Are you currently dealing with the topic “dot before line” at school and can’t do much with it yet? No issue! Here you will find everything you need to become a pro in point-to-line calculation. Come on, let’s get started!
Meaning of “point before line calculation”
Let’s take a look at what we mean by this initially strange term “dot before line” and how we can apply this principle.
Classification as a calculation law
It is important that you know from the start that the dot-before-dash principle is a Calculation rule is. You can internalize what is meant by calculation laws here:
A Calculation law is a binding calculation rule.
So that means we have to follow these rules so that at the end the correct result comes out.
Calculation rules
Of course, it’s not just the point-before-dash calculation that counts among the calculation rules. There are a total of three different calculation laws and five additional calculation rules.
The calculation laws include the following:
The calculation rules include:
Point before line calculation – definition
You already know that the point-to-line calculation is one of the calculation rules. But what exactly is that and what does this law say?
The dot-before-dash principle states that everyone comes first Point tasks (Multiplication and division must be solved before doing the Line task****n (addition and subtraction) solves.
The dot-before-dash principle represents one Calculation rule which leads to the mathematical correctness of calculations. If you do not comply with these, you will get an incorrect result on your invoice.
So in every term you have to make sure that first the terms to be multiplied or the terms to be divided are calculated. Afterwards, the line tasks, i.e. addition and subtraction, are examined.
If you can’t remember the order very well, here’s a little mnemonic for you: In the alphabet, the letter P also comes before the S. That’s why the following applies: first the dot, then the line!
Point before line calculation – areas of application
You need the point-to-line calculation in several and different areas of application. These are, on the one hand, the basic arithmetic operations, i.e. addition, subtraction, multiplication and division, and then when you calculate with brackets and powers.
But this principle must also be applied to terms or equations!
Point before line calculation – example
Why is that **Point before line-**The invoice actually that important?
In the following example you should see the importance this calculation rule can be illustrated.
Task 1
Lina and Tim are supposed to solve a problem in math class. This is 3+4·10.
Figure 1: Point before line calculation
But now they both have two different results out.
Lina’s score is 70 and Tim’s is 43.
This example shows well that it is wrong or different results can come if we don’t follow the dot-before-dash rule. And so that this doesn’t happen to you too, let’s look at it together now!
Point before line calculation – tasks
You have already seen the example of Tim and Lina above and that one of them is wrong. But who did the math correctly?
You already know how the calculation rule works. First you calculate the multiplication and division problems and then the addition and subtraction problems. But what does that look like in practice? Let’s look at this with an example.
exercise 2
The problem we want to solve is: 10+10:2
1st step: Solve point tasks
In the first step, we take a closer look at the task. You can first ask yourself whether there is even a point problem, i.e. multiplication or division.
If neither occurs, the dot-before-dash law is not relevant to this calculation.
But in our task there is a division. We’ll solve these first.
10+10:2=10+5
Now we have solved the point problem. Since there is no more, we can move on to the next step.
Step 2: Solve the line task
Now you can solve the line tasks. In our case there is only one that needs to be solved.
10+5=15
The “dot before line” calculation rule was successfully applied.
The principle of point-to-line calculation was shown using the example. Can you now answer whether Lina or Tim was right? Try it!
exercise 2
Which of the two has that? right one Result calculated? Justify using an invoice.
Figure 2: Point-to-line calculation
Solution
First we look at our problem again and have a multiplication and an addition.
First you solve it Painting task:
3+4·10=3+40
In the next step you solve it Plus task.
3+40=43
So you can say that Tim calculated the correct result. Lina, on the other hand, calculated from left to right without using the dot-before-dash calculation rule. Therefore, unfortunately it has an incorrect result.
Point before line calculation with brackets
Now you can use the dot-before-dash rule not only in theory, but also in practice**.** But what if there is still a bracket there? What applies then?
If you don’t really know how to remove parentheses, feel free to take a look at our article Resolving parentheses.
Brackets you can practically see her as the “Queen of Calculation Rules and Laws”. This calculation rule always has the top priority and Priority. The means that the bracket must always be resolved first. First then, when there are no more parentheses in the problem, you can use others Calculation laws and rules apply.
But what was that bracket again?
A bracket in a term says that the operation in the bracket first must be carried out.
If you have multiple levels of brackets, always work from the inside out.
Let’s take a look at this using an example:
Task 3
You want to solve the problem 4·(10+5):6.
According to the precedence rules, you have to resolve the bracket first:
4*(10+5):6=4*15:6
That would now be done. Since we now only have dot problems, we can solve the rest of the term by proceeding from left to right.
4·15:6=60:6=60:6=10
The result is 10.
By the way, you can get one for a term in which there are no brackets and the dot-before-dash calculation applies Clamp to help set.
You can always do that as soon as it helps you. The only important thing is that you attach the bracket to the right one and mathematically correct position puts. Otherwise you change it Value of the term.
Here you have an example of it:
Task 4
You want to solve the following task:
4:2+3
What you can do would be one bracket to set the division. This can help you remember the precedence rules and can be particularly beneficial for longer terms with several different operations.
(4:2)+3
Of course you don’t have to do that. It’s just a guide that you can use.
When placing brackets, however, you must not confuse how you place the brackets. Of course, it will only help you if you put it in the right place.
4:(2+3)
If you had put the brackets like this, then you would have ignored the dot-before-dash law and changed the value of the problem.
So always make sure that you follow the calculation rules if you want to use this help.
Point before line calculation rules
There are different ones in mathematics Priority rulesthat you need to consider.
You’ve already gotten to know one of them, and that is that they always use brackets first must be calculated. But what comes next?
The priority rules are as follows:
- Remove brackets
- Dissolve powers
- Dot-before-dash law
That is, as soon as everyone Brackets have been dissolved, they must potencyn can be calculated.
Only when these two operations are out of your term ““disappeared”, you count on that **Point before line-**Law.
We have a great article on the priority rules for you that is a little more detailed than this short section. So if you want to know a little more, you can take a look there.
Point before line calculation – example for solving independently
Can you do the whole thing?apply independently? You can test this in an exercise task here.
Task 5
Solve the following problem using the calculation rules and precedence rules that you have now learned about:
5·(4+6)+25-8:2
Solution
1st step: Remove the brackets
5·(4+6)+25-8:2=5·10+25-8:2
Step 2: Solve point tasks
5·10+25-8:2=50+25-4
3rd step: Solve line tasks
50+25-4=71
The result of this task is 71. Did you figure that out too?
Point before line calculation – the most important thing
- The point-to-line calculation is one of the calculation rules.
- The calculation rules also include the power law, parentheses rule, precedence rules and the root law.
- The law of arithmetic is called the distributive law, the associative law and the commutative law.
- The dot-before-dash principle says that all dot problems must be solved before the line problems are solved.
- Dot problems include multiplication and division.
- The line tasks include addition and subtraction.
- You need the dot-before-dash law to calculate numbers, terms and equations.
- The bracket always has priority and must be released first.
- When all parentheses are resolved, the powers must be resolved. Only then does the dot-before-dash law become relevant.