Almost every fifth grader is a little shocked after their first acquaintance with ordinary fractions. Not only do you need to understand the essence of fractions, but you also have to perform arithmetic operations with them. After this, the little students will systematically interrogate their teacher to find out when these fractions will end.
To avoid such situations, it is enough just to explain this difficult topic to children as simply as possible, and preferably in a playful way.
The essence of a fraction
Before learning what a fraction is, a child must become familiar with the concept share . The associative method is best suited here.
Imagine a whole cake that is divided into several equal parts, say four. Then each piece of the cake can be called a share. If you take one of the four pieces of cake, it will be one-fourth.
The shares are different, because the whole can be divided into a completely different number of parts. The more shares in general, the smaller they are, and vice versa.
So that the shares could be designated, they came up with such a mathematical concept as common fraction. The fraction will allow us to write down as many shares as needed.
The components of a fraction are the numerator and denominator, which are separated by a fraction line or a slash. Many children do not understand their meaning, and therefore the essence of the fraction is not clear to them. The fractional line indicates division, there is nothing complicated here.
It is customary to write the denominator below, under the fractional line or to the right of the forward line. It shows the number of parts of a whole. The numerator, it is written above the fraction line or to the left of the forward line, determines how many shares were taken. For example, the fraction 4/7. In this case, 7 is the denominator, showing that there are only 7 shares, and the numerator 4 indicates that four of the seven shares were taken.
Main shares and their writing in fractions:
In addition to the ordinary fraction, there is also a decimal fraction.
Operations with fractions 5th grade
In the fifth grade they learn to perform all arithmetic operations with fractions.
All operations with fractions are performed according to the rules, and you should not hope that without learning the rule everything will work out on its own. Therefore, you should not neglect the oral part of your math homework.
We have already understood that the notation of a decimal and an ordinary fraction is different, therefore arithmetic operations will be performed differently. Actions with ordinary fractions depend on the numbers that are in the denominator, and in the decimal - after the decimal point to the right.
For fractions that have the same denominators, the algorithm for addition and subtraction is very simple. We perform actions only with numerators.
For fractions with different denominators you need to find Least Common Denominator (LCD). This is the number that will be divisible by all denominators without a remainder, and will be the smallest of such numbers if there are several of them.
To add or subtract decimal fractions, you need to write them in a column, with a comma under the comma, and equalize the number of decimal places if required.
To multiply ordinary fractions, simply find the product of the numerators and denominators. A very simple rule.
The division is performed according to the following algorithm:
- Write the dividend unchanged
- Turn division into multiplication
- Reverse the divisor (write the reciprocal fraction to the divisor)
- Perform multiplication
Addition of fractions, explanation
Let's take a closer look at how to add fractions and decimals.
As you can see in the image above, the fraction one third and two thirds has a common denominator of three. This means that you only need to add the numerators one and two, and leave the denominator unchanged. The result is a sum of three thirds. This answer, when the numerator and denominator of the fraction are equal, can be written as 1, since 3:3 = 1.
You need to find the sum of the fractions two thirds and two ninths. In this case, the denominators are different, 3 and 9. To perform addition, you need to find a common one. There is a very simple way. We choose the largest denominator, it is 9. We check whether it is divisible by 3. Since 9:3 = 3 without a remainder, therefore 9 is suitable as a common denominator.
The next step is to find additional factors for each numerator. To do this, we divide the common denominator 9 by the denominator of each fraction in turn, the resulting numbers will be additional. plural For the first fraction: 9:3 = 3, add 3 to the numerator of the first fraction. For the second fraction: 9:9 = 1, you don’t have to add one, since when multiplied by it you get the same number.
Now we multiply the numerators by their additional factors and add the results. The resulting amount is a fraction of eight-ninths.
Adding decimals follows the same rule as adding natural numbers. In a column, the digit is written under the digit. The only difference is that in decimal fractions you need to place the correct comma in the result. To do this, fractions are written with a comma under the comma, and in the total you only need to move the comma down.
Let's find the sum of the fractions 38, 251 and 1, 56. To make it more convenient to perform the actions, we equalized the number of decimal places on the right by adding 0.
Add fractions without paying attention to the comma. And in the resulting amount we simply lower the comma down. Answer: 39, 811.
Subtracting fractions, explanation
To find the difference between the fractions two-thirds and one-third, you need to calculate the difference of the numerators 2-1 = 1, and leave the denominator unchanged. The answer gives a difference of one third.
Let's find the difference between the fractions five-sixths and seven-tenths. Finding a common denominator. We use the selection method, from 6 and 10 the largest is 10. We check: 10: 6 is not divisible without a remainder. We add another 10, it turns out 20:6, which is also not divisible without a remainder. Again we increase by 10, we get 30:6 = 5. The common denominator is 30. Also, the NOZ can be found using the multiplication table.
Finding additional factors. 30:6 = 5 - for the first fraction. 30:10 = 3 - for the second. We multiply the numerators and their additional multiplicities. We get the minuend 25/30 and the subtract 21/30. Next, we subtract the numerators and leave the denominator unchanged.
The result was a difference of 4/30. The fraction is reducible. Divide it by 2. The answer is 2/15.
Dividing decimals grade 5
This topic discusses two options:
Multiplying decimals grade 5
Remember how you multiply natural numbers, in exactly the same way you find the product of decimal fractions. First, let's figure out how to multiply a decimal fraction by a natural number. For this:
When multiplying a decimal fraction by a decimal, we act in exactly the same way.
Mixed Fractions Grade 5
Fifth graders like to call such fractions not mixed, but<<смешные>>It's probably easier to remember this way. Mixed fractions are so called because they are made by combining a whole natural number and an ordinary fraction.
A mixed fraction consists of an integer and a fractional part.
When reading such fractions, first they name the whole part, then the fractional part: one whole two thirds, two whole one fifth, three whole two fifths, four point three quarters.
How are they obtained, these mixed fractions? It's quite simple. When we receive an improper fraction in an answer (a fraction whose numerator is greater than the denominator), we must always convert it to a mixed fraction. It is enough to divide the numerator by the denominator. This action is called selecting an entire part:
Converting a mixed fraction back to an improper fraction is also easy:
Examples with decimal fractions grade 5 with explanation
Examples of several actions raise many questions in children. Let's look at a couple of such examples.
(0.4 8.25 - 2.025) : 0.5 =
The first step is to find the product of the numbers 8.25 and 0.4. We perform multiplication according to the rule. In the answer, count three digits from right to left and put a comma.
The second action is there in brackets, this is the difference. From 3,300 we subtract 2,025. We record the action in a column with a comma under the comma.
The third action is division. The resulting difference in the second step is divided by 0.5. The comma is moved one place. Result 2.55.
Answer: 2.55.
(0, 93 + 0, 07) : (0, 93 — 0, 805) =
The first step is the amount in brackets. Add it in a column, remember that the comma is under the comma. We get the answer 1.00.
The second action is the difference from the second bracket. Since the minuend has fewer decimal places than the subtrahend, we add the missing one. The result of the subtraction is 0.125.
The third step is to divide the sum by the difference. The comma is moved three places. The result is a division of 1000 by 125.
Answer: 8.
Examples with ordinary fractions with different denominators grade 5 with explanation
In the first In this example, we find the sum of the fractions 5/8 and 3/7. The common denominator will be the number 56. Find additional factors, divide 56:8 = 7 and 56:7 = 8. Add them to the first and second fractions, respectively. We multiply the numerators and their factors, we get the sum of the fractions 35/56 and 24/56. The result was 59/56. The fraction is improper, we convert it to a mixed number. The remaining examples are solved similarly.
Examples with fractions grade 5 for training
For convenience, convert mixed fractions to improper fractions and perform the operations.
How to teach your child to solve fractions easily using Legos
With the help of such a constructor, you can not only develop a child’s imagination, but also explain clearly in a playful way what a share and a fraction are.
The picture below shows that one part with eight circles is a whole. This means that if you take a puzzle with four circles, you get half, or 1/2. The picture clearly shows how to solve examples with Lego, if you count the circles on the parts.
You can build towers from a certain number of parts and label each of them, as in the picture below. For example, let's take a seven-piece turret. Each piece of the green construction set will be 1/7. If you add two more to one such part, you get 3/7. A visual explanation of the example 1/7+2/7 = 3/7.
To get A's in math, don't forget to learn the rules and practice them.
Fraction- a form of representing a number in mathematics. The fraction bar denotes the division operation. Numerator fraction is called the dividend, and denominator- divider. For example, in a fraction the numerator is 5 and the denominator is 7.
Correct A fraction is called in which the modulus of the numerator is greater than the modulus of the denominator. If a fraction is proper, then the modulus of its value is always less than 1. All other fractions are wrong.
The fraction is called mixed, if it is written as an integer and a fraction. This is the same as the sum of this number and the fraction:
The main property of a fraction
If the numerator and denominator of a fraction are multiplied by the same number, then the value of the fraction will not change, that is, for example,
Reducing fractions to a common denominator
To bring two fractions to a common denominator, you need:
- Multiply the numerator of the first fraction by the denominator of the second
- Multiply the numerator of the second fraction by the denominator of the first
- Replace the denominators of both fractions with their product
Operations with fractions
Addition. To add two fractions you need
- Add the new numerators of both fractions and leave the denominator unchanged
Example:
Subtraction. To subtract one fraction from another, you need
- Reduce fractions to a common denominator
- Subtract the numerator of the second from the numerator of the first fraction, and leave the denominator unchanged
Example:
Multiplication. To multiply one fraction by another, multiply their numerators and denominators.
In the 5th grade of secondary school, the representation of fractions is introduced. A fraction is a number made up of a whole number of fractions of units. Ordinary fractions are written in the form ±m/n, the number m is called the numerator of the fraction, and the number n is its denominator. If the modulus of the denominator is larger than the modulus of the numerator, say 3/4, then the fraction is called a correct fraction; otherwise, it is called an improper fraction. A fraction can contain an entire part, say 5 * (2/3). Various arithmetic operations can be used with fractions.
Instructions
1. Reduction to a universal denominator. Let the fractions a/b and c/d be given. - First of all, find the LCM number (smallest universal multiple) for the denominators of the fractions. - The numerator and denominator of the first fraction are multiplied by the LCM/b - Numerator and denominator of the 2nd fractions are multiplied by LCM/d An example is shown in the figure. To compare fractions, they need to be reduced to a common denominator, then compare the numerators. Let's say 3/4< 4/5, см. рисунок.
2. Addition and subtraction of fractions. To find the sum of 2 ordinary fractions, they need to be reduced to a common denominator, then add the numerators, leaving the denominator unchanged. An example of adding fractions 1/2 and 1/3 is shown in the figure. The difference of fractions is found in a similar way, after finding the common denominator, the numerators of the fractions are subtracted, see the example in the figure.
3. Multiplication and division of fractions. When multiplying ordinary fractions, the numerators and denominators are multiplied together. In order to divide two fractions, you need to get the reciprocal of the 2nd fraction, i.e. swap its numerator and denominator, then multiply the resulting fractions.
Module represents the unconditional value of the expression. Straight brackets are used to denote a module. The values in them are considered modulo. Solving a module consists of expanding the modular brackets according to certain rules and finding the set of expression values. In most cases, the module is expanded in such a way that the submodular expression receives a number of positive and negative values, including a zero value. Based on these properties of the module, further equations and inequalities of the initial expression are compiled and solved.
Instructions
1. Write down the initial equation with modulus. To solve it, expand the module. Look at every submodular expression. Determine at what value of the unknown quantities included in it the expression in modular brackets becomes zero.
2. To do this, equate the submodular expression to zero and find the solution to the resulting equation. Record the detected values. In the same way, determine the values of the unknown variable for the entire module in the given equation.
3. Consider cases of existence of variables when they are good from zero. To do this, write down a system of inequalities for all modules of the initial equation. Inequalities must cover all valid values of a variable on the number line.
4. Draw a number line and plot the resulting values on it. The values of the variable in the zero module will serve as constraints when solving the modular equation.
5. In the initial equation, you need to open the modular brackets, changing the sign of the expression so that the values of the variable correspond to those displayed on the number line. Solve the resulting equation. Check the detected variable value against the limit specified by the module. If the solution satisfies the condition, then it is true. Roots that do not satisfy the restrictions must be discarded.
6. In the same way, expand the modules of the initial expression taking into account the sign and calculate the roots of the resulting equation. Write down all the resulting roots that satisfy the constraint inequalities.
Fractional numbers allow you to express the exact value of a quantity in various forms. You can perform the same mathematical operations with fractions as with whole numbers: subtraction, addition, multiplication and division. In order to learn to decide fractions, you need to remember some of their features. They depend on the type fractions, the presence of a whole part, a common denominator. Some arithmetic operations later require the reduction of the fractional part of the total.
You will need
- - calculator
Instructions
1. Look closely at these numbers. If among the fractions there are decimals and irregular ones, sometimes it is more convenient to first perform operations with decimals, and then convert them to the incorrect form. Can you translate fractions in this form initially, writing the value after the comma in the numerator and putting 10 in the denominator. If necessary, reduce the fraction by dividing the numbers above and below the line by one divisor. Reduce fractions in which the whole part is given to the wrong form by multiplying it by the denominator and adding the numerator to the total. This value will become the new numerator fractions. In order to select an entire part from the initially incorrect one fractions, you need to divide the numerator by the denominator. Write the whole total to the left of fractions. And the remainder of the division will become the new numerator, denominator fractions it does not change. For fractions with an integer part, it is permissible to perform actions separately, first for the integer part, and then for the fractional parts. Let's say the sum is 1 2/3 and 2? can be calculated by two methods: - Converting fractions to the wrong form: - 1 2/3 + 2 ? = 5/3 + 11/4 = 20/12 + 33/12 = 53/12 = 4 5/12; - Summing separately the integer and fractional parts of the terms: - 1 2/3 + 2? = (1+2) + (2/3 + ?) = 3 +(8/12 + 9/12) = 3 + 17/12 = 3 + 1 5/12 = 4 5/12.
2. For improper fractions with different values, find the common denominator below the line. Say, for 5/9 and 7/12 the common denominator will be 36. For this, the numerator and denominator of the first fractions you need to multiply by 4 (it turns out 28/36), and the 2nd - by 3 (it turns out 15/36). Now you can perform the necessary calculations.
3. If you are going to calculate the sum or difference of fractions, first write down the discovered common denominator under the line. Perform the necessary actions between the numerators, and write the result above the new line fractions. Thus, the new numerator will be the difference or the sum of the numerators of the original fractions.
4. To calculate the product of fractions, multiply the numerators of the fractions and write the total in place of the numerator of the final fractions. Do the same for the denominators. When dividing one fractions write down one fraction for another, and then multiply its numerator by the denominator of the 2nd. In this case, the denominator of the first fractions multiplied accordingly by the 2nd numerator. In this case, an original revolution occurs 2nd fractions(divisor). The final fraction will consist of the results of multiplying the numerators and denominators of both fractions. It's not hard to learn how to solve fractions, written in the condition in the form of “four-story” fractions. If a line separates two fractions, rewrite them using the delimiter “:” and continue with ordinary division.
5. To obtain the final total, reduce the resulting fraction by dividing the numerator and denominator by one whole number, the largest permissible in this case. In this case, above and below the line must be integers.
Note!
Do not perform arithmetic operations with fractions whose denominators are different. Choose a number such that when you multiply the numerator and denominator of any fraction by it, the denominators of both fractions end up being equal.
Helpful advice
When writing fractional numbers, the dividend is written above the line. This quantity is designated as the numerator of the fraction. The divisor or denominator of the fraction is written under the line. Let's say, one and a half kilograms of rice in the form of a fraction will be written as follows: 1? kg rice. If the denominator of a fraction is 10, the fraction is called a decimal. In this case, the numerator (dividend) is written to the right of the whole part, separated by a comma: 1.5 kg of rice. For the convenience of calculations, such a fraction can invariably be written in the wrong form: 1 2/10 kg of potatoes. To make things easier, you can reduce the values of the numerator and denominator by dividing them by one integer. In this example, division by 2 is acceptable. The result will be 1 1/5 kg of potatoes. Make sure that the numbers you are going to perform arithmetic with are presented in the same form.
If you are writing a term paper or composing some other document containing a calculation part, then you cannot escape fractional expressions, which also need to be printed. Let's look at how to do this further.
Instructions
1. Click once on the “Insert” menu item, then select “Symbol”. This is one of the most primitive insertion methods fractions into the text. It concludes further. The set of ready-made symbols includes fractions. Their number, as usual, is small, but if you need to write ? in the text, and not 1/2, then a similar option will be the most optimal for you. In addition, the number of fraction characters may depend on the font. For example, for the Times New Roman font there are slightly fewer fractions than for the same Arial. Vary fonts to find the best option when it comes to primitive expressions.
2. Click on the “Insert” menu item and select the “Object” sub-item. A window will appear in front of you with a list of acceptable objects for insertion. Choose among them Microsoft Equation 3.0. This app will help you type fractions. And not only fractions, but also difficult mathematical expressions containing various trigonometric functions and other elements. Double-click on this object with the left mouse button. A window will appear in front of you containing many symbols.
3. To print a fraction, select the symbol representing a fraction with an empty numerator and denominator. Click on it once with the left mouse button. An additional menu will appear, clarifying the scheme itself. fractions. There may be several options. Select the one that is especially suitable for you and click on it once with the left mouse button.
4. Enter in numerator and denominator fractions all necessary data. This will flow more easily on the document sheet. The fraction will be inserted as a separate object, one that, if necessary, can be moved to any place in the document. You can print multi-story fractions. To do this, place in the numerator or denominator (as you need) another fraction, which you can choose in the window of the same application.
Video on the topic
An algebraic fraction is an expression of the form A/B, where the letters A and B stand for any number or letter expressions. Often the numerator and denominator in algebraic fractions have a massive form, but operations with such fractions should be done according to the same rules as actions with ordinary ones, where the numerator and denominator are regular integers.
Instructions
1. If given mixed fractions, convert them to irregular fractions (a fraction in which the numerator is larger than the denominator): multiply the denominator by the whole part and add the numerator. So the number 2 1/3 will turn into 7/3. To do this, multiply 3 by 2 and add one.
2. If you need to convert a decimal to an improper fraction, think of it as dividing a number without a decimal point by one with as many zeros as there are numbers after the decimal point. Let's say, imagine the number 2.5 as 25/10 (if you shorten it, you get 5/2), and the number 3.61 - as 361/100. Operating with improper fractions is often easier than with mixed or decimal fractions.
3. If fractions have identical denominators and you need to add them, then simply add the numerators; the denominators remain unchanged.
4. If you need to subtract fractions with identical denominators, subtract the numerator of the 2nd fraction from the numerator of the first fraction. The denominators also do not change.
5. If you need to add fractions or subtract one fraction from another, and they have different denominators, reduce the fractions to a common denominator. To do this, find a number that will be the least universal multiple (LCM) of both denominators or several if the fractions are larger than 2. LCM is a number that will be divided into the denominators of all given fractions. For example, for 2 and 5 this number is 10.
6. After the equal sign, draw a horizontal line and write this number (NOC) into the denominator. Add additional factors to each term - the number by which you need to multiply both the numerator and the denominator in order to get the LCM. Multiply the numerators step by step by additional factors, preserving the sign of addition or subtraction.
7. Calculate the total, reduce it if necessary, or select the entire part. For example, do you need to fold it? And?. The LCM for both fractions is 12. Then the additional factor for the first fraction is 4, for the 2nd fraction - 3. Total: ?+?=(1·4+1·3)/12=7/12.
8. If an example is given for multiplication, multiply the numerators together (this will be the numerator of the total) and the denominators (this will be the denominator of the total). In this case, there is no need to reduce them to a common denominator.
9. To divide a fraction by a fraction, you need to turn the second fraction upside down and multiply the fractions. That is, a/b: c/d = a/b · d/c.
10. Factor the numerator and denominator as needed. For example, move the universal factor out of the bracket or expand it according to abbreviated multiplication formulas, so that after this you can, if necessary, reduce the numerator and denominator by GCD - the minimum universal divisor.
Note!
Add numbers with numbers, letters of the same kind with letters of the same kind. Let's say it is impossible to add 3a and 4b, which means that their sum or difference will remain in the numerator - 3a±4b.
Video on the topic
To express a part as a fraction of the whole, you need to divide the part into the whole.
Task 1. There are 30 students in the class, four are absent. What proportion of students are absent?
Solution:
Answer: There are no students in the class.
Finding a fraction from a number
To solve problems in which you need to find a part of a whole, the following rule applies:
If a part of a whole is expressed as a fraction, then to find this part, you can divide the whole by the denominator of the fraction and multiply the result by its numerator.
Task 1. There were 600 rubles, this amount was spent. How much money did you spend?
Solution: to find 600 rubles or more, we need to divide this amount into 4 parts, thereby we will find out how much money one fourth part is:
600: 4 = 150 (r.)
Answer: spent 150 rubles.
Task 2. There were 1000 rubles, this amount was spent. How much money was spent?
Solution: from the problem statement we know that 1000 rubles consists of five equal parts. First, let’s find how many rubles are one-fifth of 1000, and then we’ll find out how many rubles are two-fifths:
1) 1000: 5 = 200 (r.) - one fifth.
2) 200 · 2 = 400 (r.) - two fifths.
These two actions can be combined: 1000: 5 · 2 = 400 (r.).
Answer: 400 rubles were spent.
The second way to find a part of a whole:
To find a part of a whole, you can multiply the whole by the fraction expressing that part of the whole.
Task 3. According to the charter of the cooperative, for the reporting meeting to be valid, at least at least members of the organization must be present. The cooperative has 120 members. What composition can a reporting meeting take place?
Solution: 
Answer: the reporting meeting can take place if there are 80 members of the organization.
Finding a number by its fraction
To solve problems in which you need to find a whole from its part, the following rule applies:
If part of the desired whole is expressed as a fraction, then to find this whole, you can divide this part by the numerator of the fraction and multiply the result by its denominator.
Task 1. We spent 50 rubles, which was less than the original amount. Find the original amount of money.
Solution: from the description of the problem we see that 50 rubles is 6 times less than the original amount, i.e. the original amount is 6 times more than 50 rubles. To find this amount, you need to multiply 50 by 6:
50 · 6 = 300 (r.)
Answer: the initial amount is 300 rubles.
Task 2. We spent 600 rubles, which was less than the original amount of money. Find the original amount.
Solution: We will assume that the required number consists of three thirds. According to the condition, two-thirds of the number equals 600 rubles. First, let's find one third of the original amount, and then how many rubles are three thirds (the original amount):
1) 600: 2 3 = 900 (r.)
Answer: the initial amount is 900 rubles.
The second way to find a whole from its part:
To find a whole by the value expressing its part, you can divide this value by the fraction expressing this part.
Task 3. Line segment AB, equal to 42 cm, is the length of the segment CD. Find the length of the segment CD.
Solution: 
Answer: segment length CD 70 cm.
Task 4. Watermelons were brought to the store. Before lunch, the store sold the watermelons it brought, and after lunch, there were 80 watermelons left to sell. How many watermelons did you bring to the store?
Solution: First, let’s find out what part of the brought watermelons is the number 80. To do this, let’s take the total number of watermelons brought as one and subtract from it the number of watermelons that were sold (sold):
And so, we learned that 80 watermelons make up the total number of watermelons brought. Now we find out how many watermelons from the total amount make up, and then how many watermelons make up (the number of watermelons brought):
2) 80: 4 15 = 300 (watermelons)
Answer: In total, 300 watermelons were brought to the store.
Multiplying and dividing fractions.
Attention!
There are additional
materials in Special Section 555.
For those who are very "not very..."
And for those who “very much…”)
This operation is much nicer than addition-subtraction! Because it's easier. As a reminder, to multiply a fraction by a fraction, you need to multiply the numerators (this will be the numerator of the result) and the denominators (this will be the denominator). That is:
For example:
Everything is extremely simple. And please don't look for a common denominator! There is no need for him here...
To divide a fraction by a fraction, you need to reverse second(this is important!) fraction and multiply them, i.e.:
For example:
If you come across multiplication or division with integers and fractions, it’s okay. As with addition, we make a fraction from a whole number with one in the denominator - and go ahead! For example:
In high school, you often have to deal with three-story (or even four-story!) fractions. For example:
How can I make this fraction look decent? Yes, very simple! Use two-point division:
But don't forget about the order of division! Unlike multiplication, this is very important here! Of course, we will not confuse 4:2 or 2:4. But it’s easy to make a mistake in a three-story fraction. Please note for example:
In the first case (expression on the left):
In the second (expression on the right):
Do you feel the difference? 4 and 1/9!
What determines the order of division? Either with brackets, or (as here) with the length of horizontal lines. Develop your eye. And if there are no brackets or dashes, like:
then divide and multiply in order, from left to right!
And another very simple and important technique. In actions with degrees, it will be so useful to you! Let's divide one by any fraction, for example, by 13/15:
The shot has turned over! And this always happens. When dividing 1 by any fraction, the result is the same fraction, only upside down.
That's it for operations with fractions. The thing is quite simple, but it gives more than enough errors. Take practical advice into account, and there will be fewer of them (mistakes)!
Practical tips:
1. The most important thing when working with fractional expressions is accuracy and attentiveness! These are not general words, not good wishes! This is a dire necessity! Do all calculations on the Unified State Exam as a full-fledged task, focused and clear. It’s better to write two extra lines in your draft than to mess up when doing mental calculations.
2. In examples with different types of fractions, we move on to ordinary fractions.
3. We reduce all fractions until they stop.
4. We reduce multi-level fractional expressions to ordinary ones using division through two points (we follow the order of division!).
5. Divide a unit by a fraction in your head, simply turning the fraction over.
Here are the tasks that you must definitely complete. Answers are given after all tasks. Use the materials on this topic and practical tips. Estimate how many examples you were able to solve correctly. The first time! Without a calculator! And draw the right conclusions...
Remember - the correct answer is received from the second (especially the third) time does not count! Such is the harsh life.
So, solve in exam mode ! This is already preparation for the Unified State Exam, by the way. We solve the example, check it, solve the next one. We decided everything - checked again from first to last. But only Then look at the answers.
Calculate:
Have you decided?
We are looking for answers that match yours. I deliberately wrote them down in disarray, away from temptation, so to speak... Here they are, the answers, written with semicolons.
0; 17/22; 3/4; 2/5; 1; 25.
Now we draw conclusions. If everything worked out, I’m happy for you! Basic calculations with fractions are not your problem! You can do more serious things. If not...
So you have one of two problems. Or both at once.) Lack of knowledge and (or) inattention. But this solvable Problems.
If you like this site...
By the way, I have a couple more interesting sites for you.)
You can practice solving examples and find out your level. Testing with instant verification. Let's learn - with interest!)
You can get acquainted with functions and derivatives.
