# How to find fractions?

Alexey Kryukov
January 29, 2013

Mathematics - the queen of sciences. Her greatness is limitless, and her power is great. All other sciences rely on mathematical results. Be it physics, chemistry, biology, and even philology.

As the house is made up of bricks, so in each task there are small subtasks. And having learned to solve small ones, one can learn to solve more complex problems.

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

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

If n = 〖10〗 ^ k, k = 1,2, .., then such a fraction is called decimal and is written as 0.0..0m, and the number of zeros after the decimal point is equal to k-1.

A number is called composite if it has other dividers besides 1 and itself.

## Basic operations

Fractions can be added, subtracted, multiplied, divided, raised to a power. These operations are basic. The examples are commonly used.

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

## How to reduce the fraction

For this it is necessary to decompose the numerator and denominator into prime factors, if they are composite. And further, if these prime factors coincide, then delete them.

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

## How to find a fraction of a number

Let the number be some length. And a fraction is essentially a part of this length, which means that in order to find the integer part, it is necessary to multiply the fraction by a number. For example, 2/3 of 27 = 27 * 2/3 = 27/3 * 2 = 18

## How to find a fraction from a fraction

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

## Fraction fraction

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

It is also necessary to remember that when solving complex examples, it is necessary to come up with a solution algorithm. You may have to change the division by multiplication with a fraction change, it is possible to multiply and divide by the same number.Such fairly simple instructions will help in solving examples.

As an example, take the classic textual problem. From the warehouse, which was 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 taken for recycling. The remaining fuel oil was taken for recycling. How much fuel oil was recycled?

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

Fractional tasks are the base of school arithmetic. They are not complicated in their essence, but they require assiduity and attentiveness to perform. Under these conditions, the result will not be long in coming.