Table of Contents
Why are Mathematical Properties Important?
Mathematical properties are important because they allow us to understand and describe the world around us. Mathematical properties can be used to model physical phenomena, to solve problems, and to understand the relationships between different quantities.
Properties of Addition in Mathematics
The sum of two numbers is called the addition. Addition is a binary operation that takes two numbers, a and b, as input and produces a single number, c, as output. The sum of a and b is denoted by the symbol c = a + b.
The addition is commutative, meaning that the order of the input numbers does not affect the output. That is, a + b = b + a.
The addition is associative, meaning that the grouping of the input numbers does not affect the output. That is, (a + b) + c = a + (b + c).
The addition is distributive, meaning that the sum of a number and a product of two numbers is the same as the sum of the two numbers multiplied together. That is, a + (b × c) = (a + b) × c.
The addition is compatible with the order of operations, meaning that the addition is performed according to the standard order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). For example, 3 + 4 × 2 = 3 + 8 = 11.
Properties of Cylinder
1. A cylinder is a solid figure with two congruent, parallel and circular bases.
2. The height of a cylinder is the distance between the two bases.
3. The lateral surface area of a cylinder is the sum of the areas of the two circular bases.
4. The circumference of a cylinder is the distance around the edge of the two bases.
5. The total surface area of a cylinder is the sum of the lateral and the basal surface areas.
6. The volume of a cylinder is the product of the height and the area of the base.
Properties of Definite Integral
The definite integral has the following properties:
1. The definite integral is a real number.
2. The definite integral is the limit of a Riemann sum as the number of partitions of the interval [a, b] approaches infinity.
3. The definite integral is additive in the sense that the integral of a sum is the sum of the integrals.
4. The definite integral is distributive in the sense that the integral of a product is the product of the integrals.
5. The definite integral is a measure of the area under a curve.
Properties of the Commutative Property
The commutative property states that the order of the terms in a multiplication does not affect the product. For example, 2 x 3 = 3 x 2.
Properties of the Distributive Property
The distributive property states that for every number a, there is a distributive law that states that a multiplied by the sum of two numbers is equal to the sum of a multiplied by the first number and a multiplied by the second number. In symbols:
a(b+c) = a(b) + a(c)
