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Rule

# Mathematical Operations

An operation uses an operand on two numbers to generate a new number. The most common operands are:

• Addition $+$
• Subtraction $-$
• Multiplication $\cdot$
• Division $\div$
• Exponentiation $x^a$
Rule

Addition is to add two numbers, for example adding two and three equals five. The numbers added are called terms and the result is a sum. The symbol between the terms is a plus sign, $+.$

 Term $+$ Term $=$ Sum $2$ $+$ $3$ $=$ $5$
Rule

## Subtraction

Subtraction is to remove one value from another. For example, removing four from seven equals three. The numbers used in the subtraction is called terms and the result is a difference.

 Term $-$ Term $=$ Difference $7$ $-$ $3$ $=$ $4$
Rule

## Multiplication

Multiplication is actually repeated addition. If a number is added multiple times, it can be written as a multiplication instead.

 $2+2+2=3\cdot 2$ $3$ times $2$ $3+3+3+3=4\cdot 3$ $4$ times $3$ $7+7+7+7+7=5\cdot 7$ $5$ times $7$

When $3$ is multiplied by $2,$ the numbers are called factors and the result is called a product.

 Factor $\times$ Factor $=$ Product $3$ $\times$ $2$ $=$ $6$
Rule

## Division

Division is to divide a number into parts. For example, sharing $12$ cookies with $4$ persons, each person will have $3$ cookies. The number divided is called the numerator and the number of parts to divide in is called the denominator. Finally, the result is the quotient.

 Numerator $/$ Denominator $=$ Quotient $12$ $/$ $4$ $=$ $3$

Division can be interpreted as backwards multiplication. If the quotient and the denominator are multiplied, the product will be the numerator. $3 \cdot 4 = 12$

Rule

## Exponentiation

When a number is multiplied by itself it can be expressed as the number is raised to the number of times it's multiplied by itself. $\underbrace{ b \cdot b \cdot \ldots \cdot b }_n= b^n$ The number $b$ is called the base and $n$ is the exponent, and together they represent a power.