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Numerical Expressions

what you'll learn...

overview

The arithmetic operations addition, subtraction, multiplication, and division were introduced in earlier pages. This page explains the concept of numerical expressions using the numbers and the arithmetic operations.

3+2=5$3 + 2 = 5$

Addition is one of the arithmetic operations.

Subtraction represents "taking away" part of a quantity.

52=3$5 - 2 = 3$

Subtraction is one of the arithmetic operations.

Subtraction 52=3$5 - 2 = 3$ is the inverse of addition 3+2=5$3 + 2 = 5$.

The word "inverse" means: that is opposite or reverse of something.

Multiplication represents "repeated addition" of a quantity.

3×2=6$3 \times 2 = 6$

Multiplication is one of the arithmetic operations.

Multiplication 3×2$3 \times 2$ is repeated addition $3 + 3$, that is $3$ repeated $2$ times.

Division represents "splitting" a quantity into equal parts.

$6 \div 2 = 3$.

Division is one of the arithmetic operations.

Division $6 \div 2 = 3$ is inverse of multiplication $3 \times 2 = 6$

many ways to express

Consider $2 + 4 + 3$. This can be evaluated to $9$.

This is an example of a numerical expression.

The word "expression" means: collection of numbers and arithmetic operations between them, which together represent a quantity.

Numerical Expression : A numerical expression is a statement of a value using numbers and arithmetic operations between them.

eg: $3 + 4 \times 2 - 6 \div 3$ is a numerical expression involving addition, multiplication, subtraction, and division.

The expression in the given example evaluates to $3 + 4 \times 2 - 6 \div 3 = 9$

$2 \times 4 \times 3$ is an example of a numerical expression. It is evaluated to $24$.

$a + 3 x$ is not a numerical expression. It is not entirely numbers and arithmetic operations. It has letters $a$ and $x$.

examples

Is $3 - 2$ a numerical expression?

The answer is "Yes, the subtraction of two numbers"

Is $3 + 4 - 2 + 1$ a numerical expression?
The answer is "Yes, addition and subtraction can be part of an expression".

Is $3 + 4 \times 2 - 6 \div 3$ a numerical expression?
The answer is "Yes, all arithmetic operations can be part of a numerical expression"

is $3$ a numerical expression?
The answer is "Yes. technically a number can also be considered a numerical expression".

Consider $1 + 2$ and $3 \times 1$. Note that when evaluated, both result in identical numerical value $1 + 2 = 3$ and $3 \times 1 = 3$.

They are two different expressions, evaluating to equal values.

summary

Numerical Expression : A numerical expression is a statement of a value using numbers and arithmetic operations between them.

eg: $3 + 4 \times 2 - 6 \div 3$ is a numerical expression involving addition, multiplication, subtraction, and division.

The expression in the given example evaluates to $3 + 4 \times 2 - 6 \div 3 = 9$. We'll learn about this in the coming pages.

Outline