Life Resources 

How to solve decimals. Dividing by decimals Dividing decimals online

Online calculator Fractions allows you to perform simple arithmetic operations with fractions: adding fractions, subtracting fractions, multiplying fractions, dividing fractions. To make calculations, fill in the fields corresponding to the numerators and denominators of the two fractions.

Fractions in mathematics is a number representing a part of a unit or several parts of it.

A common fraction is written as two numbers, usually separated by a horizontal line indicating the division sign. The number above the line is called the numerator. The number below the line is called the denominator. The denominator of a fraction shows the quantity equal parts, into which the whole is divided, and the numerator of the fraction is the number of these parts of the whole taken.

Fractions can be regular or improper.

  • A fraction whose numerator is less than its denominator is called a proper fraction.
  • An improper fraction is when the numerator of a fraction is greater than the denominator.

A mixed fraction is a fraction written as an integer and a proper fraction, and is understood as the sum of this number and the fractional part. Accordingly, a fraction that does not have an integer part is called a simple fraction. Any mixed fraction can be converted to an improper fraction.

In order to convert a mixed fraction into a common fraction, you need to add the product of the whole part and the denominator to the numerator of the fraction:

How to convert a common fraction to a mixed fraction

In order to convert an ordinary fraction to a mixed fraction, you must:

  1. Divide the numerator of a fraction by its denominator
  2. The result of division will be the whole part
  3. The balance of the department will be the numerator

How to convert a fraction to a decimal

In order to convert a fraction to a decimal, you need to divide its numerator by its denominator.

In order to convert a decimal fraction to an ordinary fraction, you must:


How to convert a fraction to a percentage

To convert a common or mixed fraction to a percentage, you need to convert it to a decimal and multiply by 100.

How to convert percentages to fractions

In order to convert percentages into fractions, you need to obtain a decimal fraction from the percentage (dividing by 100), then convert the resulting decimal fraction into an ordinary fraction.

Adding Fractions

The algorithm for adding two fractions is as follows:

  1. Perform addition of fractions by adding their numerators.

Subtracting Fractions

Algorithm for subtracting two fractions:

  1. Convert mixed fractions to ordinary fractions (get rid of the whole part).
  2. Reduce fractions to a common denominator. To do this, you need to multiply the numerator and denominator of the first fraction by the denominator of the second fraction, and multiply the numerator and denominator of the second fraction by the denominator of the first fraction.
  3. Subtract one fraction from another by subtracting the numerator of the second fraction from the numerator of the first.
  4. Find the largest common divisor(GCD) of the numerator and denominator and reduce the fraction by dividing the numerator and denominator by GCD.
  5. If the numerator of the final fraction is greater than the denominator, then select the whole part.

Multiplying fractions

Algorithm for multiplying two fractions:

  1. Convert mixed fractions to ordinary fractions (get rid of the whole part).
  2. Find the greatest common divisor (GCD) of the numerator and denominator and reduce the fraction by dividing the numerator and denominator by GCD.
  3. If the numerator of the final fraction is greater than the denominator, then select the whole part.

Division of fractions

Algorithm for dividing two fractions:

  1. Convert mixed fractions to ordinary fractions (get rid of the whole part).
  2. To divide fractions, you need to transform the second fraction by swapping its numerator and denominator, and then multiply the fractions.
  3. Multiply the numerator of the first fraction by the numerator of the second fraction and the denominator of the first fraction by the denominator of the second.
  4. Find the greatest common divisor (GCD) of the numerator and denominator and reduce the fraction by dividing the numerator and denominator by GCD.
  5. If the numerator of the final fraction is greater than the denominator, then select the whole part.

Online calculators and converters:

Dividing by a decimal fraction is reduced to dividing by natural number.

The rule for dividing a number by a decimal fraction

To divide a number by a decimal fraction, you need to move the decimal point in both the dividend and the divisor by as many digits to the right as there are in the divisor after the decimal point. After this, divide by a natural number.

Examples.

Divide by decimal fraction:

To divide by a decimal, you need to move the decimal point in both the dividend and the divisor by as many digits to the right as there are after the decimal point in the divisor, that is, by one digit. We get: 35.1: 1.8 = 351: 18. Now we perform the division with a corner. As a result, we get: 35.1: 1.8 = 19.5.

2) 14,76: 3,6

To divide decimal fractions, in both the dividend and the divisor we move the decimal point to the right one place: 14.76: 3.6 = 147.6: 36. Now we perform a natural number. Result: 14.76: 3.6 = 4.1.

To divide a natural number by a decimal fraction, you need to move both the dividend and the divisor to the right as many places as there are in the divisor after the decimal point. Since a comma is not written in the divisor in this case, we fill in the missing number of characters with zeros: 70: 1.75 = 7000: 175. Divide the resulting natural numbers with a corner: 70: 1.75 = 7000: 175 = 40.

4) 0,1218: 0,058

To divide one decimal fraction by another, we move the decimal point to the right in both the dividend and the divisor by as many digits as there are in the divisor after the decimal point, that is, by three decimal places. Thus, 0.1218: 0.058 = 121.8: 58. Division by a decimal fraction was replaced by division by a natural number. We share a corner. We have: 0.1218: 0.058 = 121.8: 58 = 2.1.

5) 0,0456: 3,8

The use of equations is widespread in our lives. They are used in many calculations, construction of structures and even sports. Man used equations in ancient times, and since then their use has only increased. A linear equation with decimals is solved in the same way as many other equations, but you need to start solving them by shortening the equation and getting rid of the decimals.

Suppose we are given an equation of the following form:

This equation can be solved in two different ways.

Method No. 1:

We begin the solution by simplifying the equation by opening parentheses, and since we have a number in front of the brackets, we multiply this number by each term in brackets:

Now our equation has a linear form, thanks to which we carry out the transfer of unknowns in one direction, integer to another:

\[ - 7.2x + 5.2x = 1.7 - 14.4 - 4.3\]

Divide 2 parts by the number before \

\[ - 2x = - 17\]

Answer: \

Method number 2:

In this method, multiply the left and right sides by 10:

This linear equation, which is solved by analogy with method 1:

\[ - 72x + 52x = 17 - 144 - 43\]

\[ - 20x = - 170\]

Answer: \

Where can I solve decimal equations online?

You can solve the equation on our website https://site. The free online solver will allow you to solve online equations of any complexity in a matter of seconds. All you need to do is simply enter your data into the solver. You can also watch video instructions and learn how to solve the equation on our website. And if you still have questions, you can ask them in our VKontakte group http://vk.com/pocketteacher. Join our group, we are always happy to help you.

Fraction calculator designed for quickly calculating operations with fractions, it will help you easily add, multiply, divide or subtract fractions.

Modern schoolchildren begin studying fractions already in the 5th grade, and exercises with them become more complicated every year. Mathematical terms and quantities that we learn at school can rarely be useful to us in life. adult life. However, fractions, unlike logarithms and powers, are found quite often in everyday life (measuring distances, weighing goods, etc.). Our calculator is designed for quick operations with fractions.

First, let's define what fractions are and what they are. Fractions are the ratio of one number to another; it is a number consisting of an integer number of fractions of a unit.

Types of fractions:

  • Ordinary
  • Decimal
  • Mixed

Example ordinary fractions:

The top value is the numerator, the bottom is the denominator. The dash shows us that the top number is divisible by the bottom number. Instead of this writing format, when the dash is horizontal, you can write differently. You can put an inclined line, for example:

1/2, 3/7, 19/5, 32/8, 10/100, 4/1

Decimals are the most popular type of fractions. They consist of an integer part and a fractional part, separated by a comma.

Example of decimal fractions:

0.2 or 6.71 or 0.125

Consist of a whole number and a fractional part. To find out the value of this fraction, you need to add the whole number and the fraction.

Example of mixed fractions:

The fraction calculator on our website is able to quickly perform any mathematical operations with fractions online:

  • Addition
  • Subtraction
  • Multiplication
  • Division

To carry out the calculation, you need to enter numbers in the fields and select an action. For fractions, you need to fill in the numerator and denominator; the whole number may not be written (if the fraction is ordinary). Don't forget to click on the "equal" button.

It’s convenient that the calculator immediately provides the process for solving an example with fractions, and not just a ready-made answer. It is thanks to the deployed solution that you can use this material when solving school problems and for better mastery of the material covered.

You need to perform the example calculation:

After entering the indicators into the form fields, we get:


To make your own calculation, enter the data in the form.

Simple arithmetic is the basis further education children to the exact sciences. Mathematics accompanies people everywhere throughout their lives, and therefore it is important to understand it from the very basics. Many schoolchildren have difficulty subtracting decimal fractions into a column, while operations with prime numbers they do a great job. In fact, there is nothing complicated about this - the main thing is to understand the solution algorithm.

How to subtract decimals into a column

When writing decimal fractions, the lower and upper digits of numbers must correspond to each other: integers under integers, tenths under tenths, hundredths under hundredths, thousandths under thousandths

Operations with decimal fractions are carried out in the same way as with natural ones. Basic rules that are important to know when solving column subtraction examples:

  1. First you need to equalize the number of decimal places. This is done by adding zeros. For example, you need to subtract 2.03 from the fraction 5.5. As can be seen from the example, the number of decimal places varies. To make them the same, add a zero to the fraction 5.5 (five point five) at the end and get 5.50 (five point fifty). This rule follows from the rules for subtracting simple fractions. As you know, fractions with different denominators cannot be added or subtracted. First they need to be brought to a common denominator. In the example above, the decimal fractions can be written as 5 5/10 and 2 3/100. You need to subtract integers from integers, and fractions from fractions. In the example, the denominators of the fractions are different, the smallest common denominator is equal to 100. Therefore, the numerator and denominator of the fraction 5/10 should be multiplied by 10, as a result we get 50/100, which when converted to a decimal fraction will look like 5.50.
  2. Write the numbers in such a way that the lower comma is in the same place as the upper one. The easiest way to write numbers is to start with a comma. Place two commas on top and bottom, and then write the characters on both sides. This rule, by the way, operates on the basis of the same rule for subtracting simple fractions - integers are subtracted from wholes, and fractions are subtracted from fractions. The resulting comma should be located exactly under the top two.
  3. Perform the action without paying attention to the comma. Decimal fractions are subtracted from right to left, that is, starting from the rightmost digit after the decimal point.
  4. Place a comma under the comma in your answer. This way we can correctly reflect the result of the calculation.

You need to subtract by digits: whole numbers from whole numbers, hundredths from hundredths, and so on.

Subtraction can always be checked by addition.

Cards for lessons

To make it easier to learn the algorithm of actions, you can print out special memory cards for children that will help them quickly master new material.

Photo gallery: lesson card options

Video: how to subtract decimal fractions by column

Having mastered this simple action, children will be able to study better in the future, because examples with decimal fractions are solved not only in mathematics, but also in physics, chemistry, and astronomy. The main thing is to understand the algorithm.