Example of dividing a number by a number. Table of division

Despite the fact that mathematics seems to most people a difficult science, this is far from the case. Many mathematical operations are fairly easy to understand, especially if you know the rules and formulas. So, knowing the multiplication table, you can quickly multiply in the mind large numbers. The main thing is to train constantly and not to forget the multiplication rules. The same can be said about division.

Let's analyze the division of integers, fractional and negative. Let us recall the basic rules, methods and methods.

Operation of division

Let's start, perhaps, with the very definition and name of the numbers that are involved in this operation. This will greatly facilitate the further presentation and perception of information.

Division is one of four basic mathematical operations. The study of it begins in primary school. It is then that children are shown the first example of dividing a number by a number, explaining the rules.

Two numbers are involved in the operation: dividend and divisor. The first is the number that divides, the second divides. The result of division is the quotient.

There are several notations for writing this operation: ":", "/" and the horizontal bar is a record in the form of a fraction when the dividend is at the top, and below is a divider.

rules

When studying a mathematical operation, the teacher is obliged to introduce the students to the basic rules that should be known. True, they are not always remembered as well as we would like. That's why we decided to refresh your memory four fundamental rules.

The basic rules of dividing numbers, which are worth remembering always:

1. You can not divide by zero. This rule should be remembered first.

2. You can divide zero by any number, but in the end it will always be zero.

3. If the number is divided by one, we get the same number.

4. If the number is divided into itself, we get a unit.

As you can see, the rules are fairly simple and easy to remember. Although some may forget such a simple rule as the impossibility of dividing by zero, or confuse it with dividing zero by a number.

Signs of divisibility by a number

One of the most useful rules is a criterion by which the possibility of dividing a natural number into another without a remainder is determined. So, we distinguish the divisibility signs by 2, 3, 5, 6, 9, 10. Let's consider them in more detail. They make it much easier to perform operations on numbers. Also, for each rule, we give an example of dividing a number by a number.

These rules-signs are widely used by mathematicians.

The divisibility criterion is 2

The most easy to remember feature. The number that ends in an even number (2, 4, 6, 8) or 0, is always divisible by two integers. Quite simple to remember and use. So, the number 236 ends in an even number, and therefore, is divided into two completely.

We check: 236: 2 = 118. Indeed, 236 is divisible by 2 without remainder.

This rule is best known not only to adults, but also to children.

The divisibility criterion by 3

How to correctly divide numbers by 3? Remember the following rule.

The number is divided by 3 whole if the sum of its digits is a multiple of three. For example, take the number 381. The sum of all the digits will be 12. This number is a multiple of three, which means that it is divisible by 3 without a remainder.

Also check this example. 381: 3 = 127, then all is true.

The divisibility of numbers on 5

Here, too, everything is simple. To divide by 5 without a remainder, you can only numbers that end in 5 or 0. For example, take numbers such as 705 or 800. The first one ends at 5, the second - at zero, hence they are both divided by 5. This one From the simplest rules, which makes it possible to quickly divide by a single-valued number 5.

Let's check this feature on such examples: 405: 5 = 81; 600: 5 = 120. As you can see, the sign works.

Severability by 6

If you want to know if the number is divided by 6, you first need to find out whether it divides by 2, and then - by 3. If so, the number can be divided without divide by 6. For example, the number 216 is divided by 2 , Since it ends with an even number, and by 3, since the sum of the digits is 9.

Let's check: 216: 6 = 36. The example shows that this attribute is valid.

Severability by 9

Let's talk also about how to divide numbers by 9. On this number are divided those natural numbers whose sum of digits is multiples of 9. Similarly to the rule of division by 3. For example, the number 918. Add all the digits and get 18 - a number that is a multiple of 9. Hence, it is divisible by 9 without remainder.

Let's solve this example for verification: 918: 9 = 102.

Divisibility by 10

The last sign that is worth knowing. Only those numbers that end in 0 divide by 10. This pattern is quite simple and easy to remember. So, 500: 10 = 50.

That's all the main signs. Remembering them, you can make your life easier. Of course, there are other numbers for which there are signs of divisibility, but we have identified only the main ones.

Table of division

In mathematics there is not only a multiplication table, but also a division table. Learning it, you can easily perform operations. In fact, the division table is a multiplication table in reverse. It is not difficult to compose it independently. To do this, rewrite each row from the multiplication table in this way:

1. Put the product of the number in the first place.

2. We put the division sign and write the second factor from the table.

3. After the equal sign we write the first factor.

For example, take the following line from the multiplication table: 2 * 3 = 6. Now rewrite it according to the algorithm and get: 6 ÷ 3 = 2.

Quite often, children are asked to create a table on their own, thus developing their memory and attention.

If you do not have time to write it, you can use the information provided in the article.

Types of division

Let's talk a little about the types of division.

To begin with, we can distinguish the division of integers and fractional ones. In the first case, you can talk about operations with integers and decimals, and in the second - only on fractional numbers. In this case, fractional may be a dividend or divisor, or both. This division is due to the fact that operations on fractions differ from operations with integers.

Next, we will discuss the division of fractions in more detail.

Based on the numbers that participate in the operation, we can distinguish two types of division: single-valued and multivalued. The simplest is the division into a single-valued number. Here you do not need to perform cumbersome calculations. In addition, the division table can well help. To divide the same into others - two-, three-digit numbers - is heavier.

Let's consider examples for these types of division:

14: 7 = 2 (division by a single digit).

240: 12 = 20 (dividing by a two-digit number).

45387: 123 = 369 (division by a three-digit number).

The latter can be divided into division, in which positive and negative numbers participate. When working with the latter, you should know the rules by which the result is assigned a positive or negative value.

When dividing numbers with different signs (dividend is a positive number, a divisor is a negative number, or vice versa), we get a negative number. When dividing numbers with one sign (and dividend, and divisor - positive or vice versa) - we get a positive number.

Consider the following examples for clarity:

21: (-7) = -3

-36: 6 = (-6)

-48: (-8) = 6.

Fission of fractions

So, we have analyzed the basic rules, gave an example of dividing a number by a number, now let's talk about how to correctly perform the same operations with fractions.

Despite the fact that the division of fractions at first seems rather difficult, in reality it is not so difficult to work with them. The division of the fraction is almost the same as multiplication, but with one difference.

In order to separate the fraction, we must first multiply the numerator of the divisor by the denominator of the divisor and fix the result obtained in the form of a numerator of the quotient. Then multiply the divisible denominator by the numerator of the divisor and write the result as the denominator of the quotient.

You can make it easier. Rewrite the fraction of the divisor by swapping the numerator with the denominator, and then multiply the numbers obtained.

For example, we split two fractions: 4/5: 3/9. First we flip the divisor, we get 9/3. Now multiply the fractions: 4/5 * 9/3 = 36/15.

As you can see, everything is quite easy and not more difficult than dividing by a single digit. Examples of actions with fractions are solved simply, if you do not forget this rule.

conclusions

Division is one of the mathematical operations that every child is studying in primary school. There are certain rules that you should know, techniques that facilitate the execution of this operation. The division happens with the remainder and without, there is a division of negative and fractional numbers.

Remember the features of this mathematical operation is quite easy. We have discussed the most important points, examined not one example of dividing a number by a number, even talked about how to work with fractional numbers.

If you want to improve your knowledge of mathematics, we advise you to remember these simple rules. In addition, we can advise you to develop memory and counting skills in the mind by performing mathematical dictations or simply trying to calculate orally the quotient of two random numbers. Believe me, these skills will never be superfluous.