Operaciones de enteros y clasificación de polígonos

Mathematics

Integer Operations

Integer operations include addition, subtraction, multiplication, and division. These operations are fundamental to mathematics and are essential for solving problems involving whole numbers.

Addition

In integer addition, two integers are combined to produce another integer. To perform addition, follow these steps:

1. Align the digits vertically according to place value.
2. Add the digits in each column starting from the rightmost column.
3. Carry over any excess from left columns to the next column.
4. Repeat until all columns are processed.

Example: 3 + 4 = 7

Subtraction

Integer subtraction involves removing smaller integers from larger integers. To perform subtraction, follow these steps:

1. Arrange the integers as A - B.
2. Set up the equation A + B = C, where C represents the difference.
3. Complete the equation by performing addition.
4. If necessary, borrow from previous columns to complete the operation.

Example: 5 - 2 = 3

Multiplication

Multiplication combines two sets of integers, multiplying each element in the first set by each element in the second set and adding the products together. To perform multiplication, follow these steps:

1. Recognize the pattern of zeros resulting from the repeated multiplications.
2. Multiply the first elements in both sets.
3. Place the product above the first element in the second set.
4. Multiple the first element in the first set by every element in the second set except the first element.
5. Place the products above the respective positions in the second set.
6. Multiply the remaining elements in the first set by the last element(s) in the second set.
7. Add the obtained values and place them above the position in the second set.
8. Combine consecutive products by lining up the zeroes and adding the remainder.

Example: 4 * 5 = 20

Division

Division divides an integer by another integer to determine the quotient. To perform division, follow these steps:

1. Determine whether the divisor is a factor of the dividend.
2. Divide the tens place of the dividend by the tens place of the divisor, record the quotient.
3. Multiply the divisor by the quotient and add the result to the dividend.
4. Divide the quotient by the divisor and repeat the process.
5. Continue the process until the entire dividend is divided.

Example: 20 ÷ 5 = 4

Polygon Classification

A polygon is a plane figure with multiple straight sides and angles such that the sum of the internal angles is either 180° or 360°. Polygons are typically classified by the number of sides and their properties.

Triangle Classification

Triangles are 3-sided polygons. They have specific ratios of side lengths due to their angles. The three types of triangles are:

• Equilateral: All sides are equal (equal angles too).
• Isosceles: Two sides are equal (two equal angles).
• Scalene: All sides are unequal.

Quadrilateral Classification

Quadrilaterals are 4-sided polygons. They have specific properties and can be further classified as:

• Parallelogram: Two pairs of opposite sides are parallel and equal.
• Rectangle: A parallelogram with all angles 90°.
• Rhombus: A parallelogram with all sides equal.
• Square: A rhombus that is also a rectangle.
• Trapezium: A quadrilateral with one pair of opposite sides parallel.
• Kite: A quadrilateral with two pairs of adjacent congruent sides.
• Scalene quadrilateral: A quadrilateral with no congruent sides.

Exponentiation of Integers

Exponentiation of integers is the process of raising an integer to a power. It is represented as a^n, where a is the base, n is the exponent, and the result is the base raised to the power of the exponent.

Example: 2^3 = 8