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How to Write a Numerical Expression? – Definition & Examples

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In this lesson, you will be given the definition of a numerical expression and learn how to write one. You will be provided with plenty of examples to clearly illustrate this important mathematical concept.
Numerical Expression Definition
You have likely worked with numbers since your preschool days. You started counting numbers, and pretty soon you were adding them using your fingers, Cheerios, or any other objects you used to help you count. Since then, you are now (hopefully) able to look at a piece of paper or computer screen and add, subtract, multiply, and divide small numbers in your head.

When you look at a problem with numbers, you are most likely looking at a numerical expression. A numerical expression is a mathematical sentence involving only numbers and one or more operation symbols. Examples of operation symbols are the ones for addition, subtraction, multiplication, and division. They can also be the radical symbol (the square root symbol) or the absolute value symbol.

Examples of Numerical Expressions
The only requirements for a numerical expression are that it only contain numbers and operation symbols. Some numerical expressions have only one operation symbol. Others have two or more. Here are some examples of numerical expressions:

4 + 5
134 – 75
56 * 4 + 6
68 / 8 * 7 – 2 + 1

Examples of Non-Numerical Expressions
Because numerical expressions can only contain numbers, expressions containing variables (such as x or y) cannot be considered numerical expressions. They are actually called algebraic expressions instead. Here are two examples of algebraic expressions:

4x + 5
134 – x

Writing Numerical Expressions
When given a verbal or written-down word problem, it is important to be able to translate the words to a numerical expression so you can solve the problem. Here are a few examples.

Example 1: Amanda had 12 gummy bears and gave 2 to her brother. She then ate 4 gummy bears. How many gummy bears did Amanda have left?
Amanda started with 12, gave two away (-2) and ate 4 (-4). In this example, only the subtraction operation needed to be used. The numerical expression could be written as:

12 – 2 – 4

 
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