In which direction the sign is written more/less or equal: comparison of signs, examples

In which direction is the sign more written, less or equal? Remembering simply.

Content

“Everything is known in comparison” - a phrase that each person hears many times. And indeed, the comparison goes with us through our whole life. At a certain age, children learn to compare themselves with others. Later, these attempts of comparison begin to express themselves in numbers, and mathematical signs contribute to this transition "more less" and "equals".

Read on our website another article on the topic: "Why doesn't the child understand mathematics?". You will learn how to teach a child to understand mathematics.

Over time, many have mathematics, and these designations are also, although they are so useful and easy to use. Read more more.

What does the story say more/less, equal?

Mathematical signs are a compact form of recording expressions conveying various ratios between values. In the first mathematical works (ancient world), according to history, everything was written verbally. For example, " was written not in the form of a symbol «=», and just with the words: 4 equal 4, although even then it became clear that this is completely inconvenient, and besides, everyone has a different handwriting, not always to make out what is written.

Ancient civilizations were quite isolated from each other, so each nation invented their system of recording mathematical expressions. Many works that give modern people knowledge about how in ancient times the same people like us compared and analyzed the world with the help of their original designations have been preserved. As the population grew, the integration and mixing of the peoples, the signs became more and more similar to each other until general designations appeared, including for logical expressions, less and equally. Read further.

Sign "equal": as written, examples

" It is written like this: «=». It looks just like two horizontal lines parallel to each other. It is used when two values \u200b\u200bare quantitatively similar or identical, that is, equal.

For example:

4 + 5 = 9.
The maximum efficiency coefficient \u003d 1.

Sign "more": as written, examples

"More" sign It is written like this: «>». This is a checkmark, which is directed to the wider side to the left side.

Important: The wide end of the icon always indicates a larger number.

The sign means that the number preceding it is more than the next.

Examples:

100 ›50
The number of sick students in the class ›34%
Brown -eyed people make up ›50% of the entire population of the Earth
›70% of the surface of the planet Earth occupies oceans

Additionally: In addition to the sign, there is a sign «>>»which means much more. The second arrow emphasizes that the number to the left of the expression is many times higher than the number on the right. For example, 10000000000 ›› 2.

“More or equal” sign: as written, examples

Sign "more or equal" It is recorded like this: «≥». This designation is a combination of two signs: more and equal. Accordingly, the value to the left of the logical expression may be greater or equal to the value to the right of the logical expression. This sign is written, as is heard, that is, the checkbox directed to the left is first recorded, which corresponds more, and then another stick is attributed from below, symbolizing the sign equally.

For example:

The normal body mass index should be 18.5. This expression can also be read this way: the normal body mass index should be at least 18.5.
Timur has a body mass index more or equal to 19 - ≥ 19.

Another example:

Ulyana came to a flower shop with a desire to make a bouquet of flowers of 3 or more plants of different types - ≥ 3. That is, the number of types of colors in the bouquet 3.

There are also mathematical signs that are often used for recording. Read further.

Sign "Less": which way is written, examples

Sign "Less" It is written like this: «<». This designation is directed in the opposite direction from the sign more. This means that the number is smaller in front of the sign than after it. That is, the sign is smaller than the reverse sign.

Examples:

86 ‹123
In addition to oxygen and nitrogen, the air contains other gases. Their share is ‹1%.

Additionally: As well as in the case of a sign, more, in addition to the symbol, that is, «<», there is «<<»which means much less. For example, the percentage of admission to this university ‹70%.

Sign "Less or equal": as written, examples

Sign "Less or equal" - This is a symbol «≤». It is also the unification of two logical expressions: the sign is smaller and the sign is equal.

Here is a small situation for example:

Maxim came to the clothing store to buy something to himself. He has 5 thousand rubles with him. After walking around the store, the young man, perhaps, will choose something for himself and buy, or he will not like anything. So, as a result, he may remain less than the original or equal to it. The expression can be recorded as follows: the total money is 5000 rubles.

Important: This has been mentioned more than once, but it is worth noting once again that the signs of “› ”and“ ‹” are opposite, like their combinations (more or equal or less or equal, much more and much less). Therefore, expression, for example, using the sign can be written on the contrary, but already changing the sign and numbers in places.

For example:

345 ›42. And vice versa, 42 ‹345.

In addition, the sign “equal” also has its own opposite sign. Oddly enough, this sign is called not equally and is written: «≠». This is just a crossed out of equality icon. Why is it needed? Using this symbol, it is emphasized that the number on the left is not equal to the right. It does not matter what the ratios are these numbers: the first larger than the second or vice versa. The fact that they are not equal is important.

For example:

76 ≠ 67. It is clear that 76 is more than 67, but in this case it is unprincipled.

A few more useful information below. Read further.

Icon "approximately" ("approximately"): as it is written, examples

Icon "about" It is written like this: «≈». It looks like a sign equally, but instead of straight lines, wavy ones are used. This sign is used when the difference between the two numbers can not be taken into account, because it is too small or insignificant.

For example:

The force of gravity acts on all humanity, it is because of it that people do not fly into outer space from the Earth. At the same time, this gravity depends on the acceleration of a free fall equal to 9.8 meters per second in a square. But at the school to simplify calculations and due to a slight difference as a result of calculations, acceleration of free fall is taken 10 meters per second in a square. That is, we can say that 9.8 meters per second ≈ 10 meters per second.

The “approximately equal” sign is used when the number is rounded to a certain number of characters. For example, from a school bench, everyone knows the number of PI - a constant with an infinite number of signs after aim. Usually this number is rounded to two signs after a decimal. That is, you can write down that PI ≈ 3.14.

Interesting: Often the sign “approximately equal” is used in solving problems for calculating the probability of any event.

How to remember writing signs?

The methods below are suitable for children who only learn to operate with mathematical signs. These methods are presented in an easy game form. So, how to remember the spelling of signs? Here are the tips:

The first method is a hungry crocodile or a hungry bird (as you like more). The animal always looks and spreads the mouth or beam in the direction where there is more food. For example, there are numbers 65 and 38. To make it even more clear, we can say that there are 65 and 38 worms or fish. A crocodile or a bird will look where there is more food. Based on this conclusion, a sign is placed, and the expression is obtained: 65 ›38.

It is difficult for young children to sit down and pour over the textbooks, so it is excellent if the process of understanding mathematical signs is associated with everyday life. This will help the second method. From the thumb and forefinger of the left hand (or index and middle, as conveniently), a sign is made less, and from the same fingers of the right hand - the sign is larger. Objects are laid out, and manual symbols help compare their quantities. This is an interactive method that can be used when walking, at home for meals and in other places.

You can draw points. Suppose there are numbers 25 and 89. Two points (as a single sign) will be drawn in a larger number, and one point is next to a smaller number. After that, all three points are connected, and, in this case, a sign is less.

In addition to these most basic methods, there are others that allow you to master the material. You can develop your own strategy, but most often, without even using these methods, the child begins to understand the topic with experience. In general, it is not difficult to master the skill of comparison, since instinctively almost every person understands how the process of comparison occurs.

Equality and inequality: classification, comparison of signs

After meeting with signs, it is worth introducing the concepts of equality and inequality.

Equality - This is when one is like another. That is, between the two parts of the expression, one can put an equal sign (\u003d). For example: 15 * 2 \u003d 30 is equality.
In contrast, equality is inequality. Accordingly, inequality is when one quantitatively is not like another. For example: 34 ›12 is inequality.

Classification of inequalities and comparison of signs:

Strict inequalities. This group includes expressions that contain signs «>» and «<».
Nesting inequalities. This group includes comparisons with the help of non -thorough symbols «≥» and «≤». They are nested because they allow the possibility of equality. A simple example will help to understand the difference between strict and non -thorough inequalities: 45 ›21and 45 ≥ 21 - Both expressions are true, because 45 are more than 21, but 21 ›21 and 21 ≥ 21 - The first inequality is incorrect, because 21 no more than 21, and in the second case saves an equal sign.
Other. These are inequalities that contain «≠», «≪», «≫».

Additionally: Sometimes a certain number should be compared, for example, with the other two. Then you can use double inequality. For example, 12 ‹57 and 57‹ 90 can be recorded as follows: 12 ‹57‹ 90. Such expressions are read from the middle, that is, 57 more than 12, but less than 90.

Simplification of work with inequalities

This article considers the simplest examples of inequalities for a visual understanding of the topic of using signs of comparison. But sometimes you have to face options, for example, with systems of inequalities or with letter expressions, where you need to find the meaning of unknown terms. Therefore, when working with expressions, you should adhere to some basic rules.

Here are a few such instructions:

With multiplication of inequality by a positive number, the sign of inequality does not change, and when multiplying by negative, it turns into the opposite. That is, > passes to <. The most common example: - 1 ‹30. Multiply by -1. Then -1 moves to 1, 30 -30, and the sign changes less. 1 ›-30. Everything is true, the negative number is less positive. Sometimes this rule is forgotten, so it is worth avoiding multiplication by a negative number.
Sometimes you can erect both parts of the inequality in a square. But this can be done only if both parts are positive, otherwise you can get an incorrect answer.
It is better not to share or multiply inequality by unknown variables. In this case, there is a possibility of losing the roots - solutions of inequality.
The inequality must be solved gradually, simplifying it with every step.
It is forbidden to extract a square root from inequalities.

These rules will avoid mistakes and gradually come to the correct answer.

How to put signs of comparisons on a computer?

The sign “equal” on the computer keyboard is located above all the letters at the end of the number of numbers on the key along with the sign “plus”. To print «=», You just need to click on this button. Here's how to put signs of comparisons:

Signs "more" and "less" They are located on the keys with the letters Yu and B, respectively. To print them, you need to switch to English, pinch the key Shift And press the desired letter.
Signs "much less" and "a lot more" They are printed by double pressing the corresponding letter.
For signs "more or equal" and "less or equal" There are no special buttons. But you can just first write a sign more or less, and then attribute the equal sign. And it will turn out either >=or <=.

The technology of writing a sign is not unequal from programming languages. Therefore, you can write ‹›,! \u003d Or just write in words "not equal". In text editors and other programs there is usually built -in tools that allows you to write these signs as you want, including in a standard form. Therefore, you can choose any option.

So, comparison signs are widely used in recording mathematical expressions. They are very convenient, compact, and their use is clear at the household level even to the child. It was not bad to learn how to operate on them and find the right decision if you follow valuable advice when working with them. It is important for each person to get acquainted with symbols more, less and equally and a little closer to the unknown science of mathematics.