Fractions

INTRODUCTION TO FRACTIONS

Fractions are a fundamental concept in mathematics that represent a part of a whole or a ratio between two numbers. Understanding fractions is crucial for students, as they are the basis for many mathematical operations and concepts used in everyday life, from cooking to measuring distances.

WHAT ARE FRACTIONS?

A fraction consists of two numbers separated by a line (fraction bar). The number above the line is called the numerator, which represents the number of selected parts, while the number below the line, called the denominator, indicates into how many equal parts the whole is divided. For example, the fraction 1/4 represents one part out of four equal parts of a whole.

Understanding fractions involves several key concepts:

• PROPER FRACTIONS: Have a numerator smaller than the denominator and represent a value less than 1.
• IMPROPER FRACTIONS: Have a numerator greater than or equal to the denominator, representing a value equal to or greater than 1.

BASIC OPERATIONS WITH FRACTIONS: ADDING, SUBTRACTING, MULTIPLYING, AND DIVIDING

Working with fractions involves several basic operations:

• ADDING AND SUBTRACTING: To add or subtract two fractions, they must have the same denominator. If the denominators are not the same, we must first transform the fractions so they have a common denominator. Then, we add or subtract the numerators.
• MULTIPLYING: Multiplying fractions is straightforward; the numerators are multiplied together, and the denominators are multiplied together.
• DIVIDING: Dividing fractions involves multiplying the first fraction by the reciprocal of the second fraction (invert the second fraction and then multiply).
• SIMPLIFYING: Fractions are simplified by finding the greatest common divisor (GCD) of the numerator and the denominator, and then dividing both numbers by this GCD to get the simplest form of the fraction.

WHY ARE FRACTIONS IMPORTANT?

Fractions are important because they allow us to accurately represent and manipulate parts of whole numbers or quantities. Without fractions, it would be difficult to express quantities that are not whole numbers, which would limit our ability to perform precise calculations in science, engineering, cooking, and more.

CONCLUSION

Fractions are a fundamental tool in mathematics that allow for the precise and flexible handling of division and ratios. Understanding fractions opens the door to a better comprehension of mathematical concepts and their practical application in many everyday situations. The ability to work effectively with fractions is crucial for success in mathematics and other scientific and practical disciplines.