Ordinary and decimal fractions and operations on them. Fraction Calculator: Solving Equations with Fractions Solving Decimals

A column calculator for Android devices will be a great helper for modern schoolchildren. The program not only gives the correct answer to a mathematical action, but also clearly demonstrates its step-by-step solution. If you need more complex calculators, you can look at the advanced engineering calculator.

Peculiarities

The main feature of the program is the uniqueness of the calculation of mathematical operations. Displaying the calculation process in a column allows students to get acquainted with it in more detail, understand the solution algorithm, and not just get the finished result and rewrite it in a notebook. This feature has a huge advantage over other calculators. quite often at school, teachers require intermediate calculations to be written down to make sure that the student does them in his mind and really understands the algorithm for solving problems. By the way, we have another program of a similar kind - .

To start using the program, you need to download a calculator in a column on Android. You can do this on our website absolutely free of charge without additional registrations and SMS. After installation, the main page will open in the form of a notebook sheet in a cage, on which, in fact, the calculation results and their detailed solution will be displayed. At the bottom there is a panel with buttons:

1. Numbers.
2. Signs of arithmetic operations.
3. Delete previously entered characters.

Input is carried out according to the same principle as on. All the difference is only in the interface of the application - all mathematical calculations and their results are displayed in a virtual student notebook.

The application allows you to quickly and correctly perform standard mathematical calculations for a student in a column:

• multiplication;
• division;
• addition;
• subtraction.

A nice addition to the app is the daily reminder function. homework mathematics. If you want, do your homework. To enable it, go to the settings (press the button in the form of a gear) and check the reminder box.

Advantages and disadvantages

1. It helps the student not only to quickly get the correct result of mathematical calculations, but also to understand the very principle of calculation.
2. Very simple, intuitive interface for every user.
3. You can install the application even on the most budgetary Android device with operating system 2.2 and later.
4. The calculator saves a history of mathematical calculations, which can be cleared at any time.

The calculator is limited in mathematical operations, so it will not work for complex calculations that an engineering calculator could handle. However, given the purpose of the application itself - to clearly demonstrate the principle of calculating in a column to elementary school students, this should not be considered a disadvantage.

The application will also be an excellent assistant not only for schoolchildren, but also for parents who want to get their child interested in mathematics and teach him how to correctly and consistently perform calculations. If you have already used the Stacked Calculator app, leave your impressions below in the comments.

Instruction

Learn how to convert decimals to fractions. Count how many characters are separated by a comma. One digit to the right of the decimal point means the denominator is 10, two digits are 100, three are 1000, and so on. For example, decimal 6.8 as "six point eight". When converting it, first write the number of whole units - 6. Write 10 in the denominator. The number 8 will be in the numerator. It turns out that 6.8 \u003d 6 8/10. Remember the abbreviation rules. If the numerator and denominator are divisible by the same number, then the fraction can be reduced by common divisor. In this case, that number is 2. 6 8/10 = 6 2/5.

Try adding decimals. If you are doing this in a column, then be careful. The digits of all numbers must be strictly one under the other - under the comma. The rules for addition are exactly the same as for the operation with . Add to the same number 6.8 another decimal fraction - for example, 7.3. Write a triple under an eight, a comma under a comma, and a seven under a six. Start adding from the last digit. 3+8=11, that is, write down 1, remember 1. Then add 6 + 7, get 13. Add what remained in your mind and write down the result - 14.1.

Subtraction is done in the same way. Write the digits under each other, a comma - under a comma. Always focus on it, especially if the number of digits after it in the reduced is less than in the subtracted. Subtract from a given number, for example, 2.139. Write the two under the six, the one under the eight, the remaining two numbers under the following digits, which can be denoted by zeros. It turns out that the minuend is not 6.8, but 6.800. After completing this action, you will get a total of 4,661.

Operations with negative decimals are performed in the same way as with integers. When adding, the minus is taken out of the bracket, and the given numbers are written in brackets, and a plus is placed between them. The result is a negative number. That is, adding -6.8 and -7.3 will give you the same result of 14.1, but with a "-" in front of it. If the subtrahend is greater than the minuend, then the minus is also taken out of the bracket, the smaller is subtracted from the larger number. Subtract -7.3 from 6.8. Transform the expression as follows. 6.8 - 7.3 \u003d - (7.3 - 6.8) \u003d -0.5.

To multiply decimals, forget about the comma for a while. Multiply them as if they were integers. After that, count the number of digits to the right after the decimal point in both factors. Separate the same number of characters in the work. Multiplying 6.8 and 7.3 gives you 49.64. That is, to the right of the comma you will have 2 digits, while in the multiplier and the multiplier there were one each.

Divide the given fraction by some integer. This action is performed in the same way as with integers. The main thing is not to forget about the comma and put 0 at the beginning if the number of integer units is not divisible by a divisor. For example, try dividing the same 6.8 by 26. Put 0 at the beginning, because 6 is less than 26. Separate it with a comma, tenths and hundredths will go further. The result will be approximately 0.26. In fact, in this case, an infinite non-periodic fraction is obtained, which can be rounded to the desired degree of accuracy.

When dividing two decimal fractions use the property that when multiplying a dividend and a divisor by the same number, the quotient does not change. That is, convert both fractions to integers, depending on how many decimal places there are. If you want to divide 6.8 by 7.3, it is enough to multiply both numbers by 10. It turns out that you need to divide 68 by 73. If there are more digits after the decimal point in one of the numbers, first convert it to an integer, and then second number. Multiply it by the same number. That is, when dividing 6.8 by 4.136, increase the dividend and divisor not by 10, but by 1000 times. Dividing 6800 by 1436 gives you 4.735.

Simple arithmetic operations are the basis for further teaching children the exact sciences. Mathematics accompanies people everywhere throughout life, and therefore it is important to understand it from the very beginning. Subtraction of decimal fractions in a column causes difficulties for many schoolchildren, while with actions with prime numbers they're doing great. In fact, there is nothing complicated in this - the main thing is to understand the solution algorithm.

How to subtract decimals in 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

Actions with decimal fractions are performed in the same way as with natural ones. The main rules that are important to know when solving examples for subtraction in a column:

1. First, you should equalize the number of decimal places. This is done by adding zeros. For example, you need to subtract the number 2.03 from the fraction 5.5. As you can see from the example, the number of decimal places is different. To make them the same, add zero to the fraction 5.5 (five point five) at the end and get 5.50 (five point fifty hundredth). This rule follows from the rules for subtracting simple fractions. As you know, fractions with different denominators cannot be added or subtracted. First, they must be reduced to a common denominator. In the example above, decimals can be written as 5 5/10 and 2 3/100. From integers you need to subtract integers, from fractional - fractional. In the example, the denominators of the fractions are different, the least common denominator is 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 translated into a decimal fraction, will look like 5.50.
2. Write the numbers in such a way that the comma of the lower one is in the same place as that of the upper one. It is easiest to write numbers starting with a comma. Put two commas above and below, and then paint 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 the whole, and fractional ones are subtracted from fractional ones. The comma in the result should be located exactly under the top two.
3. Perform the action, ignoring the comma. Subtract decimal fractions from right to left, that is, starting from the rightmost digit after the decimal point.
4. Put a comma under the comma in your answer. So we can correctly reflect the result of the calculation.

Subtraction can always be checked by addition.

Lesson cards

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

Photo gallery: card options for classes

Video: how to subtract decimal fractions in a 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.

The use of equations is widespread in our lives. They are used in many calculations, construction of structures and even sports. Equations have been used by man since 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 their solution must be started by reducing 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 number 1:

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

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

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

Divide 2 parts by the number before \

\[-2x=-17\]

Answer: \

Method number 2:

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

This is a 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. Free online solver will allow you to solve an online equation of any complexity in seconds. All you have to do is just enter your data into the solver. You can also watch the video instruction and learn how to solve the equation on our website. And if you have any questions, you can ask them in our Vkontakte group http://vk.com/pocketteacher. Join our group, we are always happy to help you.

Division by a decimal is the same as division by a natural number.

Rule for dividing a number by a decimal fraction

To divide a number by a decimal fraction, it is necessary both in the dividend and in the divisor to move the comma as many digits to the right as there are in the divisor after the decimal point. After that, divide by a natural number.

Examples.

Perform division by decimal:

To divide by a decimal fraction, you need to move the comma as many digits to the right in both the dividend and the divisor as there are after the decimal point in the divisor, that is, by one sign. We get: 35.1: 1.8 \u003d 351: 18. Now we perform division by a corner. As a result, we get: 35.1: 1.8 = 19.5.

2) 14,76: 3,6

To perform the division of decimal fractions, both in the dividend and in the divisor, move the comma to the right by one sign: 14.76: 3.6 \u003d 147.6: 36. Now we perform on a natural number. Result: 14.76: 3.6 = 4.1.

To perform division by a decimal fraction of a natural number, it is necessary both in the dividend and in the divisor to move as many characters to the right as there are in the divisor after the decimal point. Since the comma is not written in the divisor in this case, we fill in the missing number of characters with zeros: 70: 1.75 \u003d 7000: 175. We divide the resulting natural numbers with a corner: 70: 1.75 \u003d 7000: 175 \u003d 40.

4) 0,1218: 0,058

To divide one decimal fraction into another, we move the comma to the right both in the dividend and in the divisor by as many digits as there are in the divisor after the decimal point, that is, by three digits. Thus, 0.1218: 0.058 \u003d 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