User:Dogmorfmocion/Sandbox3

= Operations =

Basic operations
We use operations to manipulate and describe numbers, as well as peform calculations. The four basic operators in arithmetic are addition, subtraction, multiplication and division.

Addition '+'
We can add two numbers a and b together by writing $$a + b$$. The number that results from this addition is called the sum of a and b. The order in which we add these numbers is not important as they equal the same amount; if $$a + b = c$$ then $$b + a = c$$. This property is known as commutativity, as you can see by this example:

3 + 7 = 10 and 7 + 3 = 10

When we have to add three or more numbers together, the order in which we add these numbers is also not important. If $$a + b + c = d$$ then $$c + b + a = d$$ also, and so on and so forth. For example:

2 + 3 + 7 = 12 and 7 + 3 + 2 = 12 and 3 + 2 + 7 = 12 ... (etc.)

Subtraction '-'
We can subtract two numbers a and b together by writing $$a - b$$. The number that results from this subtraction is called the difference of a and b. However, unlike the rules of addition, the ordering is important; subtracting is NOT commutative and therefore $$a - b = c$$ does not nessecarily mean that $$b - a = c$$. For example:

7 - 3 = 4 but 3 - 7 = -4

You may find it important to know that the equation $$a - b = c$$ can be read explicity as $$a + -b = c$$. Subtraction is the reverse of addition and vice versa. Finally, two minuses equal a plus! Subtracting a negative number is equivalent to adding a positive number, so that $$a - (-b)$$ is the same as writing $$a + b$$.