What is 3 + 3 + 6 + 2

Dot before line / dot calculation before line calculation

We will deal with the rule dot-to-dot in this article. The following content is offered:

  • A Explanationwhat is meant by point before line.
  • Examples with numbers for better understanding.
  • tasks or. Exercises so that you can practice the point calculation yourself before the line calculation.
  • A Videowhich explains the point before the line.
  • A Question and answer area with typical questions on this topic.

We are about to deal with a very important rule in mathematics: the point calculation before line calculation. If you have problems understanding the following sections, you may lack a few prior knowledge. In this case, please read the following articles first: arithmetic up to 100, multiply / take and divide / divide. In further articles we will look at other arithmetic rules for powers and brackets (I'll link them here as soon as they are available).

Explanation: Point calculation before line calculation

Four different types of arithmetic are discussed in elementary school:

  • Addition / plus calculate "+"
  • Subtraction / minus calculate "-"
  • Multiplication / count times "·"
  • Division / divide ":"

Now it can of course happen with a task that, for example, an addition (+) and a division (:) have to be carried out. There is a rule for this case: dot before line.

Note:

Means point before line:

  • Multiplication and division are carried out first.
  • Addition and subtraction are then carried out.

Let's take a closer look at this for a few tasks:

  • 4 + 3 2 = 4 + 6 = 10 correct
  • 4 + 3 x 2 = 7 x 2 = 14 wrong
  • 6 + 4: 2 = 6 + 2 = 8 correct
  • 6 + 4: 2 = 10: 2 = 5 wrong

If you are bothered by the fact that a multiplication or division is calculated first, then you have to put a bracket. What is in the brackets is calculated first. And one more thing: if, for example, there are only additions or only multiplications, the calculation is simply from left to right. A statement about the priorities is still missing to make the list complete (whereby potencies are not yet dealt with in elementary school). The calculation is done in the following order:

Note:
  • Brackets
  • Potencies
  • Point calculation (multiplication and division)
  • Line calculation (addition and subtraction)
  • Left to right

We will look at and in the next section corresponding examples with brackets.

Display:

Examples point before line

In this section, some examples of point calculation before line calculation are presented. We start with examples where "only" addition (+), subtraction (-), multiplication (·) and division (:) occur at first. Then we look at examples with brackets.

example 1:

  • 2 + 6 : 3 = ____
  • 2 + 2 = 4

We first calculate the division 6: 3 and then add 2 + 2 = 4.

Example 2:

  • 3 · 3 + 2 · 5 = ____
  • 9 + 10 = 19

First we calculate the multiplications (·). These are 3 · 3 = 9 and 2 · 5 = 10. Then we add (+) this with 9 + 10 = 19

Example 3:

  • 4 · 2 · 2 + 4 · 2 + 3 = ____
  • 8 · 2 + 4 · 2 + 3 = ____
  • 16 + 8 + 3 = ____
  • 24 + 3 = 27

Here, too, point before line applies. Therefore the multiplications (·) have priority here. Since there are several multiplications (·), the process continues from left to right. The multiplications (·) are followed by the additions (+); here too, work is carried out from left to right.

Example 4:

  • 6 : 3 · 2 + 6 - 3 = ___
  • 2 · 2 + 6 - 3 = ___
  • 4 + 6 - 3 = ____
  • 10 - 3 = 7

In this example we have division (:), multiplication (·), addition (+) and subtraction (-). Following the dot before line rule, we start with multiplication (·) and division (:). Whereby we proceed from left to right here. Therefore first 6: 3 = 2 (in the line below). In the next line there is another multiplication by 2 · 2. This leads us to line 4 + 6 - 3 = ____. Now we go from left to right, so first 4 + 6 = 10 and then -3.

Example 5:

  • (3 + 4) · 5 + 2 · 3 = ___
  • 7 · 5 + 2 · 3 = ___
  • 35 + 2 · 3 = ___
  • 35 + 6 = 41

This was another example with a bracket. A bracket is calculated first. Therefore 3 + 4 = 7 first. Then we have to perform two multiplications (·). You can do both at the same time or one after the other as calculated here. At the end there is still the addition (+) with 35 + 6 = 41.

Exercises / exercises on point before line

Show:

Videos to the point before the line

Point to line as a video

This video shows examples of point calculation before line calculation.


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Point before the line: questions and answers

In this section we look at typical questions around point calculation before line calculation.


Q: Are there any books or software that deal with point calculation before line calculation?

A: Yes there is. For example, basic knowledge of elementary school mathematics from Duden-Verlag.

Q: Is there a saying or phrase to memorize point by line?

A: There are even several sayings:

  • Point calculation is more important than line calculation, the brackets are above everything.
  • KlaPoPuS (brackets before potency before dot before dash).
  • The brackets say: “I'll come first!” Also remember: “Always point before line”. And what is not yet there for arithmetic, you write down unchanged.