# How to find fractions?

Mathematics is the queen of sciences. Her greatness is infinite, but her power is great. All other sciences rely on mathematical results. Whether it's physics, chemistry, biology, and even philology.

As the house is made up of bricks, so in each task there are small subtasks. And by learning to solve small, you can learn to solve more complex problems.

Today we will analyze how to find fractions. The concept of fractions arose in ancient Greece, after the Greeks introduced the concept of length, equivalent to integers. Next, we needed a concept expressing a part of the length, for example half, one third of the length. So the concept of fraction appeared.

The set of rational numbers Q is the set of numbers represented in the form m / n, where m, n are integers. The number m / n is called an ordinary fraction, where m is a numerator, and n is a denominator, n ≠ 0.

If n = 〖10〗 ^ k, k = 1,2, ..., then such a fraction is called decimal and written as 0,0..0m, with the number of zeros after the comma being k-1.

A number is said to be composite if it has other divisors besides 1 and itself.

## Basic Operations

Fractions can be added, subtracted, multiplied, divided, raised to a power. These operations are basic. In the examples,

We will move from simple to complex, showing by examples how exactly these or other operations are performed.

## How to reduce a fraction

To do this, we must expand the numerator and denominator by prime factors, if they are composite factors. And further, if these simple factors coincide, then delete them.

In the absence of prime factors, the fraction is called irreducible. For example, 85/65 = (17 * 5) / (13 * 5) = 17/13

## How to find a fraction of the number

Let the number be a certain length. A fraction is essentially a part of this length, so to find the integer part, multiply the fraction by the number. For example, 2/3 of 27 = 27 * 2/3 = 27/3 * 2 = 18

## How to find a fraction from a fraction

In fact, this is a simple multiplication process, to find a fraction of a fraction, you just multiply 2 fractions. For example, 2/3 and 13/17: 2/3 * 13/17 = 26/51

## Fission of fractions

When dividing fractions a / b, c / d, the divisor c / d can be represented as d / c and multiply, and then cut. For example, 27/17? 9/34 = 27/17 * 34/9 = 2 * 3 = 6.

It is also necessary to remember that when solving complexexamples need to come up with a solution algorithm. It may be necessary to change the division into multiplication with a change of fraction, it is possible to perform multiplication and division by the same number. Such simple enough instructions will help in solving examples.

As an example, take the classical textualtask. From a warehouse on which there were 150 tons of fuel oil stolen 2/3. The stolen parts were distributed in parts in the ratio of 5/17 and 12/17, the latter was transported for processing. The remaining fuel oil was transported for processing. How much fuel oil has been recycled?

150 * 2/3 * 12/17 + 150 * (1-2 / 3) = 150 * 41/51

Tasks for fractions are the basis of school arithmetic. They are not complex in nature, but it requires to be diligent and attentive. If these conditions are met, the result will not take long.