Even and odd numbers. The notion of a decimal number

So, I'll start my story with even numbers. Which numbers are even? Any integer that can be divided into two without remainder is considered even. In addition, even numbers end in one of the given numbers: 0, 2, 4, 6 or 8.

For example: -24, 0, 6, 38 - all these are even numbers.

M = 2k is the general formula for writing even numbers, where k is an integer. This formula may be needed to solve many problems or equations in the initial classes.

There is another kind of numbers in the vast realm of mathematics - these are odd numbers. Any number that can not be divided into two without remainder, and when divided by two is equal to one, is called odd. Any of them ends with one of these numbers: 1, 3, 5, 7 or 9.

Example of odd numbers: 3, 1, 7 and 35.

N = 2k + 1 - a formula by means of which you can write any odd number, where k is an integer.

Addition and subtraction of even and odd numbers

In the addition (or subtraction) of even and odd numbers there is some regularity. We presented it with the help of the table below, in order to make it easier for you to understand and remember the material.

Even and odd numbers will behave the same if you subtract, not sum them.

Multiplication of even and odd numbers

When multiplying, even and odd numbers behave naturally. You will know in advance whether the result is odd or even. The table below shows all possible options for better assimilation of information.

Now consider fractional numbers.

Decimal notation of a number

Decimal fractions are numbers with a denominator of 10, 100, 1000, and so on, which are written without a denominator. The whole part is separated from the fractional by a comma.

For example: 3.14; 5.1; 6,789 are all decimals.

With decimal fractions, you can perform various mathematical actions, such as comparison, summation, subtraction, multiplication and division.

If you want to equalize two fractions, first equate the number of decimal places by assigning zeros to one of them, and then, having discarded the comma, compare them as integers. Consider this for an example. Compare 5.15 and 5.1. To begin with, we equate the fractions: 5,15 and 5,10. Now let's write them as integers: 515 and 510, therefore, the first number is greater than the second, then 5.15 is more than 5.1.

If you want to add two fractions, follow this simple rule: start at the end of the fraction and sum first (for example) the hundredth, then the tenth, then the whole. With this rule, you can easily subtract and multiply decimals.

But you need to divide the fractions as integers, counting down at the end where you need to put a comma. That is, first, divide the whole part, and then - the fractional part.

Also, decimals should be rounded. To do this, select to which bit you want to round the fraction, and replace the corresponding number of digits with zeros. Keep in mind, if the next digit behind this digit was between 5 and 9 inclusive, then the last digit that remained is increased by one. If the figure following this digit lies in the range from 1 to 4 inclusive, the last remaining one does not change.