 # Maths Properties  View Notes

Mathematics is based on various properties which are vital for solutions. Arithmetic, geometry, set theory, mensuration, number system, etc. can be linked to Maths properties and calculus.

## Why are Mathematical Properties Important?

The properties in Mathematics are the basic rules that mathematicians universally follow to solve problems effectively. Students need to learn all these properties to relate the concepts in particular questions with poise. It should be noted that a range of derivations needs mathematical properties and its uses.

Here is a list of all Maths properties that every student needs to learn for a high score.

### Properties of Addition in Mathematics

The addition is one of the forms of mathematical operation crucial for solving an equation. Properties of additional help in finding integers or result of adding them.

The properties of addition can be utilised to decrease the complex expressions in numerous algebraic equations. This tops the list of all maths properties due to its multiple applications.

### Properties of Cylinder

Plane geometry is the calculation of two-dimensional shapes or even shapes like polygon, lines, curves, etc. Solid geometry deals with the study of three-dimensional shapes such as spheres, cylinders, cubes, etc.

These shapes can be measured in three directions which can also be called solid shapes or three-dimensional shapes. Moreover, these dimensions can be used to calculate a three-dimensional shape’s width, depth, height, and length.

The smooth surfaces in 3D shapes are called faces. This flat surface has a vertex point which is a point of intersection of three edges. The point where two faces meet is called the edge.

### Properties of Definite Integral

A Definite Integral has an integral with lower and upper limits. It is the disparity between the principles of an integral in an independent variable which falls in a specific lower and upper limit. It is symbolised as ∫bc f(x) bx.

### Properties of the Commutative Property

In Mathematics, a commutative property is the terms that aren’t needed while operating. This property is valid only for multiplication and addition processes.

This makes p + q = q + p and p × q = q × p. But it does not relate to division and subtraction method, because, p – q ≠ q – p and p/q ≠ q/p.

If two numbers E and F are added, it gives a sum G, and then by interchanging the position of E and F, the result will be G. This makes E + F = F + E = G.

Let’s take an example where 5 + 3 = 8 = 3 + 5. Here even if 3 comes after or before the plus sign, the sum of 5 and 3 will always be 8 irrespective of their placing.

### Properties of the Distributive Property

The Distributive Property in algebra is used to multiply multiple or single values within a set of digression. This states that when a factor is multiplied by the addition of two terms, it gives the final result. One needs to multiply two numbers by a factor and perform addition to find the value.

This can be symbolically portrayed as-

B (E+ F) = BE + BF

Where B, E and F are three different values.

Let’s consider a simple example:  3(5 + 2).

Since 5 + 2 binomial is in digression, one has to calculate the value of 5 + 2 and then multiply it by 3, which gives the final value as 21.

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1. What are the Properties of a Triangle?

Ans. The properties of the triangle are as follows-

• The longest side of a triangle is always the significant angle in the opposite.

• The third side of a triangle has a greater length than the total sum of two sides of a triangle

• The disparity between a triangle’s two sides is always less than the third side’s length

• The sum of all three sides of a triangle is equal to the perimeter of a triangle

• The total of three angles of a triangle irrespective of its type is always 180°

• If corresponding angles of two triangles are matching and their side lengths are similar, then those two triangles are called similar.

2. What are the Properties of Whole Numbers?

Ans. The properties of whole numbers are arithmetic based like multiplication, addition, subtraction, and division. When two whole numbers are multiplied or added, it gives a whole number. An integral can also be a product of subtracting two whole numbers. Also, a fraction can be found by a division of two whole numbers.

The properties of the whole number are as follows-

• Commutative property of multiplication and addition

• Closure property

• Distributive

• Multiplicative identity

• Multiplication by zero,

3. What is a Rectangle? What are its Properties?

Ans. A four-sided polygon is known as a Rectangle which always equals to 900. Ideally, vertices or corners at two sides meet to form a right-angled rectangle. The opposite side of this shape is equal in length, differentiating it from squares.

The properties of the rectangle are following-

• In a rectangle, the area is always equal to its breadth and length

• This shape can also be defined as a parallelogram having four right angles

• If the total interiors are calculated, it will be 3600.

• The perimeter of a rectangle will be a total of twice breadth and length.

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