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Mathematical Operations

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 xax^a
Rule

Addition

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 2 + + 3 3 = = 5 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 7 - 3 3 = = 4 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=32 2+2+2=3\cdot 2 33 times 22
3+3+3+3=43 3+3+3+3=4\cdot 3 44 times 33
7+7+7+7+7=57 7+7+7+7+7=5\cdot 7 55 times 77

When 33 is multiplied by 2,2, the numbers are called factors and the result is called a product.

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

Division

Division is to divide a number into parts. For example, sharing 1212 cookies with 44 persons, each person will have 33 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 12 // 4 4 = = 3 3

Division can be interpreted as backwards multiplication. If the quotient and the denominator are multiplied, the product will be the numerator. 34=12 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. bbbn=bn \underbrace{ b \cdot b \cdot \ldots \cdot b }_n= b^n The number bb is called the base and nn is the exponent, and together they represent a power.