {2} {3}} {4} = \ frac {2} {3}: 4 = \ frac {2} {3}: \ frac {4} {1} = \ frac {2} {3} \ cdot \ frac {1} {4} = \ frac {2 \ cdot 1} {3 \ cdot 4} = \ frac {2} {12} = \ frac {1} {6} } $

Now let's look at an example of a fraction with one more fraction each in the numerator and denominator.

$ \ large {\ frac {\ frac {2} {3}} {\ frac {4} {5}} = \ frac {2} {3}: \ frac {4} {5} = \ frac {2} {3} \ cdot \ frac {5} {4} = \ frac {2 \ cdot 5} {3 \ cdot 4} = \ frac {10} {12} = \ frac {5} {6}} $

Double or multiple fractions can be simplified using the calculation rules for dividing fractions:

$ \ large {\ frac {\ frac {a} {b}} {c} = \ frac {a \ cdot 1} {b \ cdot c}} $

$ \ large {\ frac {\ frac {a} {b}} {\ frac {c} {d}} = \ frac {a \ cdot d} {b \ cdot c}} $

### Decimal fractions

One final group of fractions that you should know about are what are known as decimal fractions. Decimal fractions are characterized by the fact that the denominator is a power of $ 10 with a natural exponent. Simply put, decimal fractions have a denominator with the following values: $ 10, $ 100, $ 1000, and so on.

Decimal fractions have a power of ten in the denominator ($ 10, 100, 1000 ... $) belonging to the natural numbers and can be written as decimal numbers.

$ \ frac {35} {100} = $ 0.35

$ \ frac {12} {1000} = $ 0.012

$ \ frac {7} {10} = $ 0.7

You have now learned the ways in which fractions can be expected. Try out your new knowledge about fractions with our exercises. We wish you a lot of fun and success!

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