Arithmetic Operations

If you’ve been visiting regularly, you probably already know that this website explains  many aspects of this branch of mathematics, clearly and in an accessible language, so that anyone can understand. Does arithmetic operations sound complicated to you? Do you already feel put off? There’s no need: you’ve surely already been across addition, subtraction, multiplication and division. When you think about how many pairs of shoes you’ve got, that’s addition; when you rule out the ones you’re not going to take with you on vacation, that’s subtraction. These are all arithmetic operations. Sounds familiar? Thought so. These are just arithmetic operations you run across every day.

Addition is the most basic of all arithmetic operation: it combines two or more numbers, called the terms or the addends and the result is a single number, the sum of the added numbers. Repeated addition refers to adding more than two numbers. The fact that it is commutative and associative makes the order in which we add the numbers completely irrelevant. You should also know that if you add a positive number to its opposite, the result is always zero.

Subtraction, on the other hand is the exact opposite thing. In this kind of operation we always have a minuend minus a subtrahend. When the first one has a greater value than the second one, the result called the difference is positive. Or else, the result is negative. If the two are equal, the difference between them is always zero. When we subtract a negative number from a positive number, the fact that we have two minuses actually makes the whole subtraction turn into an addition: a-(-b)= a  b. This operation  is not commutative or associative so the order matters.

Multiplication is the third of the four arithmetic operations. Multiplication combines two factors and the result is called a product: a x b = c (a times b equals c). Multiplication is commutative, associative and it also is distributive over addition and subtraction. We can express this quality of multiplication as it follows:  a x(b  c)=a x b  a x c; ax(b-c)= a x b- a x c.

Division is the fourth of the arithmetic operations. In a division, we divide the dividend by the divisor and we get the result,called the quotient. Any number divided by zero is undefined. In the division of positive numbers, if the dividend is bigger than the divisor, the result is greater than one. If the dividend is smaller than the divisor, the value of the quotient will be smaller than one, but still over zero, since it’s positive. Division is not complicated at all.

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