# Mathematical Language and Symbols

## Mathematical Language and Mathematical Symbols

**Mathematical language** is a system used in the field of mathematics to communicate mathematical ideas, concepts, and theories among others. It is distinct and unique from the usual language that people are used to, and is used to communicate abstract, logical ideas.

Burns (n.d) mentioned 3 characteristics of mathematical language. These are being precise, being concise, and being powerful. Precision of mathematical language means the language is able to make very fine distinctions of things. Conciseness is able to say things briefly. Mathematical language being powerful is expressing complex thoughts with relative ease, being understood by most readers.

**Mathematical Symbols** are used to refer to certain quantities, concepts, ideas among others. The most common used in basic mathematics are numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, the four fundamental symbols of operation +, -, ×, ÷, and the inequality symbols ≠, ≤, ≥, < >, and equal sign =.

## Mathematical Expressions vs Mathematical Sentences

A** mathematical expression** is the mathematical analogue of an English noun; a correct arrangement of mathematical symbols used to represent a mathematical object of interest (Burns, n.d). It does NOT state a complete thought, and does NOT make sense to ask if an expression is true or false. In mathematics areas, e.g. Algebra, the most common expressions are numbers, sets, and functions.

A **mathematical sentence** is the mathematical analogue of an English sentence, and is a correct arrangement of mathematical symbols that state a complete thought. Hence, it makes sense to ask if a sentence is true, false, sometimes true, or sometimes false.

Take a look at the table below, to visualize the difference of expression and sentence in mathematics.

## The Language of Algebra

Mathematical sentences and expressions are commonly used in Algebra. In fact, these concepts are taught already during your 7^{th} grade. Let’s take a look back on the Language of Algebra where symbols, expressions, and mathematical sentences are first introduced.

**Common Words in Algebra **

*Variable*. It is a symbol which represents a value or a number. Usually, small letters are used as variable,*e.g. a,x ,y .**Constant.*It is a number on its own which means the value never is definite and will never change,*e.g. 4, 9, 35.**Term.*It is a constant, or a variable, or a constant and variable/s multiplied together,*e.g. 4, z, 5xy, 87xy, xyz*.Literal Coefficient is the variable in a particular term.Numerical Coefficient is the constant in a particular term.*Expression.*It is also called algebraic expression. It is a group of terms separated by the “plus” or “minus” symbols, e.g.*3x-2, x+3.*

As mentioned, mathematics uses sentences. In Algebra, these sentences can be written mathematically or verbally. Mathematical sentences are written using variables, constant, and equal sign or inequality sign; while verbal sentences are written in words using phrases. The following are most commonly used phrases in Algebra:

- Addition
*(plus, increased by, added to, the sum of, more than)* - Subtraction
*(decreased by, subtracted from, the difference of, less than, diminished by)* - Multiplication
*(multiplied by, of, the product of, times)* - Division
*(ratio of, the quotient of, divided by)* - Inequality
*(is greater than, is less than, is at least, is less than or equal, is greater than or equal to, is at most, is not equal to)* - Equality
*(the same as, is equal to, equals)*

## Try Your Understanding!

For each question, choose the best answer. The answer key is below.

**Which of the following is a symbol which represents a value or a number?**- Constant
- Variable
- Term
- Coefficient

**Which of the following is a system used in the field of mathematics to communicate mathematical ideas and concepts?**- Mathematical Language
- Mathematical Symbols
- Mathematical Sentences
- Mathematical Expressions

**The following are characteristics of Mathematical Language according to Burns, EXCEPT:**- Ambiguous
- Precise
- Concise
- Powerful

**What is an algebraic expression?**- It is a symbol which represents a value or a number.
- It is a number on its own which means the value never is definite and will never change.
- It is a group of terms separated by the “plus” or “minus” symbols.
- It is a constant, or a variable, or a constant and variable/s multiplied together.

**Which of the following is the verbal sentence for x+3=5?**- The sum of a number x and five is three.
- The sum of a number x and three is five.
- Three added to a number x is not equal to five.
- A number x is added by 3.

### Answer Key

- Variable
- Mathematical Language
- Ambiguous
- It is a group of terms separated by the “plus” or “minus” symbols.
- The sum of a number x and three is five.

**© 2020 RBN Knowledge **

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