By the same rules. “The interaction of wounds with the new ministry will follow the same rules as with Fano. Academician Valery Kozlov about the present and future of the Russian Academy of Sciences

Spelling of the words "also" and "similarly" depends on what part of speech we have. The rule is this: the union is written together, the adverb with the particle is written separately.

Separate spelling

It is correct to write “same” if “so” is an adverb and “same” is a particle. They are used to compare objects.

She strove to be like a friend in everything: she painted her lips just as brightly, spun in front of the mirror for a long time and drawled her words in a mannered way.
It was April, and the snow was still falling in flakes outside.

Clue: try to insert after "the same" the phrase "like".

Same as me She hates cream.
Animals just like people who know how to love.

Consolidated spelling

"Also" is a union that was formed by merging an adverb with a particle. It needs to be written fluently.

The artist was nervous before the performance, there was also excitement in the hall.
The dollar, like the euro, also continues to grow rapidly.

Clue: the union "also" can be replaced by another union - "and".

The artist was nervous before the performance, and there was excitement in the hall.
And The dollar, like the euro, continues to grow rapidly.

Ask a question

The spelling of the word also depends on the question. To the adverb with a particle, you can ask the question “how?”. But such a number will not work with the union, since this is not an independent part of speech.

Dropping a Particle

Consider this proposal:

My day went the same as yesterday.

Keeping in mind that the particle "same" gives only the effect of amplification, let's try to discard it. What did we get?

My day went the same as yesterday.

The sentence was absolutely not affected, which means that in this case, “the same” should be written separately.

Now another example:

My friend loves sushi and rolls, I also love Japanese food.

Let's try again to drop the same. And here's what we get:

My friend loves sushi and rolls, I love Japanese food so much.

There is clearly something wrong with the offer. No wonder, because in this case we did not discard the “same” particle, but tore off a piece of the union! Remember: in such a situation, our word is spelled together.

At the same time, if you replace also with the same, the meaning will not change. This is a compelling reason for continuous writing.

My friend loves sushi and rolls, I also love Japanese food.

Synonyms

The following synonyms correspond to the adverb with the particle “same”:

in the same way
similar,
like,
as well as,
as well as,
like,
Seems like,
equally
similarly.

The union "also" can be replaced by the words:

too,
equally,
at the same time,
in the same way.

Remember that a well-chosen synonym can solve a number of spelling problems.

Hard case

There are, however, difficult situations when the meaning can be determined only by a broad context, which includes several sentences, or by intonation.

The girl was also very beautiful.(This girl was as beautiful as the other.)
He was also determined.(And he was determined.)

Punctuation

Our words have their own punctuation features when written in writing. For example, after an adverb with the particle "same" the word "like" often follows. We are used to the fact that a comma is usually placed before "how". But this is not always fair. Let's look at examples:

I, like most students, count on a scholarship.

(= I, like most students, count.)

I, like most students, count on a scholarship.

(= I count in the same way, to the same extent.)

We hope our article helped you understand the difference between the conjunction "also" and the adverb with the particle "same". Always pay attention to the context - it will help resolve any difficulties. And also do not forget to be guided by the rules and tips. And for dessert - an instructive linguistic tale.

On the power of friendship

Once upon a time there was an adverb So and a particle Zhe. So she always shunned Zhe, because she considered herself superior to her.

- I am an independent word! And who is she? said Tak, turning up his nose.

But she silently endured insults and sometimes even left the offer so as not to be next to the arrogant Tak. Perhaps they would never have become friends, if not for one case.

Union And once fell ill. So much so that he could not get out of bed and take his rightful place in the sentence: "And friendship is important to us." And after all, as luck would have it, all his closest friends left - there was no one to replace the unfortunate one! Then the words decided to gather advice.

- How can we be! If I does not get into a sentence, it will lose its meaning!

- Sorry poor thing. But we can all lose our jobs.

And all the words quietly wept. Suddenly, Tak came up to Zhe and, lowering his head, whispered:

- Forgive me. Let's be friends. I know we can help.

Zha smiled affably, held out her hand to Tak, and said:

Friendship is also important to us.

And then a miracle happened: the proposal made sense! The words raised astonished eyes to their former enemies and beamed. They are saved!

Since then, Tak and Zhe have become such friends that you can’t spill water. And if they ended up in a proposal separately, they still supported each other.

Great company. How to Become Your Dream Employer Robin Jennifer

Chapter Four Justice "Everyone plays by the same rules"

Chapter Four

Justice

"Everyone plays by the same rules"

Those who succeed here do not believe that all people are the same. In our company, people are very diverse - they come from different countries, have different personal histories, different sexual orientations. They don't try to conform to any particular image. If you want to succeed here, you will have to deal with all these differences without shying away from them. Those who can behave in this way (and this is the majority of our employees) succeed because they are able to build business relationships with those who are arranged completely differently. And not just to build relationships, but to enjoy interacting with people who are completely different from each other.

Google employee

Trust requires reliability. Trust requires respect. However, even if you've read Chapters 2 and 3 and gave yourself and your company high marks for trustworthiness and respect, it's too early for you to put a sure checkmark in the credibility box until you figure out where your employees' perceptions of fairness fit in. Do employees feel, when it comes to decisions that affect them, that the rules of the game are the same for everyone? When employees have a sense of fairness, they feel that they are treated fairly and equally, and that their gender, age, nationality, and sexual orientation do not influence their performance evaluation. Despite the elegance of the quotation that opens this chapter, achieving a strong sense of justice is by no means easy. Managing this feeling, which serves as the third and final building block of trust, is perhaps the most difficult.

To understand how much justice can require, just look at the bar set by great companies-employers. For each item in the Confidence Index survey we talked about in Chapter 1, the Great Place to Work Institute annually calculates benchmarks. At top 100 companies, typically about 90% of employees say that their company is often or almost always an outstanding place to work, so for most survey items, the benchmark percentages fall in the late ninth or early tenth decade. However, in those items that are related to the assessment of fairness, the control values are noticeably lower even in the best companies. The situation when the average percentage score for these items of the survey from year to year falls into the end of the sixth - the beginning of the seventh decade, is not something out of the ordinary. This indicates that even in outstanding companies, many employees do not have a strong and consistent sense of justice in what is happening, although the assessment of the majority still indicates the health of the company.

Why is it so difficult to build uniform rules of the game for all? One of the reasons lies in the very nature of the sense of justice. The fact is that the perception of fairness is largely determined by the decision-making processes that the leaders of the company adhere to. Sometimes these processes take place in plain sight, as in the Whole Foods Market, where current team members are invited to vote for newcomers after they have been with the company for several weeks. This transparency has immediate benefits, providing a sort of filter that discourages the hiring of unqualified employees. In addition, however, putting hiring decisions to a vote allows current team members to be involved in the decision-making process, and this reinforces the collective sense of fairness in the decisions made.

In other cases, decisions are made in a less transparent manner. Leaders are constantly forced to deal with difficult dilemmas and try to take into account many parameters that cannot always be made public. And even when all the factors can to announce, the decision often has to be made in a very short time, which means that there is no way to explain it to all employees in advance and in detail. Therefore, no matter what legal obligations, procedures and values a company may be guided by, a sense of fairness essentially comes down to the belief of employees that managers are able to make decisions in accordance with the principle of equality - a belief that does not depend on the employee's knowledge of the reasons for a particular solutions.

Managers who are coached by us often feel in a situation of “correction 22”: trust in a leader depends on how fair his decisions are, but no one believes in the fairness of decisions until the leader has earned trust. This is where chapters 2 and 3 come in. Particularly when you discuss compensation, benefits, promotions, and other life-sustaining matters for company employees, you use other ways to build trust. A sense of justice is based on a sense of consistency in the actions of the leader (an integral part of reliability) and care on his part (an integral part of respect). Obviously, this is a complex perception that is difficult to influence.

The challenges of creating a sense of fairness are not all: leaders must also be clear that fair attitude towards employees does not mean the same relations. If this were not the case, the job of a manager would be much easier. However, in reality, decisions must be made in the interests of the organization as a whole, while taking into account the interests of individuals, which significantly complicates the task. As an example, consider Robert W. Baird & Co's employee health insurance rule: each employee pays a share of the premium based on their income level, meaning higher-paid employees pay more. On average, a company pays about 80% of health insurance premiums, but the payout percentage can vary from 99% to 63% from employee to employee. In each case, this amount depends on the health plan, the degree of coverage and the salary range of the employee. The company introduced this rule in order to allocate health insurance costs according to the ability of each employee to pay. Although this rule makes life difficult from an administrative standpoint, it reinforces the feeling among employees that the company is doing the right thing.

Finding a balance between caring for individual employees and the good of the entire organization is a task that is somewhat difficult, but somewhat simple. At the Great Place to Work conference in 2009, Tony Parella, CEO of Shared Technologies, proclaimed a very simple principle: “To hell with books!”. As part of his leadership development programs, Parella tells managers that they must put in whatever extra effort they can for outstanding employees, no matter what HR leaders say about it. If employees care about the good of the company, Parella believes, the company should look after their good. The Human Resources Manual can serve as a starting point, but it should not force the company into any box when it comes to fairness to valuable employees.

Creating an atmosphere of fairness is difficult, but equally important, both for the work environment and ultimately for the success of the organization. A sense of the fairness of the decisions made increases the company's resilience in times of change and doubt, even when changes occur so quickly that there is no way to explain every decision in detail to employees. A sense of fairness contributes to the strengthening of camaraderie, as in such an environment politics and conversations behind closed doors cease to influence decisions. When the work environment is fair, undercover competition disappears and only healthy competition remains. When people are treated fairly, they feel like equal members of the organization, and this increases their commitment and willingness to put in extra effort to achieve the goals of the organization. Finally, the reputation of a fair company helps to expand and diversify the pool of potential employees.

While benchmarks for fairness remain relatively low and are associated with the least favorable aspects of the employee experience, the performance is encouraging: since 1998, these numbers have improved dramatically, with the greatest improvement in the sense of fairness. The most powerful increase is noted in indicators indicating the absence of politicking, sitting around and talking behind one's back: here, the control values increased by almost 20 points.

There's more good news: Great employers continue to make tremendous efforts in this area, from company-wide disclosure of salaries to the introduction of a formal appeals process for when employees have any disagreement with the decisions made. These and other examples clearly show that the sense of justice is divided into three components, each of which we will discuss in this chapter.

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Secured transactions are invalidated according to the same rules as ordinary transactions, but there are some peculiarities. Lawyers explained why it is now more difficult to challenge transactions than before, what their bankruptcy risks are, and when a violation of corporate procedure will not help invalidate the contract. We also give an example of an arbitration case, when the security was declared invalid due to misrepresentation.

Security measures, such as collateral or guarantees, are used for real estate contracts, large loans, and other significant transactions. They should give the lender confidence in a “plan B” in case the counterparty is in trouble. However, unscrupulous debtors are trying in every possible way to challenge the security transactions in order to deprive the creditor of one of the fastest and easiest ways to repay the debt, says lawyer Natalya Lopatina.

Why is it harder to argue?

Security transactions are generally recognized as invalid according to the same rules as ordinary transactions. The general grounds for contesting from the Civil Code, such as sham, pretense, abuse of authority, etc., are now used much less frequently, Dmitry Konstantinov from a law firm shares his observations. The lawyer explains this by the effectiveness of special rules - on insolvency or corporate ones. In addition, in 2013, a new version of Art. 166 of the Civil Code on voidable and void transactions, which significantly limited the possibilities of challenging them, continues Yury Pustovit, managing partner of AB.

Mortgages and guarantees are challenged no less than before, but the courts have begun to refuse more often.

Yuriy Pustovit, Managing Partner of AB Yug

In particular, Art. 166 consolidated the principle of estoppel: a person cannot seek to have a transaction recognized as invalid if previously it behaved as if it were valid. In addition, earlier, “any interested persons” could demand the application of the consequences of the invalidity of the transaction, but now it is the parties or other persons specified in the law.

The practice has also stabilized on such a basis for contesting the guarantee of individuals as the lack of consent of the spouse. 10 years ago, this was one of the most popular ways to cancel security, recalls Dimitri Nurzhinsky from. But on July 12, 2012, the Plenum of the Supreme Arbitration Court issued a resolution in which it explained that the guarantor was personally responsible - and, therefore, the absence of the consent of the spouse does not indicate the invalidity of the transaction. This position concerned individual entrepreneurs, but in 2013 he applied the same approach in the case of ordinary citizens (case No. 18-KG13-27), says Nurzhinsky. Despite the unequivocal decision and established practice, banks are reinsured and continue to require the notarized consent of the spouse for suretyship, the lawyer shares.

Registers also help to stabilize the turnover. The pledge is terminated if the pledged object was acquired by a bona fide buyer who was not aware of the encumbrance (part 2, clause 1, article 352 of the Civil Code). Real estate is “protected” from this by a rights registration system, but such schemes are common in the car sales market, Nurzhinsky says. The courts, according to him, were not always ready to apply Art. 352, therefore, in 2014, the legislator introduced a system for registering a pledge of movable things with a notary (Article 339.1 of the Civil Code).

Bankruptcy and corporate disputes

In bankruptcy, it is much easier to invalidate a transaction. A mortgage or surety may be challenged on the grounds that it caused harm to creditors or was made in favor of one of them. If it is confirmed in court that the creditor knew or should have known about the pre-bankruptcy state of the debtor, the transaction is declared invalid.

Contracts concluded within three years prior to the initiation of insolvency proceedings may be at risk of bankruptcy, warns Alexander Anchugov, head of the legal support department for development projects.

Other grounds for contestation are corporate. Major transactions or related party transactions must be approved within the firm in accordance with its documents and law. If the procedure is violated, then the contract may be declared invalid, provided that the creditor knew or could have known about the violation. Therefore, it is important for him to check the corporate structure of the counterparty in advance and make sure that the transaction is approved in accordance with all the rules. This is a common ground for contesting a pledge, although it may turn out during the trial that the contract was actually approved or the statute of limitations has passed, says legal practice consultant Georgy Murzakaev. You can defend yourself against such claims, including by pointing out the bad faith of the opponent. Recently, the importance of the institution of abuse of rights has increased, Murzakaev draws attention. He gives examples of decisions that "stood" at the level of the Economic Board of the Armed Forces:

In case No. A58-8432 / 2014, the AYAM Management Company disputed the mortgage of real estate, which was mortgaged under the company’s loan by the controlled Association of Builders of the Amur-Yakutskaya Mainline. As stated in the lawsuit, the pledge was not approved by the general meeting of participants. Although corporate approval rules were violated, the courts refused to invalidate the deal. They considered that the main goal was to free the mortgagor, who had real assets, from the mortgage, which means that the company abused the right to challenge the transaction. In addition, the majority participant approved the mortgage after all.
In case No. A40-186355/2015, Oil Depot No. 1 tried to invalidate a mortgage that was approved at an extraordinary general meeting of participants, but should have been at the board of directors. But the courts rejected the claims. They noted that the necessary quorum had been reached. And the lawsuit was filed in order to evade the execution of the transaction and cause losses to the bank.

Other grounds for contestation and minimization of risks

Transactions may also be challenged on other grounds known to every lawyer. For example, the power of attorney did not give the authority to enter into just such an agreement, or it turned out that the subject of the mortgage does not actually belong to the mortgagee (for example, the contract for the sale of a building was declared invalid). People often try to challenge the building's mortgage on the grounds that the site under it is not mortgaged, says Pustovit from AB Yug. According to the lawyer, the courts tend to dismiss such claims: they explain that registration of rights to land depends only on the pledger, and the pledgee has nothing to do with it.

There are also relatively rare ways of challenging. Murzakaev cited case No. A40-216102/15 as an example. In it, the court invalidated the pledge agreement for a share in the authorized capital of an LLC as security for a bank guarantee of Peresvet Bank, since the bank misled the pledger-individual. The first and second instances drew attention to the fact that the main security had already been provided, and the share pledge agreement was concluded additionally, after the issuance of a bank guarantee and at the request of the bank. What was the meaning of this, the representatives of the bank did not explain. The courts came to the conclusion that they misled the citizen and demanded to conclude a deal that was not necessary. So, it should be declared invalid.

In one of the cases, the courts invalidated the share pledge agreement, because the pledger-individual was misled: there was no need for a transaction.

It is difficult to foresee such a risk, but the most frequent ones can and should be prevented. This is what lawyers do, whose task is to carefully study the documents, request the missing ones and correctly structure the transaction. How to protect the interests of both parties to the transaction, says Lopatina from the "Commonwealth of Land Lawyers" on the example of the purchase and sale of a plot with a "wrong" purpose. The buyer wants to purchase an agricultural land and build a cottage settlement on it. The seller promises that he will change the purpose of the land, but, of course, at the expense of the advance. “Here you need to conclude a preliminary agreement or a contract for the sale of a future thing - a plot with a legal regime for housing construction,” says Lopatina. “The term for concluding the main contract must be strictly tied to the moment the required type of use of the site is entered into the USRN.” To register it, the seller will receive an advance from the buyer. In case it is not possible to change the purpose of the land, Lopatina suggests connecting a financially reliable guarantor who guarantees the return of the advance.

Mortgages are often not enough to get a loan for business needs; banks require a personal guarantee from the CEO or members of the legal entity. As a result, these people become responsible for multi-million and multi-billion dollar debts, which, most likely, they will not be able to pay off. It is difficult to invalidate such a surety because the courts are trying to keep the security, says senior lawyer Tatiana Voronina: “They reject arguments that the debt was already there at the time of the surety or that the amount was not specified in the contracts. Also, the courts do not take into account that the guarantor did not have sufficient property to pay the debts (and it is clear that there will not be any more).”

Voronina is sure that banks enter into agreements not to receive funds, but to control the guarantor under fear of bringing him to joint and several liability. She recommends the heads and participants of companies to apply in writing to the bank with a request to do without a guarantee or try to change its conditions. You can try to limit the liability to those debts that arise during the period of office of a particular person. Otherwise, you will have to answer for the subsequent ones - after the citizen ceases to control society, Voronina concludes.

US agriculture is going through hard times. International competition from both developed and developing countries is intensifying. Opportunities for exporting products are also far from always favorable. Thus, from 1992 to 2012, agricultural exports to the Russian Federation decreased from $723 million to $267 million, according to the Foreign Trade Department of the US Bureau of Statistics. Following the failure of the WTO Doha Round talks in Geneva in July 2008, the US foreign trade authorities focused on concluding regional free trade agreements.

In October 2011, the US Congress ratified free trade agreements with South Korea, Panama and Colombia. From 2010 to the present, Australia, Brunei, Chile, Canada, Japan, Malaysia, Mexico, New Zealand, Peru, Singapore, the United States, and Vietnam have been negotiating a free trade area in the Pacific region. Last week, another round of negotiations on this treaty took place in Salt Lake City, USA. Observers expect an agreement to be signed early next year.

North America experienced its worst drought since the 1930s this summer. In October, a sudden snowfall hit several regions of the country, which was superimposed on a 16-day government "shutdown", as a result, the USDA was unable to fully document the damage suffered by farmers, which negatively affected the amount of compensation. At the same time subsidies for the village are jeopardized.

For reference: Every five years, the U.S. adopts the Agricultural Payments to Farmers program. In 2008, another farmer's bill was passed, allocating $288 billion for the next five years. However, due to the opposition of far-right Republicans in the House of Representatives and Democrats in the Senate and the White House last year, the Farm Bill was not passed. In different variations, the rural support programs were extended for one year. Moreover, this year in the House of Representatives it was divided into two separate bills: one authorizes an agro-subsidy program, the second a food stamp program for the poor. However, at a time when farmers are most in need of support, sequestration was carried out. Three years ago, the Budget Control Act of 2010 was passed, authorizing the creation of a bipartisan commission tasked with developing a system of reasonable budgetary austerity measures. As an incentive for its work, a mechanism was created to automatically sequester all articles of the federal budget in equal proportions, which was launched in March of this year.

The farm lobby, once a powerful force in Washington, is slowly losing ground. Due to changing demographics, growing urban populations and shrinking rural farmers, farmers are becoming an ever less influential electoral force. The 1930s and 50s can be called the "golden age" of the farm lobby. Then organizations such as the American Federation of Farm Bureaus, the National Farmers Union, were frequent guests at parliamentary hearings, and sometimes chaired meetings of relevant committees, a practice unprecedented in the history of the US Congress. The 1960s saw a fragmentation of the farm lobby. Hundreds of branch structures have appeared that defend the interests of producers of certain types of agricultural products. However, farmers are still strong enough to periodically extend the rural subsidy program. Although, as noted earlier, there are failures. According to the Center for Responsible Politics, since 1990, farmers have spent more than $162 million on contributions to the campaign funds of candidates for various posts, of which 38% are Democrats and 62% Republicans. Lobbying spending is also on the rise, from 1998 to the third quarter of 2013 spending increased from $8 million to $16 million.

We spoke with the Vice President for Government Relations of the National Farmers Union to learn more about the problems of American farmers. Chandler Gole.

- Last year, Russia joined the WTO, the American Federation of Farm Bureaus supported this process, what is your position? Does the White House help resolve trade disputes?

– We want Russia to play by the same rules as other countries. Constant manipulations with access of the American beef and chicken meat to the Russian market negatively affect agricultural producers in the USA. For farmers, switching the market like a light switch is extremely harmful. Japan and South Korea do the same, so Russia is not the only country with an unpredictable regulatory regime. Barack Obama has a much more positive international image than the previous US president, which has a positive effect on his ability to reach international agreements.

– What is your position on the negotiations regarding the Trans-Pacific Free Trade Agreement? Do you manage to convey your position to the administration of Barack Obama? Given the current level of confrontation between Congress and the White House, will this agreement be approved by Parliament?

– Another round of negotiations took place last week in Salt Lake City, USA. So far, we haven't even had a glimpse of the text of the document. As a result, all this causes a negative reaction from the public of different countries. We believe that Canada and Japan joining the talks was a mistake. We even managed to create a coalition with our fellow farmers from the Land of the Rising Sun, however, this did not bring results. We do not like the excessive penetration of agricultural products from Australia and New Zealand, where the state actively subsidizes farmers. I believe that we should not expect the completion of negotiations before the end of the first or even the second quarter of next year. If the White House manages to conclude an agreement, then Congress will approve it. However, I'm not sure how fast this will happen. If we had been within the framework of the initial plan of negotiations, then the final text of the agreement would have been ready by now. In addition, it is very difficult to reconcile multiple interests. Bilateral treaties are extremely difficult to conclude, I do not understand why the White House believes that it will be easier to coordinate the interests of many countries.

- What is your assessment of the situation with the Farm Bill, which should have been adopted last year?

– The National Farmers' Union strongly opposes the division of the Farmers' Bill into two parts. The current configuration of the five-year rural support programs has been a historical alliance since the late 1960s. The USDA, which administers agricultural subsidies, also administers food stamps to poor Americans. It makes sense to approve both components at the same time. Farmers are extremely compassionate, they cannot ignore those who are experiencing food shortages. That is why the union of those who produce food and those who need it has been such a well-functioning mechanism. This attempt by the House of Representatives to split the Farm Bill in two demonstrates that there is a segment of the Republican Party that simply wants to eliminate the support system for American farmers and the poor. I think both bills will eventually be merged again, it's just a matter of how big the food stamp cuts will be. I think the Farmer's Bill will be passed this year in December. Speaker bainer received a strong thrashing on this issue and needs to be rehabilitated.

This summer, the US experienced its worst drought since the 1930s. What were the implications for American farmers? Has the drought helped to raise the urgency of the issue of agricultural support to such an extent as to ensure the necessary level of subsidies for the next five years? Or did the sequestration carried out in March of this year win?

– In the 2008 Farm Bill, we managed to carry out a number of good rural support programs. Thanks to advanced farming technologies, the US has not had dust storms like in the 1930s, when all the fertile soil was blown away by the wind. The legislators passed this terrible law, which, by design, was not supposed to come into force, but in the end it began to act. Unfortunately, the sequestration turned out to be more of a factor, and agricultural subsidies were cut by millions of dollars while the population suffered from drought.

– How did the 16-day “lockdown” of the government affect farmers?

- Many farmers harvest in September-October, and if you had a loan guaranteed by the state, or you were expecting payment under one or another rural support program, then you simply remained without money. At this time, there was an unexpected snow storm in Montana, South Dakota and Nebraska, more than 40 thousand heads of cattle died. As a result, it was not possible to document the damage due to the lack of appropriate inspectors from the Ministry of Agriculture and receive appropriate compensation afterwards. The Ministry of Agriculture after the “opening” tried to help these farmers, but time had already passed and not everything could be fixed. Thus, the “closure” of the government had extremely negative consequences for American farmers, which, unfortunately, did not receive adequate coverage in the media.

Since the fraction is equal to the quotient 2: 3, then the quotient from dividing one expression by another can be written using a dash. For example, the expression (41.3 - 4.4) : (15.3 + 33.9) can be written like this: . Having performed the indicated actions, we will find the value of this expression: 0.75, or .

For example, - fractional expressions.

The expression above the line is called the numerator, and the expression below the line is called the denominator of the fractional expression. The numerator and denominator of a fractional expression can be any number, as well as numeric or alphabetic expressions.

With fractional expressions, you can perform actions according to the same rules as with ordinary fractions. Example 1. Find the value of the expression .

Decision. Multiplying the numerator and denominator of this fractional expression by 6, we get:

Example 2 Let's find a work.

Decision.

Example 3 Let's find the sum.

Decision.

When adding fractional expressions, it is more convenient to first represent them as ordinary fractions, and then perform addition:

Questions for self-examination

What is a fractional expression?
What is the expression above the line called? below the line?

Do the exercises

692. Name the numerator and denominator of the expression:

693. Write a fractional expression whose numerator 3a is 2b and the denominator is 6.7x + y.

694. Write the quotient as a fractional expression:

(3,8 4,5 - 0,7) : (6,3: 2,1 - 2,6).

Find the value of this expression.

695. Find the value of the expression:

696. Perform an action:

697. Follow these steps:

698. Find the value of an expression if:

699. Find the value of the expression if:

700. You can find the value of an expression using a microcalculator using the program:

and the value of the expression under this program:

Perform calculations on these programs.

Build a program for finding the value of an expression and perform calculations on it:

701. Calculate orally:

702. Numbers a and b are marked on the coordinate ray (Fig. 30). Is it possible to specify a point on a ray with coordinate ?

Rice. thirty

703. Calculate:

704. Find the product of fractions and the product of fractions reciprocal of data. What properties do these two works have? Test your guess with another example. Prove this property in general form (using literal expressions).

705. Find the largest and smallest values of the expression if x = .

706. Write a problem according to the equation:

707. Vanya and Tanya were supposed to meet at the station to take the train together, which leaves at 8 am. Vanya thinks that his watch is 35 minutes faster, when in reality it is 15 minutes behind. And Tanya thinks that her watch is 15 minutes behind, when in fact it is 10 minutes behind. What happens if each of them, relying on his watch, tries to arrive 5 minutes before the train leaves?

708. Seryozha's age is the age of his father. Sergei is 12 years old. How old is father?

709. A combine harvester mowed wheat from an area of 3 hectares in 1 hour, which is 15% of what he mowed in a day. What area was mowed by the combine harvester in a day?

710. Pears make up 25% of all trees in the garden, the remaining 150 trees are apple trees. How many pear trees are in the garden?

711. The area of 60 hectares is 0.75 of the field area. What is the area of the field?

712. Find a number if:

713. A piece of land with an area of 6 a is a garden, and the area of a garden is the entire plot of land. What is the area of the entire homestead?

714. According to the plan, the brigade must repair 25% of the road between the two villages in a month. During the first week, 2 km 100 m of the road were repaired, which amounted to 30% of the monthly plan. What is the length of the entire road between the villages?

715. Solve the problem:

The book has 240 pages. On Saturday, the boy read 7.5% of the entire book, and on Sunday - 12 pages more. How many pages does he have left to read?
2600 tons of feed were prepared for the poultry farm. In the first month, 8.5% of feed was consumed, and in the second month - 30 tons more. How many tons of feed are left?

716. Find the value of the expression:

717. Forwards Kolya and Nikita brought all the points to their team during the basketball game. How many points did this team score in the match if Kolya scored 7 points more than Nikita?

718. A train traveling at a speed of 68 km/h covers the distance between cities in 6 hours. How long does it take for a cyclist to travel this distance at a speed of 17 km/h?

719. An alloy was obtained from a piece of copper with a volume of 15 cm 3 and a piece of zinc with a volume of 10 cm 3. What is the mass of 1 cm 3 of the alloy, if the mass of 1 cm 3 of copper is 8.9 g, and the mass of 1 cm 3 of zinc is 7.1 g? Round the result to the nearest tenth of a gram.

720. A kitchen of 10 m 2 is 0.4 of all non-residential premises of the apartment. The area of non-residential premises is the area of the entire apartment. Find the area of the entire apartment.

721. Cut out the figures shown in Figure 31 from thick paper and glue the figures shown in Figure 32. These figures are called prisms. In a straight prism, the side faces are rectangles, and the upper and lower bases are equal polygons. Figure 32, a shows a triangular prism, and Figure 32.6 shows a quadrangular one. Each cuboid is a quadrangular prism.

Rice. 31

Rice. 32

Stories about the history of the emergence and development of mathematics

In the most ancient written sources that have come down to us - Babylonian clay tablets and Egyptian papyri - there are not only natural numbers, but also fractions.

Fractions were needed to express the result of measuring length, mass, area in cases where the unit of measurement did not fit into the measured value an integer number of times.

Then a new, smaller unit of measurement was introduced. The names of these new units of measurement became the first names of fractions. For example, a fraction is still called "half"; among the Romans, the word "ounce" was at first the name of the twelfth of a unit of mass, but then the ounce began to denote one twelfth of any value (they said: "Seven ounces of the way", that is, seven twelfths of the way).

In ancient Babylon, as you know, fractions were sexagesimal. Using modern notation, the number could be written, for example, as 4; 52; 03. This meant: .

And now, when we write 3 hours 21 minutes 47 seconds, then, in fact, we write down fractions of an hour in the sexagesimal number system:

The Egyptians had special signs for fractions and a common notation for fractions (i.e., fractions with a numerator of 1). All other fractions were written as a sum of shares.

For example:

(Think about how you can quickly find such a sum.)

Recording fractions using the numerator and denominator appeared in ancient Greece, only the Greeks wrote the denominator from above, and the numerator from below. Fractions in the form familiar to us were first recorded by the Hindus about 1500 years ago, but they did not use a line between the numerator and denominator. The feature of the fraction became commonly used only from the 16th century.

In the old days, mostly ordinary fractions were used. This was explained by different ratios between units of measurement: they were divided into 12, and 16, and 40 parts. But then it was noticed that the most convenient for calculations are decimal fractions. From the XVII-XVIII centuries. they have become widespread, especially after the creation and introduction of the metric system of measures in most countries.