Like four zero equals 24

Division of numbers

Dividing is one of the basic tasks of mathematics, division is the reverse of multiplication. In this article we explain how it works and why you need it.

To introduce an example: Kai has 20 gummy bears and would like to distribute them to his 5 friends. Everyone should receive the same number of gummy bears. To solve this problem you need the division. The calculation method of the problem and the solution is 20: 5 = 4. Kai can give each friend 4 gummy bears. And this is how it works: The ":" is the symbol for the division. The number at the beginning is the dividend, the second number is the divisor. The result of the task is called the quotient. Ultimately, this means:

  • Dividend: Divisor = quotient

Dividing is actually very easy, provided you can multiply. If you still have problems with this, click on the link above. The following examples should make the division easier to understand:

  • 20: 5 = 4, because 4 5 = 20
  • 12: 4 = 3, because 3 4 = 12
  • 10: 2 = 5, because 5 2 = 10
  • 18: 6 = 3, because 3 6 = 18
  • 15: 5 = 3, because 3 5 = 15
  • 24: 6 = 4, because 4 6 = 24


As you can see, you have to look for a number that you multiply by the divisor to get the dividend. If this is not yet entirely clear to you, take another look at the examples. As always, it takes some practice to master this method of mathematics. In any case, do the exercises for this chapter (see links at the end of this article).

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Divisions with rest

The examples just shown all had one thing in common: There was no so-called "rest". To understand this, let's take another small example.

Why is that so? Now actually quite simple: 5 · 4 = 20. And 5 · 5 = 25. The first result would be too small, the second is too big. So you go over and take the first result: 5 · 4 = 20. But to get to 22, the number 2 has to be added. If that doesn't make sense now, it is best to take a look at the next examples.

  • 17: 3 = 5 remainder 2, because 5 3 = 15. Missing 2 until 17.
  • 22: 6 = 3 remainder 4, because 3 6 = 18. Missing 4 until 22.
  • 13: 5 = 2 remainder 3, because 2 · 5 = 10. Missing 3 up to the 13th
  • 27: 4 = 6 remainder 3, because 6 4 = 24. Missing 3 until 27.
  • 31: 5 = 6 remainder 1, because 6 5 = 30. Still missing 1 until 31.
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Peculiarities of the division

Before we go on with the material, I would like to briefly point out a few peculiarities of the division.

  • Division is the reverse of multiplication
  • The division is not commutative: This means that 24: 3 does not produce the same result as 3: 24. The numbers are therefore allowed Not be turned over!
  • If the dividend is zero, the result is always zero. Example: 0 : 25 = 0
  • You must never divide by zero! 25: 0 must not be expected!

Practice exercises, written division

So far we have worked with relatively small dividends (the number at the beginning). Unfortunately, this is not always the case. How to calculate with larger numbers is covered on the following pages. The topic is then called written division. Before you read this, however, you should first complete the exercises for this article.

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