Come to a common denominator value. Reducing fractions to a common denominator. From particular to general and from general to particular
LEAD TO ONE DENOMINATOR. Book Same as . [All] paintings and sculptures had the same meaning. Everything seemed reduced to the same denominator, the Parisian
(V. Stasov. From the Berlin exhibition). Phraseological dictionary of the Russian literary language. - M.: Astrel, AST
.
A. I. Fedorov. 2008. See what “Reduce to one denominator” is in other dictionaries:
Reduce to one denominator- To bring to one denominator (foreign language) to one common goal, to agree, to equalize (to bring under the same conditions) a hint of an arithmetic problem. Wed. Raznochinets... what is this? Not a nobleman... From a taxable state. Only now it’s all the same... ... Michelson's Large Explanatory and Phraseological Dictionary (original spelling)
Reduce to one denominator reduce to one denominator - (foreign language) to one common goal, to agree, to equalize (to bring under the same conditions); allusion to an arithmetic problem Wed. Commoner... what is this? Not a nobleman... From a taxable state. Only now everything is reduced to one denominator... as in problems...
Michelson's Large Explanatory and Phraseological Dictionary - Reduce / to one (common) denominator Equalize, make similar in what l. regarding...
Dictionary of many expressions LEAD TO ONE DENOMINATOR. LEAD TO ONE DENOMINATOR. Book Same as Reduce to a common denominator. All [paintings and sculptures] had the same meaning. Everything seemed reduced to the same denominator, the Parisian one (V.... ... Phraseological Dictionary of the Russian Literary Language
BRING- BRING, I’ll bring, you’ll bring, please. vr. brought, brought; brought, brought, sovereign. (to lead). 1. who what. Leading, delivering somewhere, helping to get somewhere. Bring the kids home. “The Cossack who brought me went to report about me.”... ... - (foreign language) to one common goal, to agree, to equalize (to bring under the same conditions); allusion to an arithmetic problem Wed. Commoner... what is this? Not a nobleman... From a taxable state. Only now everything is reduced to one denominator... as in problems...
Ushakov's Explanatory Dictionary bring - I lead/, you lead; brought, led/, lo/; brought/dish; brought; den, den/, o/; bringing/; St. see also bring, drive, drive, drive 1) ...
BRING- I’m leading, you’re leading; brought, led, lo; brought; brought; den, dena, o; bringing; St. 1. whom. Leading, delivering, helping to get to where. P. child home. P. a cow to the veterinarian. He came on his own and brought his friends with him. P. a girl into the house, into the family (marry, ... ... encyclopedic Dictionary
Reduce / bring to a common (one, single) denominator- who, what. Book or Publ. 1. Destroy the differences between who is l., what is l., to equalize who is l., what is l. in which l. relation., put who l., what l. to the same position. 2. New Discipline team members, equalize their rights. FSRY,... ... Large dictionary of Russian sayings
denominator- Bring to one denominator (book) translation. make a number of objects similar, coinciding in some way. regarding... Phraseological Dictionary of the Russian Language
I originally wanted to include common denominator techniques in the Adding and Subtracting Fractions section. But there turned out to be so much information, and its importance is so great (after all, not only numerical fractions have common denominators), that it is better to study this issue separately.
So, let's say we have two fractions with different denominators. And we want to make sure that the denominators become the same. The basic property of a fraction comes to the rescue, which, let me remind you, sounds like this:
A fraction will not change if its numerator and denominator are multiplied by the same number other than zero.
Thus, if you choose the factors correctly, the denominators of the fractions will become equal - this process is called reduction to a common denominator. And the required numbers, “evening out” the denominators, are called additional factors.
Why do we need to reduce fractions to a common denominator? Here are just a few reasons:
- Adding and subtracting fractions with different denominators. There is no other way to perform this operation;
- Comparing fractions. Sometimes reduction to a common denominator greatly simplifies this task;
- Solving problems involving fractions and percentages. Percentages are essentially ordinary expressions that contain fractions.
There are many ways to find numbers that, when multiplied by them, will make the denominators of fractions equal. We will consider only three of them - in order of increasing complexity and, in a sense, effectiveness.
Criss-cross multiplication
The simplest and most reliable method, which is guaranteed to equalize the denominators. We will act “in a headlong manner”: we multiply the first fraction by the denominator of the second fraction, and the second by the denominator of the first. As a result, the denominators of both fractions will become equal to the product of the original denominators. Take a look:
As additional factors, consider the denominators of neighboring fractions. We get:
Yes, it's that simple. If you are just starting to study fractions, it is better to work using this method - this way you will insure yourself against many mistakes and are guaranteed to get the result.
The only drawback of this method is that you have to count a lot, because the denominators are multiplied “all the way”, and the result can be very large numbers. This is the price to pay for reliability.
Common Divisor Method
This technique helps to significantly reduce calculations, but, unfortunately, it is used quite rarely. The method is as follows:
- Before you go straight ahead (i.e., using the criss-cross method), take a look at the denominators. Perhaps one of them (the one that is larger) is divided into the other.
- The number resulting from this division will be an additional factor for the fraction with a smaller denominator.
- In this case, a fraction with a large denominator does not need to be multiplied by anything at all - this is where the savings lie. At the same time, the probability of error is sharply reduced.
Task. Find the meanings of the expressions:
Note that 84: 21 = 4; 72: 12 = 6. Since in both cases one denominator is divided without a remainder by the other, we use the method of common factors. We have:
Note that the second fraction was not multiplied by anything at all. In fact, we cut the amount of computation in half!
By the way, I didn’t take the fractions in this example by chance. If you're interested, try counting them using the criss-cross method. After reduction, the answers will be the same, but there will be much more work.
This is the power of the common divisors method, but, again, it can only be used when one of the denominators is divisible by the other without a remainder. Which happens quite rarely.
Least common multiple method
When we reduce fractions to a common denominator, we are essentially trying to find a number that is divisible by each denominator. Then we bring the denominators of both fractions to this number.
There are a lot of such numbers, and the smallest of them will not necessarily be equal to the direct product of the denominators of the original fractions, as is assumed in the “criss-cross” method.
For example, for denominators 8 and 12, the number 24 is quite suitable, since 24: 8 = 3; 24: 12 = 2. This number is much less than the product 8 · 12 = 96.
The smallest number that is divisible by each of the denominators is called their least common multiple (LCM).
Notation: The least common multiple of a and b is denoted by LCM(a ; b) . For example, LCM(16, 24) = 48 ; LCM(8; 12) = 24 .
If you manage to find such a number, the total amount of calculations will be minimal. Look at the examples:
Task. Find the meanings of the expressions:
Note that 234 = 117 2; 351 = 117 3. Factors 2 and 3 are coprime (have no common factors other than 1), and factor 117 is common. Therefore LCM(234, 351) = 117 2 3 = 702.
Likewise, 15 = 5 3; 20 = 5 · 4. Factors 3 and 4 are coprime, and factor 5 is common. Therefore LCM(15, 20) = 5 3 4 = 60.
Now let's reduce the fractions to common denominators:
Notice how useful it was to factorize the original denominators:
- Having discovered identical factors, we immediately arrived at the least common multiple, which, generally speaking, is a non-trivial problem;
- From the resulting expansion you can find out which factors are “missing” in each fraction. For example, 234 · 3 = 702, therefore, for the first fraction the additional factor is 3.
To appreciate how much of a difference the least common multiple method makes, try calculating these same examples using the criss-cross method. Of course, without a calculator. I think after this comments will be unnecessary.
Don't think that there won't be such complex fractions in the real examples. They meet all the time, and the above tasks are not the limit!
The only problem is how to find this very NOC. Sometimes everything is found in a few seconds, literally “by eye,” but in general this is a complex computational task that requires separate consideration. We won't touch on that here.
LEAD TO A COMMON DENOMINATOR.
(V. Stasov. From the Berlin exhibition). Phraseological dictionary of the Russian literary language. - M.: Astrel, AST
Book Destroy differences, equalize.
Reduce to one denominator reduce to one denominator - (foreign language) to one common goal, to agree, to equalize (to bring under the same conditions); allusion to an arithmetic problem Wed. Commoner... what is this? Not a nobleman... From a taxable state. Only now everything is reduced to one denominator... as in problems...
See what “Bring to a common denominator” is in other dictionaries: - Reduce / to one (common) denominator Equalize, make similar in what l. regarding...
Reduce / bring to a common (one, single) denominator- who, what. Book or Publ. 1. Destroy the differences between who is l., what is l., to equalize who is l., what is l. in which l. relation., put who l., what l. to the same position. 2. New Discipline team members, equalize their rights. FSRY,... ... Large dictionary of Russian sayings
BRING- I’m leading, you’re leading; brought, led, lo; brought; brought; den, dena, o; bringing; St. 1. whom. Leading, delivering, helping to get to where. P. child home. P. a cow to the veterinarian. He came on his own and brought his friends with him. P. a girl into the house, into the family (marry, ... ... encyclopedic Dictionary
Michelson's Large Explanatory and Phraseological Dictionary - Reduce / to one (common) denominator Equalize, make similar in what l. regarding...
LEAD TO A COMMON DENOMINATOR. LEAD TO A COMMON DENOMINATOR. Book Destroy differences, equalize... Fraction (mathematics)
- This term has other meanings, see Fraction. 8 / 13 numerator numerator denominator denominator Two entries of the same fraction A fraction in mathematics is a number consisting of one or more parts... ... Wikipedia- If some integer a is divided by another integer b, i.e., a number x is sought that satisfies the condition bx = a, then two cases can arise: either in the series of integers there is a number x that satisfies this condition, or it turns out...... Encyclopedic Dictionary F.A. Brockhaus and I.A. Efron
level out- bring under one rank, equalize, equalize, bring to one denominator, cut to one comb, adjust to one color, level, bring to one denominator, depersonalize, bring to a common denominator, cut to one... ... Synonym dictionary
LEAD TO A COMMON DENOMINATOR. LEAD TO A COMMON DENOMINATOR. Book Destroy differences, equalize.
- - Bring ● To the court - to send death, as a predestination of fate: Glory brought Boris Vyacheslavlich to the court, and laid a green papoleum on Kanina for insulting Olgov, the brave and young prince. 15-16...
The Word about Igor's Campaign - dictionary-reference book
- - one of the methods for calculating gross income from the sale of goods at sales prices...
Great Accounting Dictionary
- - in preparation for the general meeting, the shareholder must take the following actions: 1. Receive a copy of the register of shareholders. 2. Familiarize yourself with the agenda of the general meeting of shareholders. 3...
Encyclopedic Dictionary of Economics and Law
- - is based on measuring in milliliters the ratio of the total amount of lead to the amount of lead content. U and Th. The method was used before the publication of Neer's work (1939-1940, active minerals, non-radiogenic isotope with a mass of 204...
Geological encyclopedia
- - see Bring...
Marine dictionary
- - ".....
Official terminology
- - to one common goal, to agree, to equalize; allusion to an arithmetic problem Wed. Commoner... what is this? Not a nobleman... From a taxable state. Only now everything is reduced to one denominator... “as in problems”...
Mikhelson Explanatory and Phraseological Dictionary
- - To bring to one denominator - to one common goal, to agree, to equalize - a hint of an arithmetic problem. Wed. Raznochinets... what is this? Not a nobleman... From a taxable estate...
Michelson Explanatory and Phraseological Dictionary (orig. orf.)
- - LEAD TO A COMMON DENOMINATOR. LEAD TO A COMMON DENOMINATOR. Book Destroy differences, equalize...
Phraseological Dictionary of the Russian Literary Language
- - LEAD TO ONE DENOMINATOR. LEAD TO A SAME DENOMINATOR. Book Same as Reduce to a common denominator. They all had the same meaning. Everything seemed reduced to the same denominator, the Parisian one...
Phraseological Dictionary of the Russian Literary Language
- - who, what. Book or Publ. 1. To destroy differences between someone or something, to equalize someone or something. in some respect., to put smb., sth. to the same position. 2...
Large dictionary of Russian sayings
- - ...
Synonym dictionary
- - ...
Synonym dictionary
- - adj., number of synonyms: 9 leveled, depersonalized, cut with one brush, brought under one rank, adjusted to one color, brought to one denominator ...
Synonym dictionary
- - adj., number of synonyms: 9 leveled, depersonalized, cut with one brush, brought under one rank, adjusted to one color, brought to a common denominator ...
Synonym dictionary
"Bring to a common denominator" in books
SERVING THE COMMON GOOD
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Return to the general tax regime
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Attitude to the common cause
From the book Great Team. What You Need to Know, Do, and Say to Build a Great Team by Miller DouglasAttitude to the common cause The “attitude to the common cause” parameter helps to decide exactly how you (the team) want (wants) to do it (in the context of the book - how to achieve the goal): “This is how I (we) will (will) do it” .The way you or your team choose to accomplish your
Confuse
From the book Spirit of the Warrior author Kholin Yuri EvgenievichConfuse This means to cause the enemy to lose confidence in himself. In a major battle, we can use our units to confuse the enemy on the battlefield. By observing the spirit of the enemy, we can make him think: “Here? There? So? That way? Slowly? Fast?"
Don't go to the "general" until you need it
From the book Firebird DATABASE DEVELOPER'S GUIDE by Borri HelenDon't go "generic" until you need it Common database application interfaces, such as ODBC or Borland BDE, combine a single database connection with a single transaction. Since their task is to hide the difference between simple, file-based
From particular to general and from general to particular
From the book Active Sales 3.1: The Beginning author Rysev Nikolay YurievichFrom specific to general and from general to specific Two mirror methods of presenting key points of a presentation in its main part. If you have not worked as a sales representative for a wine and vodka company, try it. I haven't worked myself, but for some reason it seems very
From the book How people gradually reached real arithmetic [without tables] authorI. By layout and general structure
From the book Bronya, 2009 No. 01 by the authorI. According to the layout and general design, the engine is located behind the control compartment in a common well with the generator block. This placement of the power plant limited access to its main units, complicated installation and dismantling work and led to a shift in the combat
Refer to shared experience
From the book Brilliant Performance. How to become a successful speaker author Sednev AndreyRefer to Shared Experiences Another good way to start a presentation is to mention something that everyone in the room has seen or heard, such as making a comment about the speaker who spoke before you or something that happened in front of everyone during the conference. .
The difficult path to the common good
From the book The World is on edge: the spring is unclenched author Lukyanov FedorThe difficult path to the common good Sebastiano Maffettone, Dean of the Faculty of Political Science and Professor of Political Philosophy at LUISS Guido Carli University, Rome, Italy. Hakan A. Altynay, President of the World Citizenship Academy, Visiting Senior Fellow
Reducing fractions and bringing them to the same denominator.
From the book How people gradually reached real arithmetic [with table] author Bellustin Vsevolod KonstantinovichReducing fractions and bringing them to the same denominator. The ability to reduce fractions goes back quite a long way and dates back to mathematicians who lived before Christ. The simplest method was the one that is practiced among us, that is, dividing the numerator and denominator by one -
THORNS TO A SINGLE DENOMINATOR
From the book Man with a Ruble author Mikhail KhodorkovskyTHORNS TO A COMMON DENOMINATOR The fight against privileges was going on in the country with enormous difficulties. What about the country if even in MENATEP they did not immediately come to a common denominator. The psychology of yesterday's nomenklatura no, no, and even gave relapses. Department heads have a salary if
TENDENCY TO THE DENOMINATOR, or TWENTIETH CENTURY POSTURE? (About the book “Players of Profit” by Alexander Dragomirs)
From the book Closer to the Truth author Rotov Viktor SemenovichFrom private to general
From the book Literary Newspaper 6316 (No. 12 2011) author Literary NewspaperFrom the private to the general Art From the private to the general ISO-TAPE The names of many art collectors, as they say, are inscribed in golden letters in the history of museums, and therefore of fine art. The work started during the Renaissance by royalty was
From royal affairs to the general...
From the book Literary Newspaper 6447 (No. 4 2014) author Literary NewspaperFrom the Tsar's affair to the general... The five-part historical film "The Romanovs. The Tsar's Affair" (producer and scriptwriter E. Chavchavadze, director G. Ogurnaya) at first glance examines the history of Russia from the point of view of the noble class, whose role in the formation of the state
Nothing prevents you from seeing more than your own point of view.
V. Kabrut
I can say about someone that he is a scoundrel or mediocrity. Speak on him. And this is natural, because I have accumulated a lot of anger towards people. I don’t want to meet them halfway, try to understand, show sympathy. Yes, I agree that by doing this I do not bring people closer to me, but only push them away. But, in principle, I don’t care about it.
It's all about me. The only obstacle to contact is myself.
I blame myself for not giving him what he expects from me, not giving him pleasure, not fulfilling his desires.
Let's say he likes to listen and read about high, spiritual things. He strives to feel this spirituality in himself and wants the high to be expressed in the appropriate high syllable. He is all ablaze with anticipated pleasure!
And suddenly I come and talk about such an important subject to him in extremely low, ugly words. I'm vulgarizing the topic. This is completely against his expectations. And this makes you suffer! To suffer from the fact that I do not express myself the way he would like to see or hear. Not the way he imagines it. He can’t stand it and criticizes me... He doesn’t want to suffer, he pushes away suffering... No! Give me someone else to tell me what I want to hear!
Why are we not ready to understand and accept the other? Is it really better to consider only your worldview as true, and yourself, if not perfect, then still a special person?
If I could find something in common between me and another that we would both agree on, how much we would advance in understanding each other, connect with each other...
We would discover that despite all the differences between us, there is still room for unity. Moreover, unification is impossible without the existence of disagreements.
Because only from mutual misunderstanding is the opportunity to yield born. Without mutual concessions there is no connection.
In the meantime, my opinion kind of draws the line: that’s it, I think so! But there is also a general opinion. This thing is special. By absorbing information from others, we develop each other and come to a common denominator. Each of us is enriched by everyone else.
As a result, while remaining ourselves, we acquire knowledge of others, add to ourselves sensations and ideas of them. And then the individual strength of everyone increases significantly...
And then it’s just a stone’s throw away from admiring each other...
By connecting together, we will discover a new reality. Let's expand the boundaries of the body, and our common desires will show the way there, to a new world, a huge, magnificent one. He will open up for us, open us up. He will take it in, and we will continue to live in it.
And so, trying together to tighten the knot of connection between us, we merge into one cell, and another, and another... Seven billion nodes create a network on which the whole world rests!
I understood all this when I decided to accept another as he is... I threw out my own assessments and judgments...
Opened my heart... Allowed it to do whatever it wanted. The main thing is not to be afraid, the heart is not the brain, it cannot make mistakes.
I simply stepped over a certain threshold, beyond which my cruel nature remained, which created my character in me and gave me the appropriate upbringing.
Broke my heart of stone with love...
We stand at a crossroads. We need to come to a new way of thinking. Towards the idea that everything in the world is interconnected and interdependent. That love should rule the world...
In fact, since such thoughts are increasingly manifested in people, it means that we are already experiencing such a transition, we are already in it.
By acting out of love, we will create a universal man, inclusive of all and included in all. This is the only thing you and I can do...
And we will be happy.
