# 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.