On the this lesson addition and subtraction will be considered algebraic fractions with different denominators. We already know how to add and subtract common fractions with different denominators. To do this, the fractions must be reduced to common denominator. It turns out that algebraic fractions follow the same rules. At the same time, we already know how to reduce algebraic fractions to a common denominator. Adding and subtracting fractions with different denominators is one of the most important and difficult topics in the 8th grade course. Wherein this topic will be found in many of the topics of the algebra course that you will study in the future. As part of the lesson, we will study the rules for adding and subtracting algebraic fractions with different denominators, and also analyze whole line typical examples.

Consider the simplest example for common fractions.

Example 1 Add fractions: .

Decision:

Remember the rule for adding fractions. To begin with, fractions must be reduced to a common denominator. The common denominator for ordinary fractions is least common multiple(LCM) of the original denominators.

Definition

The smallest natural number that is divisible by both numbers and .

To find the LCM, it is necessary to expand the denominators into prime factors, and then choose all the prime factors that are included in the expansion of both denominators.

; . Then the LCM of numbers must include two 2s and two 3s: .

After finding the common denominator, it is necessary to find an additional factor for each of the fractions (in fact, divide the common denominator by the denominator of the corresponding fraction).

Then each fraction is multiplied by the resulting additional factor. We get fractions with the same denominators, which we learned to add and subtract in previous lessons.

We get: .

Answer:.

Consider now the addition of algebraic fractions with different denominators. First consider fractions whose denominators are numbers.

Example 2 Add fractions: .

Decision:

The solution algorithm is absolutely similar to the previous example. It is easy to find a common denominator for these fractions: and additional factors for each of them.

.

Answer:.

So let's formulate algorithm for adding and subtracting algebraic fractions with different denominators:

1. Find the smallest common denominator of fractions.

2. Find additional factors for each of the fractions (by dividing the common denominator by the denominator of this fraction).

3. Multiply the numerators by the appropriate additional factors.

4. Add or subtract fractions using the rules for adding and subtracting fractions with the same denominators.

Consider now an example with fractions whose denominator contains literal expressions.

Example 3 Add fractions: .

Decision:

Since the literal expressions in both denominators are the same, you should find a common denominator for numbers. The final common denominator will look like: . So the solution this example looks like:.

Answer:.

Example 4 Subtract fractions: .

Decision:

If you can’t “cheat” when choosing a common denominator (you can’t factor it or use the abbreviated multiplication formulas), then you have to take the product of the denominators of both fractions as a common denominator.

Answer:.

In general, when deciding similar examples, most difficult task is to find a common denominator.

Let's look at a more complex example.

Example 5 Simplify: .

Decision:

When finding a common denominator, you must first try to factorize the denominators of the original fractions (to simplify the common denominator).

In this particular case:

Then it is easy to determine the common denominator: .

We determine additional factors and solve this example:

Answer:.

Now we will fix the rules for adding and subtracting fractions with different denominators.

Example 6 Simplify: .

Decision:

Answer:.

Example 7 Simplify: .

Decision:

.

Answer:.

Consider now an example in which not two, but three fractions are added (after all, the rules for addition and subtraction for more fractions remain the same).

Example 8 Simplify: .

Consider the fraction $\frac63$. Its value is 2, since $\frac63 =6:3 = 2$. What happens if the numerator and denominator are multiplied by 2? $\frac63 \times 2=\frac(12)(6)$. Obviously, the value of the fraction has not changed, so $\frac(12)(6)$ is also equal to 2 as y. multiply the numerator and denominator by 3 and get $\frac(18)(9)$, or by 27 and get $\frac(162)(81)$ or by 101 and get $\frac(606)(303)$. In each of these cases, the value of the fraction that we get by dividing the numerator by the denominator is 2. This means that it has not changed.

The same pattern is observed in the case of other fractions. If the numerator and denominator of the fraction $\frac(120)(60)$ (equal to 2) is divided by 2 (result of $\frac(60)(30)$), or by 3 (result of $\frac(40)(20) $), or by 4 (the result of $\frac(30)(15)$) and so on, then in each case the value of the fraction remains unchanged and equal to 2.

This rule also applies to fractions that are not equal. whole number.

If the numerator and denominator of the fraction $\frac(1)(3)$ are multiplied by 2, we get $\frac(2)(6)$, that is, the value of the fraction has not changed. And in fact, if you divide the cake into 3 parts and take one of them, or divide it into 6 parts and take 2 parts, you will get the same amount of pie in both cases. Therefore, the numbers $\frac(1)(3)$ and $\frac(2)(6)$ are identical. Let's formulate a general rule.

The numerator and denominator of any fraction can be multiplied or divided by the same number, and the value of the fraction does not change.

This rule is very useful. For example, it allows in some cases, but not always, to avoid operations with large numbers.

For example, we can divide the numerator and denominator of the fraction $\frac(126)(189)$ by 63 and get the fraction $\frac(2)(3)$ which is much easier to calculate. One more example. We can divide the numerator and denominator of the fraction $\frac(155)(31)$ by 31 and get the fraction $\frac(5)(1)$ or 5, since 5:1=5.

In this example, we first encountered a fraction whose denominator is 1. Such fractions play important role when calculating. It should be remembered that any number can be divided by 1 and its value will not change. That is, $\frac(273)(1)$ is equal to 273; $\frac(509993)(1)$ equals 509993 and so on. Therefore, we do not have to divide numbers by , since every integer can be represented as a fraction with a denominator of 1.

With such fractions, the denominator of which is equal to 1, it is possible to produce the same arithmetic operations, as with all other fractions: $\frac(15)(1)+\frac(15)(1)=\frac(30)(1)$, $\frac(4)(1) \times \frac (3)(1)=\frac(12)(1)$.

You may ask what is the use of representing an integer as a fraction, which will have a unit under the bar, because it is more convenient to work with an integer. But the fact is that the representation of an integer as a fraction allows us to more efficiently produce various activities when we are dealing with both integers and fractional numbers at the same time. For example, to learn add fractions with different denominators. Suppose we need to add $\frac(1)(3)$ and $\frac(1)(5)$.

We know that you can only add fractions whose denominators are equal. So, we need to learn how to bring fractions to such a form when their denominators are equal. In this case, we again need the fact that you can multiply the numerator and denominator of a fraction by the same number without changing its value.

First, we multiply the numerator and denominator of the fraction $\frac(1)(3)$ by 5. We get $\frac(5)(15)$, the value of the fraction has not changed. Then we multiply the numerator and denominator of the fraction $\frac(1)(5)$ by 3. We get $\frac(3)(15)$, again the value of the fraction has not changed. Therefore, $\frac(1)(3)+\frac(1)(5)=\frac(5)(15)+\frac(3)(15)=\frac(8)(15)$.

Now let's try to apply this system to the addition of numbers containing both integer and fractional parts.

We need to add $3 + \frac(1)(3)+1\frac(1)(4)$. First, we convert all the terms into fractions and get: $\frac31 + \frac(1)(3)+\frac(5)(4)$. Now we need to bring all the fractions to a common denominator, for this we multiply the numerator and denominator of the first fraction by 12, the second by 4, and the third by 3. As a result, we get $\frac(36)(12) + \frac(4 )(12)+\frac(15)(12)$, which is equal to $\frac(55)(12)$. If you want to get rid of improper fraction, it can be turned into a number consisting of an integer and a fractional part: $\frac(55)(12) = \frac(48)(12)+\frac(7)(12)$ or $4\frac(7)( 12)$.

All the rules that allow operations with fractions, which we have just studied, are also valid in the case of negative numbers. So, -1: 3 can be written as $\frac(-1)(3)$, and 1: (-3) as $\frac(1)(-3)$.

Since both dividing a negative number by a positive number and dividing a positive number by a negative result in negative numbers, in both cases we will get the answer in the form of a negative number. I.e

$(-1) : 3 = \frac(1)(3)$ or $1 : (-3) = \frac(1)(-3)$. The minus sign when written this way refers to the entire fraction as a whole, and not separately to the numerator or denominator.

On the other hand, (-1) : (-3) can be written as $\frac(-1)(-3)$, and since when dividing a negative number by a negative number, we get positive number, then $\frac(-1)(-3)$ can be written as $+\frac(1)(3)$.

Addition and subtraction negative fractions carried out in the same way as the addition and subtraction of positive fractions. For example, what is $1- 1\frac13$? Let's represent both numbers as fractions and get $\frac(1)(1)-\frac(4)(3)$. Let's reduce the fractions to a common denominator and get $\frac(1 \times 3)(1 \times 3)-\frac(4)(3)$, i.e. $\frac(3)(3)-\frac(4) (3)$, or $-\frac(1)(3)$.

Online calculator.
Expression evaluation with fractions.
Multiplication, subtraction, division, addition and reduction of fractions with different denominators.

With this online calculator you can multiply, subtract, divide, add and reduce numerical fractions with different denominators.

The program works with correct, improper and mixed numeric fractions.

This program (online calculator) can:
- add mixed fractions with different denominators
- Subtract mixed fractions with different denominators
- divide mixed fractions with different denominators
- Multiply mixed fractions with different denominators
- bring fractions to a common denominator
- Convert mixed fractions to improper
- reduce fractions

You can also enter not an expression with fractions, but one single fraction.
In this case, the fraction will be reduced and the integer part will be selected from the result.

The online calculator for calculating expressions with numerical fractions does not just give the answer to the problem, it gives detailed solution with explanations, i.e. displays the process of finding a solution.

This program can be useful for high school students general education schools in preparation for control work and exams, when testing knowledge before the exam, parents to control the solution of many problems in mathematics and algebra. Or maybe it's too expensive for you to hire a tutor or buy new textbooks? Or do you just want to get it done as soon as possible? homework math or algebra? In this case, you can also use our programs with a detailed solution.

Thus, you can carry out your own training and/or training their younger brothers or sisters, while the level of education in the field of tasks being solved increases.

If you are not familiar with the rules for entering expressions with numeric fractions, we recommend that you familiarize yourself with them.

Rules for entering expressions with numeric fractions

Only a whole number can act as the numerator, denominator and integer part of a fraction.

The denominator cannot be negative.

When entering a numerical fraction, the numerator is separated from the denominator by a division sign: /
Input: -2/3 + 7/5
Result: \(-\frac(2)(3) + \frac(7)(5) \)

The integer part is separated from the fraction by an ampersand: &
Input: -1&2/3 * 5&8/3
Result: \(-1\frac(2)(3) \cdot 5\frac(8)(3) \)

Division of fractions is introduced with a colon: :
Input: -9&37/12: -3&5/14
Result: \(-9\frac(37)(12) : \left(-3\frac(5)(14) \right) \)
Remember that you cannot divide by zero!

Parentheses can be used when entering expressions with numeric fractions.
Input: -2/3 * (6&1/2-5/9) : 2&1/4 + 1/3
Result: \(-\frac(2)(3) \cdot \left(6 \frac(1)(2) - \frac(5)(9) \right) : 2\frac(1)(4) + \frac(1)(3) \)

Enter an expression with numeric fractions.

Calculate

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A bit of theory.

Ordinary fractions. Division with remainder

If we need to divide 497 by 4, then when dividing, we will see that 497 is not divisible by 4, i.e. remains the remainder of the division. In such cases, it is said that division with remainder, and the solution is written as follows:
497: 4 = 124 (1 remainder).

The division components on the left side of the equality are called the same as in division without a remainder: 497 - dividend, 4 - divider. The result of division when dividing with a remainder is called incomplete private. In our case, this number is 124. And finally, the last component, which is not in the usual division, is remainder. When there is no remainder, one number is said to be divided by another. without a trace, or completely. It is believed that with such a division, the remainder is zero. In our case, the remainder is 1.

The remainder is always less than the divisor.

You can check when dividing by multiplying. If, for example, there is an equality 64: 32 = 2, then the check can be done like this: 64 = 32 * 2.

Often in cases where division with a remainder is performed, it is convenient to use the equality
a \u003d b * n + r,
where a is the dividend, b is the divisor, n is the partial quotient, r is the remainder.

Quotient of division natural numbers can be written as a fraction.

The numerator of a fraction is the dividend, and the denominator is the divisor.

Since the numerator of a fraction is the dividend and the denominator is the divisor, believe that the line of a fraction means the action of division. Sometimes it is convenient to write division as a fraction without using the ":" sign.

The quotient of division of natural numbers m and n can be written as a fraction \(\frac(m)(n) \), where the numerator m is the dividend, and the denominator n is the divisor:
\(m:n = \frac(m)(n) \)

The following rules are correct:

To get a fraction \(\frac(m)(n) \), you need to divide the unit by n equal parts(shares) and take m such parts.

To get the fraction \(\frac(m)(n) \), you need to divide the number m by the number n.

To find a part of a whole, you need to divide the number corresponding to the whole by the denominator and multiply the result by the numerator of the fraction that expresses this part.

To find a whole by its part, you need to divide the number corresponding to this part by the numerator and multiply the result by the denominator of the fraction that expresses this part.

If both the numerator and the denominator of a fraction are multiplied by the same number (except zero), the value of the fraction will not change:
\(\large \frac(a)(b) = \frac(a \cdot n)(b \cdot n) \)

If both the numerator and the denominator of a fraction are divided by the same number (except zero), the value of the fraction will not change:
\(\large \frac(a)(b) = \frac(a: m)(b: m) \)
This property is called basic property of a fraction.

The last two transformations are called fraction reduction.

If fractions need to be represented as fractions with the same denominator, then such an action is called reducing fractions to a common denominator.

Proper and improper fractions. mixed numbers

You already know that a fraction can be obtained by dividing a whole into equal parts and taking several such parts. For example, the fraction \(\frac(3)(4) \) means three-fourths of one. In many of the problems in the previous section, fractions were used to denote part of a whole. Common sense suggests that the part must always be less than the whole, but then what about fractions such as \(\frac(5)(5) \) or \(\frac(8)(5) \)? It is clear that this is no longer part of the unit. This is probably why such fractions, in which the numerator is greater than or equal to the denominator, are called improper fractions. The remaining fractions, i.e., fractions whose numerator less than the denominator, called proper fractions.

As you know, any common fraction, both correct and incorrect, can be considered as the result of dividing the numerator by the denominator. Therefore, in mathematics, in contrast to ordinary language, the term "improper fraction" does not mean that we did something wrong, but only that this fraction has a numerator greater than or equal to the denominator.

If a number consists of an integer part and a fraction, then such fractions are called mixed.

For example:
\(5:3 = 1\frac(2)(3) \) : 1 is the integer part and \(\frac(2)(3) \) is the fractional part.

If the numerator of the fraction \(\frac(a)(b) \) is divisible by a natural number n, then in order to divide this fraction by n, its numerator must be divided by this number:
\(\large \frac(a)(b) : n = \frac(a:n)(b) \)

If the numerator of the fraction \(\frac(a)(b) \) is not divisible by a natural number n, then to divide this fraction by n, you need to multiply its denominator by this number:
\(\large \frac(a)(b) : n = \frac(a)(bn) \)

Note that the second rule is also valid when the numerator is divisible by n. Therefore, we can use it when it is difficult at first glance to determine whether the numerator of a fraction is divisible by n or not.

Actions with fractions. Addition of fractions.

With fractional numbers, as with natural numbers, you can perform arithmetic operations. Let's look at adding fractions first. It's easy to add fractions with the same denominators. Find, for example, the sum of \(\frac(2)(7) \) and \(\frac(3)(7) \). It is easy to see that \(\frac(2)(7) + \frac(2)(7) = \frac(5)(7) \)

To add fractions with the same denominators, you need to add their numerators, and leave the denominator the same.

Using letters, the rule for adding fractions with the same denominators can be written as follows:
\(\large \frac(a)(c) + \frac(b)(c) = \frac(a+b)(c) \)

If you want to add fractions with different denominators, they must first be reduced to a common denominator. For example:
\(\large \frac(2)(3)+\frac(4)(5) = \frac(2\cdot 5)(3\cdot 5)+\frac(4\cdot 3)(5\cdot 3 ) = \frac(10)(15)+\frac(12)(15) = \frac(10+12)(15) = \frac(22)(15) \)

For fractions, as well as for natural numbers, the commutative and associative properties of addition are valid.

Addition of mixed fractions

Recordings such as \(2\frac(2)(3) \) are called mixed fractions. The number 2 is called whole part mixed fraction, and the number \(\frac(2)(3) \) is its fractional part. The entry \(2\frac(2)(3) \) is read like this: "two and two thirds".

Dividing the number 8 by the number 3 gives two answers: \(\frac(8)(3) \) and \(2\frac(2)(3) \). They express the same fractional number, i.e. \(\frac(8)(3) = 2 \frac(2)(3) \)

Thus, the improper fraction \(\frac(8)(3) \) is represented as a mixed fraction \(2\frac(2)(3) \). In such cases, they say that from an improper fraction singled out the whole.

Subtraction of fractions (fractional numbers)

Subtraction fractional numbers, as well as natural ones, is determined on the basis of the operation of addition: subtracting another from one number means finding a number that, when added to the second, gives the first. For example:
\(\frac(8)(9)-\frac(1)(9) = \frac(7)(9) \) since \(\frac(7)(9)+\frac(1)(9 ) = \frac(8)(9) \)

The rule for subtracting fractions with like denominators is similar to the rule for adding such fractions:
To find the difference between fractions with the same denominators, subtract the numerator of the second fraction from the numerator of the first fraction, and leave the denominator the same.

Using letters, this rule is written as follows:
\(\large \frac(a)(c)-\frac(b)(c) = \frac(a-b)(c) \)

Multiplication of fractions

To multiply a fraction by a fraction, you need to multiply their numerators and denominators and write the first product as the numerator and the second as the denominator.

Using letters, the rule for multiplying fractions can be written as follows:
\(\large \frac(a)(b) \cdot \frac(c)(d) = \frac(a \cdot c)(b \cdot d) \)

Using the formulated rule, it is possible to multiply a fraction by a natural number, by mixed fraction and also multiply mixed fractions. To do this, you need to write a natural number as a fraction with a denominator of 1, a mixed fraction as an improper fraction.

The result of multiplication should be simplified (if possible) by reducing the fraction and highlighting the integer part of the improper fraction.

For fractions, as well as for natural numbers, the commutative and associative properties of multiplication are valid, as well as the distributive property of multiplication with respect to addition.

Division of fractions

Take the fraction \(\frac(2)(3) \) and “flip” it by swapping the numerator and denominator. We get the fraction \(\frac(3)(2) \). This fraction is called reverse fractions \(\frac(2)(3) \).

If we now “reverse” the fraction \(\frac(3)(2) \), then we get the original fraction \(\frac(2)(3) \). Therefore, fractions such as \(\frac(2)(3) \) and \(\frac(3)(2) \) are called mutually inverse.

For example, the fractions \(\frac(6)(5) \) and \(\frac(5)(6) \), \(\frac(7)(18) \) and \(\frac (18)(7) \).

Using letters, mutually inverse fractions can be written as follows: \(\frac(a)(b) \) and \(\frac(b)(a) \)

It is clear that the product of reciprocal fractions is 1. For example: \(\frac(2)(3) \cdot \frac(3)(2) =1 \)

Using reciprocal fractions, division of fractions can be reduced to multiplication.

The rule for dividing a fraction by a fraction:
To divide one fraction by another, you need to multiply the dividend by the reciprocal of the divisor.

Fractional expressions are difficult for a child to understand. Most people have difficulties with . When studying the topic "addition of fractions with integers", the child falls into a stupor, finding it difficult to solve the task. In many examples, a series of calculations must be performed before an action can be performed. For example, convert fractions or convert an improper fraction to a proper one.

Explain to the child clearly. Take three apples, two of which will be whole, and the third will be cut into 4 parts. Separate one slice from the cut apple, and put the remaining three next to two whole fruits. We get ¼ apples on one side and 2 ¾ on the other. If we combine them, we get three whole apples. Let's try to reduce 2 ¾ apples by ¼, that is, remove one more slice, we get 2 2/4 apples.

Let's take a closer look at actions with fractions, which include integers:

First, let's recall the calculation rule for fractional expressions with a common denominator:

At first glance, everything is easy and simple. But this applies only to expressions that do not require conversion.

How to find the value of an expression where the denominators are different

In some tasks, it is necessary to find the value of an expression where the denominators are different. Consider a specific case:
3 2/7+6 1/3

Find the value of this expression, for this we find a common denominator for two fractions.

For the numbers 7 and 3, this is 21. We leave the integer parts the same, and reduce the fractional parts to 21, for this we multiply the first fraction by 3, the second by 7, we get:
6/21+7/21, do not forget that whole parts are not subject to conversion. As a result, we get two fractions with one denominator and calculate their sum:
3 6/21+6 7/21=9 15/21
What if the result of addition is an improper fraction that already has an integer part:
2 1/3+3 2/3
AT this case Adding the integer parts and fractional parts, we get:
5 3/3, as you know, 3/3 is one, so 2 1/3+3 2/3=5 3/3=5+1=6

With finding the sum, everything is clear, let's analyze the subtraction:

From what has been said follows the rule of action on mixed numbers which sounds like this:

• If it is necessary to subtract an integer from a fractional expression, it is not necessary to represent the second number as a fraction, it is enough to operate only on integer parts.

Let's try to calculate the value of expressions on our own:

Let's take a look more example under the letter "m":

4 5/11-2 8/11, the numerator of the first fraction is less than the second. To do this, we take one integer from the first fraction, we get,
3 5/11+11/11=3 whole 16/11, subtract the second from the first fraction:
3 16/11-2 8/11=1 whole 8/11

• Be careful when completing the task, do not forget to convert improper fractions into mixed, highlighting the whole part. To do this, it is necessary to divide the value of the numerator by the value of the denominator, what happened, takes the place of the integer part, the remainder will be the numerator, for example:

19/4=4 ¾, check: 4*4+3=19, in the denominator 4 remains unchanged.

Summarize:

Before proceeding with the task related to fractions, it is necessary to analyze what kind of expression it is, what transformations need to be performed on the fraction in order for the solution to be correct. Look for more rational solutions. Don't go complicated ways. Plan all actions, decide first in draft version, then transfer to a school notebook.

To avoid confusion when solving fractional expressions, it is necessary to follow the sequence rule. Decide everything carefully, without rushing.

In the article, we will show how to solve fractions on simple understandable examples. Let's understand what a fraction is and consider solving fractions!

concept fractions is introduced into the course of mathematics starting from the 6th grade of secondary school.

Fractions look like: ±X / Y, where Y is the denominator, it tells how many parts the whole was divided into, and X is the numerator, it tells how many such parts were taken. For clarity, let's take an example with a cake:

In the first case, the cake was cut equally and one half was taken, i.e. 1/2. In the second case, the cake was cut into 7 parts, from which 4 parts were taken, i.e. 4/7.

If the part of dividing one number by another is not a whole number, it is written as a fraction.

For example, the expression 4:2 \u003d 2 gives an integer, but 4:7 is not completely divisible, so this expression is written as a fraction 4/7.

In other words fraction is an expression that denotes the division of two numbers or expressions, and which is written with a slash.

If the numerator is less than the denominator, the fraction is correct, if vice versa, it is incorrect. A fraction can contain an integer.

For example, 5 whole 3/4.

This entry means that in order to get the whole 6, one part of four is not enough.

If you want to remember how to solve fractions for 6th grade you need to understand that solving fractions basically comes down to understanding a few simple things.

• A fraction is essentially an expression for a fraction. I.e numeric expression what part is given value from one whole. For example, the fraction 3/5 expresses that if we divide something whole into 5 parts and the number of parts or parts of this whole is three.
• A fraction can be less than 1, for example 1/2 (or essentially half), then it is correct. If the fraction is greater than 1, for example 3/2 (three halves or one and a half), then it is incorrect and to simplify the solution, it is better for us to select the whole part 3/2= 1 whole 1/2.
• Fractions are the same numbers as 1, 3, 10, and even 100, only the numbers are not whole, but fractional. With them, you can perform all the same operations as with numbers. Counting fractions is not more difficult, and further on concrete examples we will show it.

How to solve fractions. Examples.

A variety of arithmetic operations are applicable to fractions.

Bringing a fraction to a common denominator

For example, you need to compare the fractions 3/4 and 4/5.

To solve the problem, we first find the lowest common denominator, i.e. smallest number, which is divisible without remainder by each of the denominators of the fractions

Least common denominator(4.5) = 20

Then the denominator of both fractions is reduced to the lowest common denominator

Answer: 15/20

Addition and subtraction of fractions

If it is necessary to calculate the sum of two fractions, they are first brought to a common denominator, then the numerators are added, while the denominator remains unchanged. The difference of fractions is considered in a similar way, the only difference is that the numerators are subtracted.

For example, you need to find the sum of fractions 1/2 and 1/3

Now find the difference between the fractions 1/2 and 1/4

Multiplication and division of fractions

Here the solution of fractions is simple, everything is quite simple here:

• Multiplication - numerators and denominators of fractions are multiplied among themselves;
• Division - first we get a fraction, the reciprocal of the second fraction, i.e. swap its numerator and denominator, after which we multiply the resulting fractions.

For example:

On this about how to solve fractions, all. If you have any questions about solving fractions, something is not clear, then write in the comments and we will answer you.

If you are a teacher, it is possible to download the presentation for elementary school(http://school-box.ru/nachalnaya-shkola/prezentazii-po-matematike.html) will come in handy.