# Fractions: Theory and Online Calculators. Automatically perform mathematical operations with fractions, accompanied by detailed explanations. Learn by seeing and doing, through hundreds of thousands or even millions of step-by-step solved examples

## Fractions operations that can be run automatically, with explanations:

### Mathematical operations with fractions, plus the theory behind: addition, subtraction, multiplication, division, fractions reducing (simplifying), comparing, sorting in ascending order, converting numbers to fractions and percentages.

## Ordinary fractions: what are they?

If we have to divide evenly 6 apples to 3 children, then we perform the operation:

- 6 ÷ 3 = 2
- so we know that each child will get 2 apples.

If we have to divide evenly 2 apples to 3 children, then we perform the operation:

- 2 ÷ 3 = ?
- this operation has no solution in the set of natural numbers;
- however we will be able to divide the apples with the help of a knife: the quantity of apple for each child will be defined using the fraction
^{2}/_{3} - all similar cases lead to fractions.

### Fractions are formed by dividing numbers:

- each fraction has the form
^{a}/_{b} - "a" is the
**numerator**, written above the fraction bar; - "b" is the
**denominator**, written below the fraction bar; "b" may not be zero; - "b" shows us in how many equal parts "a" has been divided;
**the value of the fraction** is calculated by dividing the numerator, "a", by the denominator, "b": - "a" ÷ "b"
- these fractions, in which both the numerator and the denominator are integers, are called
**ordinary fractions** (also called normal, or simple).

## More on ordinary (common) fractions / theory: