So, I will start my story with even numbers. Which numbers are even? Any integer that can be divided into two without a remainder is considered even. In addition, even numbers end with a digit in one of the given series: 0, 2, 4, 6, or 8.
For example: -24, 0, 6, 38 - these are all 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 primary grades.
There is another kind of numbers in the vast realm of mathematics - these are odd numbers. Any number that cannot be divided into two without a remainder, and when divided by two, the remainder 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 is a formula with which you can write any odd numbers, 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 pattern. We presented it using the table below, in order to make it easier for you to understand and remember the material.
Operation | Result | Example |
Even + Even | Even | 2 + 4 = 6 |
Even + Odd | Odd | 4 + 3 = 7 |
Odd + Odd | Even | 3 + 5 = 8 |
Even and odd numbers will behave the same if you subtract, rather than summarize them.
Multiplication of even and odd numbers
When multiplying, even and odd numbers behave naturally. You will know in advance whether the result will be even or odd. The table below shows all the possible options for better assimilation of information.
Operation | Result | Example |
Even * Even | Even | 2 * 4 = 8 |
Even Odd | Even | 4 * 3 = 12 |
Odd * Odd | Odd | 3 * 5 = 15 |
Now consider fractional numbers.
Decimal number
Decimals are numbers with a denominator of 10, 100, 1000, and so on, that are written without a denominator. The whole part is separated from the fractional one using a comma.
For example: 3.14; 5.1; 6,789 are all decimal fractions.
With decimal fractions, various mathematical operations can be performed, such as comparison, summation, subtraction, multiplication and division.
If you want to compare two fractions, first equalize the number of decimal places, assigning zeros to one of them, and then, discarding the comma, compare them as integers. Consider this as an example. Compare 5.15 and 5.1. To start, let's equalize the fractions: 5.15 and 5.10. Now we write them as integers: 515 and 510, therefore, the first number is greater than the second, which means 5.15 is greater than 5.1.
If you want to sum two fractions, follow this simple rule: start at the end of the fraction and sum first (for example) hundredths, then tenths, then integers. With this rule, you can easily subtract and multiply decimal fractions.
But you need to divide the fractions as integers, at the end of counting where to put a comma. That is, first divide the integer part, and then - the fractional.
Decimal fractions should also be rounded. To do this, select to which category you want to round the fraction, and replace the corresponding number of digits with zeros. Keep in mind that if the next digit after this digit was in the range from 5 to 9 inclusive, then the last digit that remains is increased by one. If the next digit after this digit was in the range from 1 to 4 inclusive, then the last remaining one is not changed.