water and bread. It is always said that water and bread are the things that a human being needs for mere survival. While it’s a bit unspectacular to solely feed on it, many other foods build on it.
There is something similarly essential in mathematics too: basic arithmetic operations. Nothing works here without a plus, minus, mark and shared. In this article you can get an overview of what the basic arithmetic operations are and what else might be involved.
The terms of the four basic arithmetic operations – overview
You may only know the basic arithmetic operations under the terms mentioned above. However, there are also technical terms to describe the different types of calculation and their components. You will learn about these and how the types of calculation work in this section.
Note: All four basic arithmetic operations are also available in fractions. For this you can look in the chapter Fractions!
The addition – the «plus calculation»
Addition is also often referred to as «plus calculation» because of its arithmetic sign plus (+). Addition always makes something counted together, so the number will be enlarged.
In the addition become two or more numbers summed up. The result of adding two or more summands is referred to as total.
You can imagine the addition as follows: You have a certain number of an object. In this case you have 2 cookies. Then you go to your grandma and she gives you 3 more biscuits. So now you have a total of 5 cookies. So your addition is:
Figure 1: Addition
summands
total
The summands are numbered from left to right.
The sum denotes the calculation of the 1st summand added to the 2nd summand. The value of the sum is the result of this calculation.
Subtraction – the «minus calculation»
Subtraction is also often referred to as «minus calculation» because of its arithmetic sign minus (-). With subtraction there is always something deducted, so the number will be scaled down.
In the subtraction becomes a number from another number deducted.
The starting number (minute end) is therefore about theirs subtrahends diminished and the result is the Difference.
You can imagine the subtraction as follows:
You have a certain number of an object. In this case you have 5 candies. Your brother loves candy canes, so you give him the two candy canes you have. So now you only have 3 candies left. Your subtraction is:
Figure 2: Subtraction
Multiplication – the «times arithmetic»
Multiplication is because of its operator Times (·) also often referred to as «painting calculation». The best way to imagine multiplication is by using the term «Multiply» – because actually multiplication is also one multiple Addition.
When multiplying counts you something together, so the number will be enlarged.
In the multiplication will the add the same number more than once. The result of multiplying two or more factors will as product designated.
You can imagine multiplication as follows.
You have 3 friends and want to give each of your friends 2 cookies. So you need a total of 6 biscuits. You could calculate the following:
That’s three times 2 biscuits. Accordingly, you can summarize the calculation like this:
Figure 3: Multiplication
The division – the “divided arithmetic”
Division becomes because of its operator Divided (:) also often referred to as «split billing». The best way to imagine division is with the term «Split» – because actually the division is used to check how many times a number can be divided into another number.
In the division a number is divided into other numbers. The result of dividing by dividend and divisor will as quotient designated.
You can imagine the division as follows.
You have 6 cookies and want to divide them between your 3 friends so that everyone gets the same number. So each of your 3 friends gets 2 cookies. So you calculate the following:
Figure 4: Division
Calculate with basic arithmetic
In the following example you will find a few exercises for basic arithmetic operations. Here you can test your knowledge.
Task 1
Calculate the following tasks:
a)
b)
c)
d)
solution
a)
b)
c)
d)
Would you like to calculate more tasks? The tasks were too easy for you? You can find more in the appropriate articles on the individual basic arithmetic operations!
arithmetic laws
In mathematics there are some laws that simplify the calculation of terms, the so-called arithmetic laws. They are a binding calculation rule that you must adhere to when calculating tasks. The three laws of arithmetic that are most commonly used are the commutative law, the associative law, and the distributive law. However, these laws do not apply to all types of calculation.
commutative law
The commutative law is also called the law of permutations. It allows you to swap two numbers in certain calculations. The commutative law only applies to addition and multiplication. When subtracting and dividing, you must not simply mix up the numbers, otherwise the result will change.
Commutative law of addition:
Commutative law of multiplication:
associative law
The associative law will also connection law called. It allows you to connect certain calculations with brackets in certain situations and calculate them first. This allows you to gain arithmetic advantages and calculate complex terms faster and easier. The associative law only applies to addition and multiplication. When subtracting and dividing, you must not simply put brackets and swap them around, otherwise the result will change.
Associative law of addition:
Associative law of multiplication:
distributive law
The distributive law also becomes distribution law called. It allows you to multiply out brackets or factor out factors. This allows you to calculate terms or summarize them clearly.
With the distributive law, a line calculation – i.e. plus or minus – is always connected with a point calculation – times or divided.
Unlike the associative law and commutative law, which both apply to addition and multiplication, the distributive law applies to multiplication and division.
The distributive law is:
Other calculation methods
In addition to the four basic arithmetic operations, there are a few other arithmetic operations that are also considered to be the basis of mathematics. These types of calculations are a bit more advanced. So if you don’t understand all the topics, that’s not bad at all.
The potentiation
When raising to a power, a number x b- is multiplied by itself. x is called the base. b is an exponent and is called an exponent. A potency is therefore nothing more than a product of nothing but the same factors.
Figure 5: Exponentiation
Powers that have a 2 in the exponent also become square numbers.
When raising to a power, there are also the power rules. These are calculation rules that make it easier for you to calculate with powers.
Here is a brief overview of the calculation rules for powers:
Rooting – “extracting the root”
Rooting is the inverse operation of raising to a power. The “normal” root, which is also called the square root, is the inverse of squaring. The third root is then the inverse of raising to the power of 3, the fourth root of raising to the power of 4, and so on.
Under square root is used in mathematics to determine the unknown x in the power equation
Roger that. Solving the equation for x gives:
The root exponent n is the value to which the root value x must be raised to the power to get the radicand a of the root.
Figure 6: Square root
There are also rules when rooting, which must be observed when calculating with roots.
Here is a brief overview of the calculation rules for roots:
Round, guess and rollover
When you hear the three terms rollover, rounds and treasure, you probably imagine almost the same thing at first. However, there are differences and they are also important. You can therefore go through each term individually below.
Round
Sometimes it is not possible or even useful to state the result of a calculation exactly.
Under the Round is to be understood as simplifying numbers or results according to certain rules.
If the digit to be considered is less than or equal to 4, then you round down. If the digit to be considered is greater than or equal to 5, then you round up!
An approximate value is therefore given. This is used to indicate the result in a meaningful way at the end of a calculation.
Estimate
The goal of estimating is to always get as much as possible close to reality are you. In order to be able to estimate as accurately as possible, there are different methods that you can apply.
Would you like to learn more about the methods? You can read all about this in the article “Estimating”.
The principle of estimation describes a approximate Indication of size or quantity through mental processes that prior knowledge and experiences based.
When estimating, you think about what the result could be before you calculate. You often use it when calculating with sizes.