Fractions. Mixed numbers and operations

Fractions are a fundamental part of mathematics. They are used to represent numbers that are not whole numbers, allowing to express relationships of parts of a whole. A fraction consists of two parts: the numerator and the denominator. The numerator indicates the number of parts that are taken or considered, while the denominator indicates how many parts the whole is divided into. For example, in the fraction 3/4, the numerator is 3 and the denominator is 4.

Fractions can be represented in different ways. In addition to the common fraction notation, they can be expressed in decimal or percent form. For example, the fraction 1/2 is equal to 0.5 in decimal form and 50% in percent form.

Fractions allow you to perform mathematical operations such as addition, subtraction, multiplication and division. To add or subtract fractions, it is necessary to have the same denominator. If the denominators are different, common denominators must be found using the least common multiple (LCM) technique. To multiply fractions, multiply the numerators together and the denominators together. To divide fractions, multiply the first fraction by the inverse of the second fraction.

Mixed numbers are a combination of whole numbers and fractions. They are composed of a whole part and a fraction. For example, the mixed number 3 1/2 is composed of the whole number 3 and the fraction 1/2.

Fractions have various applications in everyday life. For example, they are used in cooking to measure ingredients in recipes, in commerce to calculate discounts and percentages, and in construction to estimate lengths and areas. They are also used in problems of proportion, probability and statistics.

It is important to understand the concept of fractions and their mathematical manipulation to have a solid foundation in mathematics. Knowing the basic operations with fractions can make work easier and help solve more complex mathematical problems.