# Equal

Being equal means being identical or having the same amount, size, or value. The concept of equality is one that is used throughout mathematics. It is addressed in depth within algebra which is used to some degree in most mathematical applications.

Below are a few figures that illustrate the concept of equality. There are 3 cups and 3 saucers. It can therefore be said that there are an equal number of cups and saucers. This is one simple way to introduce the concept of equality. Any number of types of objects can be used. Simply pair the objects together until all the objects are paired, demonstrating that there are an equal (or unequal) number of objects.

Another way to introduce the concept of equality (and also fractions) is to divide something into equal parts. For example, the pizza below is cut into 8 equal slices. Each slice is equal in size to any of the other slices.

## Equality in measurement

In the context of measurement, equality commonly presents in the form of comparing units of measurement. Most of the world has adopted the International System of Units (SI) with the goal of standardizing units of measurement. However, some countries, such as the United States, have not, and even within countries that have adopted SI, local units of measurement may still be used. As such, it is important to be able to convert between the different units of measurement used in different regions. To be able to do so, it is necessary to know the equivalences between various units of measurement. More simply, how many of one unit of measurement is equal to another.

For example, there are 2.54 centimeters in 1 inch, or 2.54 cm = 1 in. Knowing this equivalence allows us to convert between units of inches and centimeters. The calculation is the same regardless of the relationships between various units, so being able to convert between units given their relationships enables us to convert any other units, assuming that we know their equivalences.

Example

Convert 45.819 cm to inches.

There are 2.54 cm in 1 inch, so to convert 45.819 cm to inches, divide by 2.54:

45.819 ÷ 2.54 = 18.039 in

## Equality symbols

There are many different equality symbols used. In mathematics the most common symbol used is the equal sign, which is written as "=". It can be used to denote a statement of fact (2 + 2 = 4), to create definitions in algebra (let x = 12), to write conditional statements (if x = 12, then ...), or to show some universal equivalence or identity: (x + y)^{2} = x^{2} + 2xy + y^{2}. The latter three examples all involve algebra. There are also different equal signs used in programming languages that denote specific properties of the equality.