Shares, ordinary fractions, definitions, designations, examples, action with fractions. Improper fraction
Ordinary fractions are divided into \\ textit (correct) and \\ textit (incorrect) fractions. Such a separation is based on the comparison of the numerator and the denominator.
Right fractions
Proper shot called ordinary fraction $ \\ FRAC (M) (N) $, which has a numerator less than the denominator, i.e. $ M.
Example 1.
For example, the fractions $ \\ FRAC (1) (3) $, $ \\ FRAC (9) (123) $, $ \\ FRAC (77) (78) $, $ \\ FRAC (378567) (456298) $ are correct, so As in each of them, the numerator is less than the denominator, which corresponds to the definition of the correct fraction.
There is a definition of the correct fraction, which is based on the comparison of the fraction with unit.
rightif it is less than one:
Example 2.
For example, the ordinary fraction $ \\ FRAC (6) (13) $ is correct, because Conditions $ \\ FRAC (6) (13)
Incorrect fractions
Incorrect fraction It is called an ordinary fraction $ \\ FRAC (M) (N) $, in which the numerator is greater than or equal to the denominator, i.e. $ M \\ GE N $.
Example 3.
For example, the fractions $ \\ FRAC (5) (5) $, $ \\ FRAC (24) (3) $, $ \\ FRAC (567) (113) $, $ \\ FRAC (100001) (100000) $ are incorrect, so As in each of them, the numerator is greater than or equal to the denominator, which corresponds to the definition of incorrect fraction.
Let us give the definition of the wrong fraction, which is based on its comparison with one.
Ordinary fraction $ \\ FRAC (M) (N) $ is wrongIf it is equal to or more units:
\\ [\\ FRAC (M) (N) \\ GE 1 \\]
Example 4.
For example, an ordinary fraction $ \\ FRAC (21) (4) $ is incorrect, because The condition is $ \\ FRAC (21) (4)\u003e $ 1;
ordinary fraction $ \\ FRAC (8) (8) $ is incorrect, because The condition is $ \\ FRAC (8) (8) \u003d 1 $.
Consider in more detail the concept of incorrect fraction.
Take for the example the wrong fraction of $ \\ FRAC (7) (7) $. The value of this fraction - took seven fractions of the subject, which is divided into seven identical fractions. Thus, from seven shares that are in stock, you can make a whole subject. Those. Improper fraction $ \\ FRAC (7) (7) $ describes a whole subject and $ \\ FRAC (7) (7) \u003d 1 $. So, incorrect fractionswhose numerator is equal to the denominator, describe one whole subject and such a fraction can be replaced with a natural number of $ 1 $.
$ \\ FRAC (5) (2) $ is quite obvious that $ 2 $ can be $ 2 $ from these five second fractions (one whole subject will be $ 2 $ shares, and for the preparation of two whole items you need $ 2 + 2 \u003d $ 4 Shares) and remains one second share. Those., Wrong fraction of $ \\ FRAC (5) (2) $ describes $ 2 $ object and $ \\ FRAC (1) (2) $ share of this subject.
$ \\ FRAC (21) (7) $ - from twenty-one seventh shares, you can make $ 3 $ whole object ($ 3 $ 3 $ $ 7 $ share in each). Those. The fraction of $ \\ FRAC (21) (7) $ describes $ 3 $ entire object.
From the considered examples, you can draw the following conclusion: The irregular fraction can be replaced with a natural number, if the numerator is divided into a denominator (for example, $ \\ FRAC (7) (7) \u003d 1 $ and $ \\ FRAC (21) (7) \u003d $ 3) , or the sum of natural number and the correct fraction, if the numerator is not divided into a denominator (for example, $ \\ \\ FRAC (5) (2) \u003d 2 + \\ FRAC (1) (2) $). Therefore, such fractions are called wrong.
Definition 1.
The process of representing the incorrect fraction as the sum of the natural number and proper fraction (for example, $ \\ FRAC (5) (2) \u003d 2 + \\ FRAC (1) (2) $) is called allocation of the whole part of the wrong fraction.
When working with incorrect fractions, a close relationship between them and mixed numbers can be traced.
Incorrect fraction is often written in the form of a mixed number - a number that consists of an entire fractional part.
To record the wrong fraction in the form of a mixed number, you must divide the numerator to the denominator with the residue. Private will be the whole part of the mixed number, the residue is the numerator of the fractional part, and the divider is an denominator of the fractional part.
Example 5.
Write the wrong fraction $ \\ FRAC (37) (12) $ as a mixed number.
Decision.
We divide the numerator to the denominator with the residue:
\\ [\\ FRAC (37) (12) \u003d 37: 12 \u003d 3 \\ (residue \\ 1) \\] \\ [\\ FRAC (37) (12) \u003d 3 \\ FRAC (1) (12) \\]
Answer. $ \\ FRAC (37) (12) \u003d 3 \\ FRAC (1) (12) $.
To record a mixed number in the form of an incorrect fraction, a denominator is needed to multiply by an integer part of the number, to the product, which turned out, add a fractional parts numerator and write the resulting amount into the fractional numerator. The denominator of the irregular fraction will be equal to the denominator of the fractional part of the mixed number.
Example 6.
Write a mixed number $ 5 \\ FRAC (3) (7) $ as an incorrect fraction.
Decision.
Answer. $ 5 \\ FRAC (3) (7) \u003d \\ FRAC (38) (7) $.
Addition of mixed number and proper fraction
Addition of mixed number $ A \\ FRAC (B) (C) $ and correct fractions $ \\ FRAC (D) (E) $ is adding to this fraction of fractional part of this mixed number:
Example 7.
Perform the addition of proper fract $ \\ FRAC (4) (15) $ and the mixed number $ 3 \\ FRAC (2) (5) $.
Decision.
We use the formula for the addition of a mixed number and proper fraction:
\\ [\\ FRAC (4) (15) +3 \\ FRAC (2) (5) \u003d 3 + \\ left (\\ FRAC (2) (5) + \\ FRAC (4) (15) \\ RIGHT) \u003d 3 + \\ fifteen)\\]
According to the sign of division, the number \\ TexTit (5) can determine that the fraction of $ \\ FRAC (10) (15) $ is reduced. Perform a reduction and find the result of addition:
So, the result of the addition of the correct fraction $ \\ FRAC (4) (15) $ and the mixed number $ 3 \\ FRAC (2) (5) $ will be $ 3 \\ FRAC (2) (3) $.
Answer: $ 3 \\ FRAC (2) (3) $
Addition of mixed number and incorrect fraction
Addition of incorrect fraction and mixed number We reduce the addition of two mixed numbers, for which it is enough to highlight the whole part of the wrong fraction.
Example 8.
Calculate the amount of the mixed number $ 6 \\ FRAC (2) (15) $ and incorrect fraction $ \\ FRAC (13) (5) $.
Decision.
First, we allocate the whole part of the wrong fraction $ \\ FRAC (13) (5) $:
Answer: $ 8 \\ FRAC (11) (15) $.
This article pro ordinary fractions. Here we will get acquainted with the concept of the share of the whole, which will lead us to the definition of ordinary fraction. Further we will stop on the adopted designations for ordinary fractions and give examples of fractions, let's say about the numerator and denominator of the fraction. After that, we will give the definition of correct and incorrect, positive and negative fractions, as well as consider the situation of fractional numbers on the coordinate beam. In conclusion, we list the main steps with fractions.
Navigating page.
Founding
First introduce the concept of a share.
Suppose that we have some object compiled from several completely identical (that is, equal to) parts. For clarity, you can imagine, for example, an apple cut into several equal parts, or an orange consisting of several equal lobes. Each of these equal parts constituting a whole subject, called fraction of the whole or simply share.
Note that the shares are different. Let's explain it. Let we have two apples. We cut the first apple into two equal parts, and the second - on 6 equal parts. It is clear that the proportion of the first apple will differ from the share of the second apple.
Depending on the number of shares that make up a whole subject, these shares have their own names. We will understand names. If the subject is two shares, any of them is called one second share of a whole object; If the subject is three shares, any of them is called one third share, and so on.
One second share has a special name - half. One third share is called third, and one quadruple share - quarter.
For brief recording, the following were introduced designations of Share. One second share is referred to as or 1/2, one third share - like 1/3; One fourth share - like 1/4, and so on. Note that the record with a horizontal feature is used more often. To secure the material, we give another example: the record indicates one hundred and sixty-seventh fraction of the whole.
The concept of shares naturally spreads from items by magnitude. For example, one of the measurement measures is a meter. To measure lower lengths than meter, you can use the meter shares. This can use, for example, half meter or tenth or thousandth meters. Similarly, the shares of other values \u200b\u200bare used.
Ordinary fractions, definition and examples of fractions
To describe the number of shares are used ordinary fractions. Let us give an example that will allow us to approach the definition of ordinary fractions.
Let the orange consists of 12 fractions. Each share in this case represents one twelfth share of the whole orange, that is,. Two shares are denoted by, three shares - like, and so on, we denote by 12 stakes as. Each of the above records is called an ordinary fraction.
Now give general definition of ordinary fractions.
The voiced definition of ordinary fractions allows you to bring examples of ordinary fractions: 5/10, 21/1, 9/4 ,. But records 
Not suitable for the voiced definition of ordinary fractions, that is, are not ordinary fractions.
Numerator and denominator
For convenience in ordinary fraction distinguish numerator and denominator.
Definition.
Numerator Ordinary fraction (M / N) is a natural number m.
Definition.
Denominator Ordinary fraction (m / n) is a natural number N.
So, the numerator is located on top above the fraction (left of the inclined line), and the denominator is from below below the fraction (to the right of the inclined line). For example, we give an ordinary fraction 17/29, the numerator of this fraction is the number 17, and the denominator is the number 29.
It remains to discuss the meaning concluded in the numerator and denominator of the ordinary fraction. An indicator of the fraction shows, one object consists of many fractions, the numerator in turn indicates the number of such fractions. For example, denominator 5 fractions 12/5 means that one object consists of five pieces, and the numerator 12 means that 12 such fractions are taken.
Natural number as a fraction with denominator 1
An indicator of ordinary fraction can be equal to one. In this case, we can assume that the subject of weathering, in other words, is something. The numerator of such a fraction indicates how much items are taken. Thus, the ordinary fraction of the form M / 1 has the meaning of the natural number M. So we substantiated the validity of the equality M / 1 \u003d m.
I rewrite the last equality: m \u003d m / 1. This equality gives us the possibility of any natural number M representing in the form of an ordinary fraction. For example, the number 4 is a fraction 4/1, and the number 103 498 is the fraction 103 498/1.
So, any natural number M can be represented as an ordinary fraction with a denominator 1 as M / 1, and any ordinary fraction of the form M / 1 can be replaced with a natural number M.
Damn fraction as a sign of division
The representation of the initial object in the form of n shares is nothing more than dividing on n equal parts. After the subject is divided into N share, we can divide it equally between N people - everyone will receive in one share.
If we have initially m identical objects, each of which is divided into N share, then these M objects we can equally divide between n people, distribute to each person in one share of each of the objects. At the same time, each person will have M shares 1 / n, and M shares 1 / N gives an ordinary fraction M / N. Thus, the ordinary fraction M / n can be used to designate division M of objects between n people.
So we received a clear connection between ordinary fractions and division (see the general idea of \u200b\u200bdividing natural numbers). This connection is expressed as follows: damage fraction can be understood as a sign of division, that is, m / n \u003d m: n.
Using an ordinary fraction, you can record the result of dividing two natural numbersFor which the division is not performed. For example, the result of dividing 5 apples for 8 people can be written as 5/8, that is, everyone will get five eighth apple shares: 5: 8 \u003d 5/8.
Equal and unequal ordinary fractions, fraction comparison
Enough natural action is comparison of ordinary fractionsBut it is clear that 1/12 orange is different from 5/12, and 1/6 of the apple share is the same as another 1/6 share of this apple.
As a result of the comparison of two ordinary fractions, one of the results is obtained: the fractions are either equal or not equal. In the first case we have equal ordinary fractions, and in the second - unequal ordinary fractions. We give the definition of equal and unequal ordinary fractions.
Definition.
equalif equality A · d \u003d b · c.
Definition.
Two ordinary fractions A / B and C / D not equalIf the equality A · d \u003d b · C is not performed.
Let us give a few examples of equal fractions. For example, an ordinary fraction of 1/2 is equal to 2/4, as 1 · 4 \u003d 2 · 2 (if necessary, see the rules and examples of multiplication of natural numbers). For clarity, you can imagine two identical apples, the first cut in half, and the second - on 4 stakes. It is obvious that the two fourth shares of the apple make up 1/2 share. Other examples of equal ordinary fractions are fractions 4/7 and 36/63, as well as a pair of fractions 81/50 and 1,620/1,000.
And ordinary fractions 4/13 and 5/14 are not equal, since 4 · 14 \u003d 56, and 13 · 5 \u003d 65, that is, 4 · 14 ≠ 13 · 5. Another example of unequal ordinary fractions are the fractions 17/7 and 6/4.
If, when comparing two ordinary fractions, it turned out that they are not equal, it may be necessary to know which of these ordinary fractions less another, and what - more. To find out, a rule of comparison of ordinary fractions is used, the essence of which is reduced to bringing compared fractions to the general denominator and the subsequent comparison of the numerators. Detailed information on this topic is collected in the article Comparison of fractions: Rules, examples, solutions.
Fractional numbers
Each fraction is a record fractional number. That is, the fraction is just a "shell" of a fractional number, its appearance, and all the selligent load is contained in the fractional number. However, for brevity and convenience, the concept of a fraction and fractional number is combined and said simply fraction. It is appropriate to rephrase the famous saying: we speak fraction - mean a fractional number, we say a fractional number - we mean the fraction.
Fraction on the coordinate beam
All fractional numbers that correspond to ordinary fractions have their own unique place on, that is, there is a mutually unique correspondence between the fractions and points of the coordinate beam.
So that on the coordinate beam to get to the point corresponding to the fraction M / N, from the beginning of the coordinates in the positive direction, to postpone M segments, the length of which is 1 / N share of a single segment. Such segments can be obtained by separating a single segment to n equal parts, which can always be made using a circulation and a ruler.
For example, we show the point M on the coordinate beam corresponding to the fraction 14/10. The length of the segment with the ends at the point O and the point close to it marked with a small stroke is 1/10 share of a single segment. The point with the coordinate 14/10 was removed from the origin at a distance of 14 of these segments.
Equal fractions correspond to the same fractional number, that is, equal to the fractions are the coordinates of the same point on the coordinate beam. For example, one point corresponds to 1/2, 2/4, 16/32, 55/110 coordinate on the coordinate beam, since all recorded fractions are equal (it is located at a distance of half a single segment, peculiar from the beginning of the reference in the positive direction).
On the horizontal and directed to the right coordinate beam point, the coordinate of which is a big fraction, is the right point, the coordinate of which is a smaller fraction. Similarly, a point with a smaller coordinate lies to the left of the point with the greater coordinate.
Right and incorrect fractions, definitions, examples
Among ordinary fractions distinguish right and incorrect fractions. This separation is based on a comparison of the numerator and denominator.
Let us give the definition of the right and wrong ordinary fractions.
Definition.
Proper fraction - this is an ordinary fraction, the numerator of which is less than the denominator, that is, if M Definition.
Improper fraction - This is an ordinary fraction in which the numerator is greater than or equal to the denominator, that is, if M≥N, then the ordinary fraction is incorrect. Let us give a few examples of the correct fractions: 1/4, 32 765/909 003. Indeed, in each of the recorded ordinary fractions, the numerator is less than the denominator (if necessary, see the article comparing natural numbers), so they are correct by definition. But examples of incorrect fractions: 9/9, 23/4 ,. Indeed, the numerator of the first of the recorded ordinary fractions is equal to the denominator, and in the other fractions the numerator more denominator. There is also a definition of correct and incorrect fractions, based on the comparison of fractions with a unit. Definition. rightif it is less than one. Definition. Ordinary fraction is called wrongIf it is either equal to one, or more than 1. So ordinary fraction 7/11 - correct, as 7/11<1
, а обыкновенные дроби 14/3
и 27/27
– неправильные, так как 14/3>1, a 27/27 \u003d 1. Let's think about how ordinary fractions with a numerator, superior or equal to the denominator, deserve such a name - "wrong". For example, take the wrong fraction 9/9. This fraction means that the nine share of the subject is taken, which consists of nine shares. That is, from the existing nine fractions we can make a whole subject. That is, the wrong fraction 9/9 in essence gives a whole subject, that is, 9/9 \u003d 1. In general, incorrect fractions with a numerator equal to the denominator denote one whole subject, and such a fraction can replace the natural number 1. Now consider incorrect fractions 7/3 and 12/4. It is quite obvious that from these seven third fractions we can make two whole objects (one whole subject is 3 shares, then it will take 3 + 3 \u003d 6 pieces to compile two whole objects) and one third share will remain. That is, the wrong shot 7/3 in essence means 2 items and another 1/3 share of such an item. And from twelve fourth fractions we can make three whole objects (three subjects of four stakes in each). That is, the fraction 12/4 in essence means 3 entire objects. The considered examples lead us to the following conclusion: incorrect fractions, can be replaced by either natural numbers when the numerator shares aimed at the denominator (for example, 9/9 \u003d 1 and 12/4 \u003d 3), or the sum of the natural number and correct fraction when the numerator It is not divided by a denominator (for example, 7/3 \u003d 2 + 1/3). Perhaps this is exactly what the wrong fraction has been deserved. "Wrong". Separate interest is caused by the representation of the wrong fraction in the form of the sum of the natural number and the correct fraction (7/3 \u003d 2 + 1/3). This process is called the allocation of a whole part of incorrect fraction, and deserves a separate and more attentive consideration. It is also worth noting that there is a very close relationship between incorrect fractions and mixed numbers. Each ordinary fraction corresponds to a positive fractional number (see the article positive and negative numbers). That is, ordinary fractions are positive fractions. For example, ordinary fractions 1/5, 56/18, 35/144 - positive fractions. When it is necessary to highlight the positivity of the fraction, then it is put in front of it plus, for example, +3/4, +72/34. If before an ordinary shot, put a minus sign, then this entry will correspond to a negative fractional number. In this case, you can talk about negative fractions. Let us give a few examples of negative fractions: -6/10, -65/13, -1/18. Positive and negative fractions M / N and -M / N are opposite numbers. For example, the fractions 5/7 and -5/7 are opposite fractions. Positive fractions, as well as positive numbers in general, denote the addition, income, change of any value in the direction of magnification, etc. Negative fractions meet the flow, debt, a change in any value towards the decrease. For example, a negative fraction of -3/4 can be interpreted as a debt, the value of which is 3/4. On the horizontal and directed right, negative fractions are located to the left of the beginning of the reference. The points of the coordinate direct whose coordinates are the positive fraction M / N and the negative fraction of -M / N are located at the same distance from the origin, but on different sides of the point O. It is worth saying about the fractions of the type 0 / n. These fractions are equal to the number zero, that is, 0 / n \u003d 0. Positive fractions, negative fractions, and also fractions 0 / N are combined into rational numbers. One action with ordinary fractions is a comparison of fractions - we have already considered higher. Four more arithmetic actions with fractions - Addition, subtraction, multiplication and division of fractions. Let us dwell on each of them. The general essence of action with fractions is similar to the essence of the corresponding actions with natural numbers. We draw an analogy. Multiplication of fractions It can be considered as an action in which the fraction fraction is located. For explanation, we give an example. Let us have 1/6 of the apple and we need to take 2/3 parts from it. The part we need is the result of the multiplication of fractions 1/6 and 2/3. The result of multiplying two ordinary fractions is an ordinary fraction (which is in a particular case equal to a natural number). Further, we recommend to study the information of the article multiplication of fractions - rules, examples and solutions. Bibliography. Studying the queen of all sciences - mathematics, at a certain point everyone faced with fractions. Although this concept (as well as the types of fractions or mathematical actions with them) is completely simple, it is necessary to treat it carefully, because in real life outside the school it is very useful. So, let's refresh your knowledge of the fraud: what is it, for which you need, what kinds of them are and how to make various arithmetic acts with them. By fractions in mathematics are called numbers, each of which consists of one or more parts of the unit. Such fractions are also called ordinary or simple. As a rule, they are written in the form of two numbers, which are separated by a horizontal or slash, it is called "fractional". For example: ½, ¾. The top, or the first of these numbers, is a numerator (shows how much a fraction is taken from the number), and the bottom, or the second - the denominator (demonstrates, the unit is divided into as many parts). Fractional feature actually performs fission sign functions. For example, 7: 9 \u003d 7/9 Traditionally ordinary fractions less than one. While decimal can be more her. What are the fractions for? Yes, for everything, because in the real world, not all numbers are whole. For example, two schoolgirls in the dining room bought one delicious chocolate in a fold. When they already gathered to share the dessert, met a girlfriend and decided to treat it and and her. However, now it is necessary to correctly divide the chocolate chip, if we consider that it consists of 12 squares. At first, girls wanted to divide everything equally, and then each would get four pieces. But, in thought, they decided to treat a girlfriend, not 1/3, and 1/4 chocolates. And since schoolgirls were poorly studied the fraction, they did not take into account that with a similar situation as a result they will remain 9 pieces that are very poorly divided into two. This rather simple example shows how important it is to be able to correctly find a part of the number. But in the life of such cases much more. All mathematical fractions are divided into two big discharges: ordinary and decimal. The features of the first of them were told in the previous paragraph, so now it is worth paying attention to the second. The decimal is called the position of the chimney of the number, which is fixed on the letter through the comma, without dash or slash. For example: 0.75, 0.5. In fact, the decimal fraction is identical to ordinary, however, in its denominator there is always a unit with subsequent zeros - from here there was also its name. The number preceding the comma is a whole part, and all after - fractional. Any simple fraction can be translated into a decimal. So, the decimal fractions specified in the previous example can be written as ordinary: ¾ and ½. It is worth noting that decimal and ordinary fractions can be both positive and negative. If there is a sign "-", this fraction is negative, if "+" is positive. There are such types of fractions of simple. Unlike a simple, decimal fraction shares only 2 types. Conduct various arithmetic manipulations with fractions a little more complicated than with ordinary numbers. However, if you assimilate the basic rules, it will not be much difficult to solve any example. For example: 2/3 + 3/4. The smallest common multiple for them will be 12, therefore, it is necessary that this number stands in each denominator. To do this, the numerator and denominator of the first fraction is multiplying by 4, it turns out to be 8/12, but I am going with the second term, but only multiply by 3 - 9/12. Now you can easily solve an example: 8/12 + 9/12 \u003d 17/12. The resulting fraction is an incorrect value, since the numerator is greater than the denominator. Its one can and should be predicted into the correct mixed, separating 17: 12 \u003d 1 and 5/12. In the event that mixed fractions are composed, first actions are performed with integers, and then with fractional. If an example is present a decimal fraction and usual, it is necessary that both become simple, then bring them to one denominator and fold. For example, 3.1 + 1/2. The number 3.1 can be written as mixed fraction 3 and 1/10 or as incorrect - 31/10. The total denominator for the terms will be 10, so you need to multiply the numerator alternately and the denominator 1/2 to 5, it turns out 5/10. Next, you can easily calculate everything: 31/10 + 5/10 \u003d 35/10. The result obtained is an incorrect cutting fraction, bring it into a normal form, reducing to 5: 7/2 \u003d 3 and 1/2, or decimal - 3.5. If we seen 2. decimal fractions, It is important that after the comma had the same number of numbers. If this is not the case, you just need to add the required number of zeros, because in the decimal fraction it can be made painlessly. For example, 3.5 + 3.005. To solve this task, it is necessary to add 2 zero to the first number and then alternately seen: 3,500 + 3.005 \u003d 3.505. Summary of the fraction, it is worth acting as well as when adding: to reduce to a common denominator, to take one numerator from another, if necessary, translate the result in a mixed fraction. For example: 16 / 20-5 / 10. The total denominator will be 20. It is necessary to bring the second fraction to this denominator, multiplying both of its parts by 2, it turns out 10/20. Now you can solve an example: 16/20-10 / 20 \u003d 6/20. However, this result refers to the reduced fractions, therefore it is worth sharing both parts by 2 and the result is 3/10. Decision and multiplication of fractions are significantly simpler actions, rather than addition and subtraction. The fact is that by performing these tasks, there is no need to look for a common denominator. To multiply the fraction, it is necessary to simply multiply between any numerator, and then both denominator. The resulting result is reduced if the fraction is a reduced value. For example: 4 / 9x5 / 8. After alternate multiplication, such a result is 4x5 / 9x8 \u003d 20/72. Such a fraction is reduced by 4, so the final answer in Example is 5/18. The division of fractions is also an easy effect, in fact it still comes down to their multiplication. To split one fraction to another, you need to turn the second and multiply to the first. For example, dividing fractions 5/19 and 5/7. To solve an example, you need to swap a denominator and the second fraction numerator and multiply: 5 / 19x7 / 5 \u003d 35/95. The result can be reduced by 5 - it turns out 7/19. In case it is necessary to divide the fraction on a simple number, the technique is slightly different. Initially, it is worth writing this number as an irregular fraction, and then divide by the same scheme. For example, 2/13: 5 need to write as 2/13: 5/1. Now you need to flip 5/1 and multiply the resulting fractions: 2 / 13x1 / 5 \u003d 2/65. Sometimes you have to make division of frains of mixed. They need to do, as with whole numbers: turn into incorrect fractions turn the divider and multiply everything. For example, 8 ½: 3. We turn everything into incorrect fractions: 17/2: 3/1. Next follows the coup 3/1 and the multiplication: 17 / 2x1 / 3 \u003d 17/6. Now it is necessary to translate the wrong fraction in the correct - 2 whole and 5/6. So, understanding that such a fraction is and as possible with them to make various arithmetic actions, you need to try not to forget about it. After all, people are always more inclined to share something on the part, rather than add, so you need to be able to do it right.Positive and negative fractions
Actions with fractions
Her Majesty fraction: what is what
Types of fractions: Ordinary and decimal
Subspecies of ordinary fractions
Subspecies decimal fractions
Adopting fractions
Subtraction of fractions
Multiplication of fractions
How to share the fraci
