The numerator, and that by which it is divided is the denominator.
To write a fraction, first write its numerator, then draw a horizontal line under this number, and write the denominator under the line. The horizontal line separating the numerator and denominator is called a fractional bar. Sometimes it is depicted as an oblique "/" or "∕". In this case, the numerator is written to the left of the line, and the denominator to the right. So, for example, the fraction "two-thirds" will be written as 2/3. For clarity, the numerator is usually written at the top of the line, and the denominator at the bottom, that is, instead of 2/3, you can find: ⅔.
To calculate the product of fractions, first multiply the numerator of one fractions to another numerator. Write the result to the numerator of the new fractions. Then multiply the denominators as well. Specify the final value in the new fractions. For example, 1/3? 1/5 = 1/15 (1 × 1 = 1; 3 × 5 = 15).
To divide one fraction by another, first multiply the numerator of the first by the denominator of the second. Do the same with the second fraction (divisor). Or, before performing all the steps, first “flip” the divisor, if it’s more convenient for you: the denominator should be in place of the numerator. Then multiply the denominator of the dividend by the new denominator of the divisor and multiply the numerators. For example, 1/3: 1/5 = 5/3 = 1 2/3 (1 × 5 = 5; 3 × 1 = 3).
Sources:
- Basic tasks for fractions
Fractional numbers allow you to express the exact value of a quantity in different ways. With fractions, you can perform the same mathematical operations as with integers: subtraction, addition, multiplication, and division. To learn how to decide fractions, it is necessary to remember some of their features. They depend on the type fractions, the presence of an integer part, a common denominator. Some arithmetic operations after execution require reduction of the fractional part of the result.
You will need
- - calculator
Instruction
Look carefully at the numbers. If there are decimals and irregulars among the fractions, it is sometimes more convenient to first perform actions with decimals, and then convert them to the wrong form. Can you translate fractions in this form initially, writing the value after the decimal point in the numerator and putting 10 in the denominator. If necessary, reduce the fraction by dividing the numbers above and below by one divisor. Fractions in which the whole part stands out, lead to the wrong form by multiplying it by the denominator and adding the numerator to the result. This value will become the new numerator fractions. To extract the whole part from the initially incorrect fractions, divide the numerator by the denominator. Write the whole result from fractions. And the remainder of the division becomes the new numerator, the denominator fractions while not changing. For fractions with an integer part, it is possible to perform actions separately, first for the integer and then for the fractional parts. For example, the sum of 1 2/3 and 2 ¾ can be calculated:
- Converting fractions to the wrong form:
- 1 2/3 + 2 ¾ = 5/3 + 11/4 = 20/12 + 33/12 = 53/12 = 4 5/12;
- Summation separately of integer and fractional parts of terms:
- 1 2/3 + 2 ¾ = (1+2) + (2/3 + ¾) = 3 + (8/12 + 9/12) = 3 + 17/12 = 3 + 1 5/12 = 4 5 /12.
Rewrite them through the separator ":" and continue the usual division.
To get the final result, reduce the resulting fraction by dividing the numerator and denominator by one whole number, the largest possible in this case. In this case, there must be integer numbers above and below the line.
note
Don't do arithmetic with fractions that have different denominators. Choose a number such that when the numerator and denominator of each fraction are multiplied by it, as a result, the denominators of both fractions are equal.
Useful advice
When writing fractional numbers, the dividend is written above the line. This quantity is referred to as the numerator of a fraction. Under the line, the divisor, or denominator, of the fraction is written. For example, one and a half kilograms of rice in the form of a fraction will be written as follows: 1 ½ kg of rice. If the denominator of a fraction is 10, it is called a decimal fraction. 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 always be written in the wrong form: 1 2/10 kg of potatoes. To simplify, you can reduce the numerator and denominator values by dividing them by a single whole number. In this example, dividing by 2 is possible. The result is 1 1/5 kg of potatoes. Make sure that the numbers you are going to do arithmetic with are in the same form.
Actions with fractions. In this article, we will analyze examples, everything is detailed with explanations. We will consider ordinary fractions. In the future, we will analyze decimals. I recommend to watch the whole and study sequentially.
1. Sum of fractions, difference of fractions.
Rule: when adding fractions with equal denominators, the result is a fraction - the denominator of which remains the same, and its numerator will be equal to the sum of the numerators of the fractions.
Rule: when calculating the difference of fractions with the same denominators, we get a fraction - the denominator remains the same, and the numerator of the second is subtracted from the numerator of the first fraction.
Formal notation of the sum and difference of fractions with equal denominators:
Examples (1):
It is clear that when ordinary fractions are given, then everything is simple, but if they are mixed? Nothing complicated...
Option 1- you can convert them into ordinary ones and then calculate them.
Option 2- you can separately "work" with the integer and fractional parts.
Examples (2):
Yet:
And if the difference of two mixed fractions is given and the numerator of the first fraction is less than the numerator of the second? It can also be done in two ways.
Examples (3):
* Translated into ordinary fractions, calculated the difference, converted the resulting improper fraction into a mixed one.
* Divided into integer and fractional parts, got three, then presented 3 as the sum of 2 and 1, with the unit presented as 11/11, then found the difference between 11/11 and 7/11 and calculated the result. The meaning of the above transformations is to take (select) the unit and present it as a fraction with the denominator we need, then from this fraction we can already subtract another.
Another example:
Conclusion: there is a universal approach - in order to calculate the sum (difference) of mixed fractions with equal denominators, they can always be converted into improper ones, then perform the necessary action. After that, if as a result we get an improper fraction, we translate it into a mixed one.
Above, we looked at examples with fractions that have equal denominators. What if the denominators differ? In this case, the fractions are reduced to the same denominator and the specified action is performed. To change (transform) a fraction, the main property of the fraction is used.
Consider simple examples:
In these examples, we immediately see how one of the fractions can be converted to get equal denominators.
If we designate ways to reduce fractions to one denominator, then this one will be called METHOD ONE.
That is, immediately when “evaluating” the fraction, you need to figure out whether such an approach will work - we check whether the larger denominator is divisible by the smaller one. And if it is divided, then we perform the transformation - we multiply the numerator and denominator so that the denominators of both fractions become equal.
Now look at these examples:
This approach does not apply to them. There are other ways to reduce fractions to a common denominator, consider them.
Method SECOND.
Multiply the numerator and denominator of the first fraction by the denominator of the second, and the numerator and denominator of the second fraction by the denominator of the first:
*In fact, we bring fractions to the form when the denominators become equal. Next, we use the rule of adding timid with equal denominators.
Example:
*This method can be called universal, and it always works. The only negative is that after the calculations, a fraction may turn out that will need to be further reduced.
Consider an example:
It can be seen that the numerator and denominator are divisible by 5:
Method THIRD.
Find the least common multiple (LCM) of the denominators. This will be the common denominator. What is this number? This is the smallest natural number that is divisible by each of the numbers.
Look, here are two numbers: 3 and 4, there are many numbers that are divisible by them - these are 12, 24, 36, ... The smallest of them is 12. Or 6 and 15, 30, 60, 90 are divisible by them .... Least 30. Question - how to determine this least common multiple?
There is a clear algorithm, but often this can be done immediately without calculations. For example, according to the above examples (3 and 4, 6 and 15), no algorithm is needed, we took large numbers (4 and 15), doubled them and saw that they are divisible by the second number, but pairs of numbers can be others, such as 51 and 119.
Algorithm. In order to determine the least common multiple of several numbers, you must:
- decompose each of the numbers into SIMPLE factors
- write out the decomposition of the BIGGER of them
- multiply it by the MISSING factors of other numbers
Consider examples:
50 and 60 50 = 2∙5∙5 60 = 2∙2∙3∙5
in the expansion of a larger number, one five is missing
=> LCM(50,60) = 2∙2∙3∙5∙5 = 300
48 and 72 48 = 2∙2∙2∙2∙3 72 = 2∙2∙2∙3∙3
in the expansion of a larger number, two and three are missing
=> LCM(48,72) = 2∙2∙2∙2∙3∙3 = 144
* The least common multiple of two prime numbers is equal to their product
Question! And why is it useful to find the least common multiple, because you can use the second method and simply reduce the resulting fraction? Yes, you can, but it's not always convenient. See what the denominator will be for the numbers 48 and 72 if you simply multiply them 48∙72 = 3456. Agree that it is more pleasant to work with smaller numbers.
Consider examples:
*51 = 3∙17 119 = 7∙17
in the expansion of a larger number, a triple is missing
=> LCM(51,119) = 3∙7∙17
And now we apply the first method:
* Look at the difference in the calculations, in the first case there is a minimum of them, and in the second you need to work separately on a piece of paper, and even the fraction that you got needs to be reduced. Finding the LCM simplifies the work considerably.
More examples:
* In the second example, it is already clear that the smallest number that is divisible by 40 and 60 is 120.
TOTAL! GENERAL CALCULATION ALGORITHM!
- we bring fractions to ordinary ones, if there is an integer part.
- we bring fractions to a common denominator (first we look to see if one denominator is divisible by another, if it is divisible, then we multiply the numerator and denominator of this other fraction; if it is not divisible, we act through the other methods indicated above).
- having received fractions with equal denominators, we perform actions (addition, subtraction).
- if necessary, we reduce the result.
- if necessary, select the whole part.
2. Product of fractions.
The rule is simple. When multiplying fractions, their numerators and denominators are multiplied:
Examples:
A task. 13 tons of vegetables were brought to the base. Potatoes make up ¾ of all imported vegetables. How many kilograms of potatoes were brought to the base?
Let's finish with the work.
*Earlier I promised you to give a formal explanation of the main property of the fraction through the product, please:
3. Division of fractions.
The division of fractions is reduced to their multiplication. It is important to remember here that the fraction that is a divisor (the one that is divided by) is turned over and the action changes to multiplication:
This action can be written as a so-called four-story fraction, because the division itself “:” can also be written as a fraction:
Examples:
That's all! Good luck to you!
Sincerely, Alexander Krutitskikh.
An equation is an equality containing a letter whose value is to be found.
In equations, the unknown is usually denoted by a lowercase Latin letter. The most commonly used letters are "x" [x] and "y" [y].
Having solved the equation, we always write down the check after the answer.
Information for parents
Dear parents, we draw your attention to the fact that in elementary school and in grade 5, children do NOT know the topic "Negative numbers".
Therefore, they must solve equations using only the properties of addition, subtraction, multiplication, and division. Methods for solving equations for grade 5 are given below.
Do not try to explain the solution of equations by transferring numbers and letters from one part of the equation to another with a sign change.
You can refresh your knowledge on the concepts related to addition, subtraction, multiplication and division in the lesson "Laws of arithmetic".
Solving equations for addition and subtraction
How to find the unknown
term
How to find the unknown
minuend
How to find the unknown
subtrahend
To find the unknown term, subtract the known term from the sum.
To find the unknown minuend, you need to add the subtrahend to the difference.
To find the unknown subtrahend, it is necessary to subtract the difference from the minuend.
x + 9 = 15
x = 15 − 9
x=6
Examination
x − 14 = 2
x = 14 + 2
x=16
Examination
16 − 2 = 14
14 = 14
5 − x = 3
x = 5 − 3
x=2
Examination
Solving equations for multiplication and division
How to find the unknown
factor
How to find the unknown
dividend
How to find the unknown
divider
To find the unknown factor, the product must be divided by the known factor.
To find the unknown dividend, you need to multiply the quotient by the divisor.
To find the unknown divisor, divide the dividend by the quotient.
y 4 = 12
y=12:4
y=3
Examination
y:7=2
y = 2 7
y=14
Examination
8:y=4
y=8:4
y=2
Examination
An equation is an equation containing the letter whose sign is to be found. The solution to an equation is the set of letter values that turns the equation into a true equality:
Recall that in order to solve equation it is necessary to transfer the terms with the unknown to one part of the equality, and the numerical terms to the other, bring similar ones and get the following equality:
From the last equality, we determine the unknown by the rule: "one of the factors is equal to the quotient divided by the second factor."
Since the rational numbers a and b can have the same and different signs, the sign of the unknown is determined by the rules for dividing rational numbers.
The procedure for solving linear equations
The linear equation must be simplified by opening the brackets and performing the actions of the second stage (multiplication and division).
Move the unknowns to one side of the equals sign, and the numbers to the other side of the equals sign, getting identical to the given equality,
Bring like to the left and to the right of the equal sign, obtaining an equality of the form ax = b.
Calculate the root of the equation (find the unknown X from equality x = b : a),
Test by substituting the unknown into the given equation.
If we get an identity in numerical equality, then the equation is solved correctly.
Special cases of solving equations
- If a the equation is given by a product equal to 0, then to solve it we use the property of multiplication: "the product is equal to zero if one of the factors or both factors are equal to zero."
27 (x - 3) = 0
27 is not equal to 0, so x - 3 = 0
The second example has two solutions to the equation, since
This is an equation of the second degree:
If the coefficients of the equation are ordinary fractions, then first of all you need to get rid of the denominators. For this:
Find a common denominator;
Determine additional factors for each term of the equation;
Multiply the numerators of fractions and integers by additional factors and write down all the terms of the equation without denominators (the common denominator can be discarded);
Move the terms with unknowns to one part of the equation, and the numerical terms to the other from the equal sign, obtaining an equivalent equality;
Bring like terms;
Basic properties of equations
In any part of the equation, you can bring like terms or open the bracket.
Any term of the equation can be transferred from one part of the equation to another by changing its sign to the opposite.
Both sides of the equation can be multiplied (divided) by the same number except 0.
In the example above, all of its properties were used to solve the equation.
How to solve an equation with an unknown in a fraction
Sometimes linear equations take the form when unknown appears in the numerator of one or more fractions. Like in the equation below.
In such cases, such equations can be solved in two ways.
I way of solution
Reducing an Equation to a Proportion
When solving equations using the proportion method, you must perform the following steps:
So, back to our equation. On the left side, we already have only one fraction, so no transformations are needed in it.
We will work with the right side of the equation. Simplify the right side of the equation so that only one fraction remains. To do this, recall the rules for adding a number with an algebraic fraction.
Now we use the rule of proportion and solve the equation to the end.
II method of solution
Reduction to a linear equation without fractions
Consider the equation above again and solve it in a different way.
We see that there are two fractions in the equation "
How to solve equations with fractions. Exponential solution of equations with fractions.
Solving equations with fractions let's look at examples. The examples are simple and illustrative. With their help, you can understand in the most understandable way,.
For example, you need to solve a simple equation x/b + c = d.
An equation of this type is called linear, because the denominator contains only numbers.
The solution is performed by multiplying both sides of the equation by b, then the equation takes the form x = b*(d – c), i.e. the denominator of the fraction on the left side is reduced.
For example, how to solve a fractional equation:
x/5+4=9
We multiply both parts by 5. We get:
x+20=45
Another example where the unknown is in the denominator:
Equations of this type are called fractional rational or simply fractional.
We would solve a fractional equation by getting rid of fractions, after which this equation, most often, turns into a linear or quadratic one, which is solved in the usual way. You should only take into account the following points:
- the value of a variable that turns the denominator to 0 cannot be a root;
- you cannot divide or multiply the equation by the expression =0.
Here comes into force such a concept as the area of permissible values (ODZ) - these are the values \u200b\u200bof the roots of the equation for which the equation makes sense.
Thus, solving the equation, it is necessary to find the roots, and then check them for compliance with the ODZ. Those roots that do not correspond to our DHS are excluded from the answer.
For example, you need to solve a fractional equation:
Based on the above rule, x cannot be = 0, i.e. ODZ in this case: x - any value other than zero.
We get rid of the denominator by multiplying all terms of the equation by x
And solve the usual equation
5x - 2x = 1
3x=1
x = 1/3
Let's solve the equation more complicated:
ODZ is also present here: x -2.
Solving this equation, we will not transfer everything in one direction and bring fractions to a common denominator. We immediately multiply both sides of the equation by an expression that will reduce all the denominators at once.
To reduce the denominators, you need to multiply the left side by x + 2, and the right side by 2. So, both sides of the equation must be multiplied by 2 (x + 2):
This is the most common multiplication of fractions, which we have already discussed above.
We write the same equation, but in a slightly different way.
The left side is reduced by (x + 2), and the right side by 2. After the reduction, we get the usual linear equation:
x \u003d 4 - 2 \u003d 2, which corresponds to our ODZ
Solving equations with fractions not as difficult as it might seem. In this article, we have shown this with examples. If you are having any difficulty with how to solve equations with fractions, then unsubscribe in the comments.
Solving equations with fractions Grade 5
Solution of equations with fractions. Solving problems with fractions.
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"Solving Equations with Fractions Grade 5"
- Adding fractions with the same denominators.
- Subtraction of fractions with the same denominators.
Adding fractions with the same denominators.
To add fractions with the same denominators, add their numerators and leave the denominator the same.
Subtraction of fractions with the same denominators.
To subtract fractions with the same denominators, subtract the numerator of the subtrahend from the numerator of the minuend, and leave the denominator the same.
When solving equations, it is necessary to use the rules for solving equations, the properties of addition and subtraction.
Solving equations using properties.
Solving equations using rules.
The expression on the left side of the equation is the sum.
term + term = sum.
To find the unknown term, subtract the known term from the sum.
minuend – subtrahend = difference
To find the unknown subtrahend, subtract the difference from the minuend.
The expression on the left side of the equation is the difference.
To find the unknown minuend, you need to add the subtrahend to the difference.
USING RULES FOR SOLVING EQUATIONS.
On the left side of the equation, the expression is the sum.
Equations containing a variable in the denominator can be solved in two ways:
Reducing fractions to a common denominator
Using the basic property of proportion
Regardless of the method chosen, after finding the roots of the equation, it is necessary to choose from the found values the acceptable values, i.e. those that do not turn the denominator to $0$.
1 way. Bringing fractions to a common denominator.
Example 1
$\frac(2x+3)(2x-1)=\frac(x-5)(x+3)$
Solution:
1. Move the fraction from the right side of the equation to the left
\[\frac(2x+3)(2x-1)-\frac(x-5)(x+3)=0\]
In order to do this correctly, we recall that when moving elements to another part of the equation, the sign in front of the expressions changes to the opposite. So, if on the right side there was a “+” sign before the fraction, then on the left side there will be a “-” sign in front of it. Then on the left side we get the difference of the fractions.
2. Now we note that the fractions have different denominators, which means that in order to make up the difference, it is necessary to bring the fractions to a common denominator. The common denominator will be the product of the polynomials in the denominators of the original fractions: $(2x-1)(x+3)$
In order to obtain an identical expression, the numerator and denominator of the first fraction must be multiplied by the polynomial $(x+3)$, and the second by the polynomial $(2x-1)$.
\[\frac((2x+3)(x+3))((2x-1)(x+3))-\frac((x-5)(2x-1))((x+3)( 2x-1))=0\]
Let's perform the transformation in the numerator of the first fraction - we will multiply the polynomials. Recall that for this it is necessary to multiply the first term of the first polynomial, multiply by each term of the second polynomial, then multiply the second term of the first polynomial by each term of the second polynomial and add the results
\[\left(2x+3\right)\left(x+3\right)=2x\cdot x+2x\cdot 3+3\cdot x+3\cdot 3=(2x)^2+6x+3x +9\]
We present similar terms in the resulting expression
\[\left(2x+3\right)\left(x+3\right)=2x\cdot x+2x\cdot 3+3\cdot x+3\cdot 3=(2x)^2+6x+3x +9=\] \[(=2x)^2+9x+9\]
Perform a similar transformation in the numerator of the second fraction - we will multiply the polynomials
$\left(x-5\right)\left(2x-1\right)=x\cdot 2x-x\cdot 1-5\cdot 2x+5\cdot 1=(2x)^2-x-10x+ 5=(2x)^2-11x+5$
Then the equation will take the form:
\[\frac((2x)^2+9x+9)((2x-1)(x+3))-\frac((2x)^2-11x+5)((x+3)(2x- 1))=0\]
Now fractions with the same denominator, so you can subtract. Recall that when subtracting fractions with the same denominator from the numerator of the first fraction, it is necessary to subtract the numerator of the second fraction, leaving the denominator the same
\[\frac((2x)^2+9x+9-((2x)^2-11x+5))((2x-1)(x+3))=0\]
Let's transform the expression in the numerator. In order to open the brackets preceded by the “-” sign, all signs in front of the terms in brackets must be reversed
\[(2x)^2+9x+9-\left((2x)^2-11x+5\right)=(2x)^2+9x+9-(2x)^2+11x-5\]
We present like terms
$(2x)^2+9x+9-\left((2x)^2-11x+5\right)=(2x)^2+9x+9-(2x)^2+11x-5=20x+4 $
Then the fraction will take the form
\[\frac((\rm 20x+4))((2x-1)(x+3))=0\]
3. A fraction is equal to $0$ if its numerator is 0. Therefore, we equate the numerator of the fraction to $0$.
\[(\rm 20x+4=0)\]
Let's solve the linear equation:
4. Let's sample the roots. This means that it is necessary to check whether the denominators of the original fractions turn into $0$ when the roots are found.
We set the condition that the denominators are not equal to $0$
x$\ne 0.5$ x$\ne -3$
This means that all values of the variables are allowed, except for $-3$ and $0.5$.
The root we found is a valid value, so it can be safely considered the root of the equation. If the found root were not a valid value, then such a root would be extraneous and, of course, would not be included in the answer.
Answer:$-0,2.$
Now we can write an algorithm for solving an equation that contains a variable in the denominator
An algorithm for solving an equation that contains a variable in the denominator
Move all elements from the right side of the equation to the left side. To obtain an identical equation, it is necessary to change all the signs in front of the expressions on the right side to the opposite
If on the left side we get an expression with different denominators, then we bring them to a common one using the main property of the fraction. Perform transformations using identical transformations and get the final fraction equal to $0$.
Equate the numerator to $0$ and find the roots of the resulting equation.
Let's sample the roots, i.e. find valid variable values that do not turn the denominator to $0$.
2 way. Using the basic property of proportion
The main property of a proportion is that the product of the extreme terms of the proportion is equal to the product of the middle terms.
Example 2
We use this property to solve this task
\[\frac(2x+3)(2x-1)=\frac(x-5)(x+3)\]
1. Let's find and equate the product of the extreme and middle members of the proportion.
$\left(2x+3\right)\cdot(\ x+3)=\left(x-5\right)\cdot(2x-1)$
\[(2x)^2+3x+6x+9=(2x)^2-10x-x+5\]
Solving the resulting equation, we find the roots of the original
2. Let's find admissible values of a variable.
From the previous solution (1st way) we have already found that any values are allowed except $-3$ and $0.5$.
Then, having established that the found root is a valid value, we found out that $-0.2$ will be the root.
In the article, we will show how to solve fractions with simple clear 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. That is, a numerical expression of what part a given value is 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 we will show this with specific examples.
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. the smallest number that 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, then it is possible to download a presentation for an elementary school (http://school-box.ru/nachalnaya-shkola/prezentazii-po-matematike.html) which will come in handy.
