Mathematical-Calculator-Online v.1.0

The calculator performs following operations: addition, subtraction, multiplication, division, working with decimals, root extraction, exponentiation, percent calculation and other operations.

Solution:

How to use a math calculator

Key	Designation	Explanation
5	numbers 0-9	Arabic numerals. Entering natural integers, zero. To get a negative integer, you must press the +/- key
.	semicolon)	Separator to indicate a decimal fraction. If there is no number before the point (comma), the calculator will automatically substitute a zero before the point. For example: .5 - 0.5 will be written
+	plus sign	Adding numbers (integers, decimals)
-	minus sign	Subtracting numbers (integers, decimals)
÷	division sign	Dividing numbers (integers, decimals)
X	multiplication sign	Multiplying numbers (integers, decimals)
√	root	Extracting the root of a number. When you press the “root” button again, the root of the result is calculated. For example: root of 16 = 4; root of 4 = 2
x 2	squaring	Squaring a number. When you press the "squaring" button again, the result is squared. For example: square 2 = 4; square 4 = 16
1/x	fraction	Output in decimal fractions. The numerator is 1, the denominator is the entered number
%	percent	Getting a percentage of a number. To work, you need to enter: the number from which the percentage will be calculated, the sign (plus, minus, divide, multiply), how many percent in numerical form, the "%" button
(	open parenthesis	An open parenthesis to specify the calculation priority. A closed parenthesis is required. Example: (2+3)*2=10
)	closed parenthesis	A closed parenthesis to specify the calculation priority. An open parenthesis is required
±	plus minus	Reverses sign
=	equals	Displays the result of the solution. Also above the calculator, in the “Solution” field, intermediate calculations and the result are displayed.
←	deleting a character	Removes the last character
WITH	reset	Reset button. Completely resets the calculator to position "0"

Algorithm of the online calculator using examples

Addition.

Addition of integers natural numbers { 5 + 7 = 12 }

Addition of whole natural and negative numbers { 5 + (-2) = 3 }

Adding decimal fractions (0.3 + 5.2 = 5.5)

Subtraction.

Subtracting natural integers ( 7 - 5 = 2 )

Subtracting natural and negative integers ( 5 - (-2) = 7 )

Subtracting decimal fractions ( 6.5 - 1.2 = 4.3 )

Multiplication.

Product of natural integers (3 * 7 = 21)

Product of natural and negative integers ( 5 * (-3) = -15 )

Product of decimal fractions ( 0.5 * 0.6 = 0.3 )

Division.

Division of natural integers (27 / 3 = 9)

Division of natural and negative integers (15 / (-3) = -5)

Division of decimal fractions (6.2 / 2 = 3.1)

Extracting the root of a number.

Extracting the root of an integer ( root(9) = 3)

Extracting the root from decimals( root(2.5) = 1.58 )

Extracting the root of a sum of numbers ( root(56 + 25) = 9)

Extracting the root of the difference between numbers (root (32 – 7) = 5)

Squaring a number.

Squaring an integer ( (3) 2 = 9 )

Squaring decimals ((2,2)2 = 4.84)

Conversion to decimal fractions.

Calculating percentages of a number

Increase the number 230 by 15% ( 230 + 230 * 0.15 = 264.5 )

Reduce the number 510 by 35% ( 510 – 510 * 0.35 = 331.5)

18% of the number 140 is (140 * 0.18 = 25.2)

How to subtract by column

Subtraction of multi-digit numbers is usually performed in a column, writing the numbers under each other (minuend from above, subtract from below) so that the digits of the same digits are located under each other (units under units, tens under tens, etc.). An action sign is placed on the left between the numbers. A line is drawn under the deductible. The calculation begins with the units digit: units are subtracted from ones, then tens are subtracted from tens, etc. The result of the subtraction is written under the line:

Let's consider an example when in some digit the digit of the minuend less number deductible:

We cannot subtract 9 from 2, what should we do in this case? We have a shortage in the units category, but in the tens category the minuend has as many as 7 tens, so we can transfer one of these tens to the units category:

In the units category we had 2, we threw a ten, it became 12 units. Now we can easily subtract 9 from 12. We write 3 under the line in the units place. In the tens place we had 7 units, we transferred one of them to simple units, leaving 6 tens. We write 6 under the line in the tens place. As a result, we get the number 63:

Column subtraction is usually not written down in such detail; instead, a dot is placed above the digit of the digit in which a unit will be occupied, so as not to remember which digit will need to additionally subtract a unit:

At the same time, they say this: you cannot subtract 9 from 2, we take one, from 12 we subtract 9 - we get 3, we write 3, in the tens place we had 7 ones, we transferred one, there are 6 left, we write 6.

Now consider columnar subtraction from numbers containing zeros:

Let's start subtracting. From 7 we subtract 3, write 4. We cannot subtract 5 from zero, so we are forced to take one in the highest rank, but in the highest rank we also have 0, so for this digit we are forced to take in a higher rank. Taking one from the thousands place, we get 10 hundreds:

We place one of the units in the hundreds place in the low order, resulting in 10 tens. Subtract 5 from 10, write 5:

In the hundreds place we have 9 units left, so we subtract 6 from 9 and write 3. In the thousands place we had a unit, but we spent it on the lower digits, so there remains a zero here (there is no need to write it down). As a result, we got the number 354:

Such a detailed record of the solution was given to make it easier to understand how column subtraction is performed from numbers containing zeros. As already mentioned, in practice the solution is usually written like this:

And all the mentioned actions are performed in the mind. To make subtraction easier, remember this simple rule:

When subtracting by a column, if there is a dot above the zero, the zero turns into 9.

Column subtraction calculator

This calculator will help you subtract numbers in a column. Simply enter the minuend and subtrahend and click the Calculate button.

Problems on the topic: "Division. Dividing multi-digit numbers with a column"

Additional materials
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Educational aids and simulators in the Integral online store for grade 4
Manual for the textbook M.I. Moreau Manual for the textbook L.G. Peterson

Dividing two-digit numbers by a single-digit number

1. Write the given sentences in the form of numerical expressions and solve them.

1.1. Divide the number 72 by the number 8.

1.2. Divide the number 81 by the number 9.

1.3. Divide the number 62 by the number 21.

2. Perform division of numbers.

Solving word problems involving dividing a multi-digit number by a single-digit number

1. How many notebooks for 14 rubles can you buy for 84 rubles?

2. The apple harvest amounted to 81 kg. How many boxes are needed to arrange apples if one box holds 9 kg?

3. A car transports 7 tons of sand in one trip. How many trips does he need to make to transport 140 tons of sand?

4. 176 kg of sugar needs to be transported from the warehouse to the store. How many bags for transporting sugar will be needed if the bag holds 8 kg of sugar?

5. One square meter of floor requires 14 kg of cement. How long square meters Is 126 kg of cement enough?

Dividing a multi-digit number by a two-digit number

1. Do division.

Solving word problems involving dividing a multi-digit number by a multi-digit number

1. The farmer harvested cabbage and onions. He collected 10,455 kg of cabbage, and 123 times less onions. How many kg of onions did the farmer harvest?

2. Three guys divided the number 26668 by 59. The first got 457, the second got 452, and the third got 251. Which answer is correct?

3. For the winter, the farmer prepared 2720 kg of feed for sheep. 85 kg were prepared for each sheep. How many sheep does the farmer have?

4. 13 beds of carrots of equal length were planted in the school garden. A total of 5863 kg of carrots were harvested. How many kg of carrots were collected from each bed?

Division multi-digit or multi-digit numbers are convenient to produce in writing in a column. Let's figure out how to do this. Let's start by dividing a multi-digit number by a single-digit number, and gradually increase the digit of the dividend.

So let's divide 354 on 2 . First, let's place these numbers as shown in the figure:

We place the dividend on the left, the divisor on the right, and the quotient will be written under the divisor.

Now we begin to divide the dividend by the divisor bitwise from left to right. We find first incomplete dividend, for this we take the first digit on the left, in our case 3, and compare it with the divisor.

3 more 2 , Means 3 and there is an incomplete dividend. We put a dot in the quotient and determine how many more digits will be in the quotient - the same number as remained in the dividend after selecting the incomplete dividend. In our case, the quotient has the same number of digits as the dividend, that is, the most significant digit will be hundreds:

In order to 3 divide by 2 remember the multiplication table by 2 and find the number, when multiplied by 2 we get the greatest product, which is less than 3.

2 × 1 = 2 (2< 3)

2 × 2 = 4 (4 > 3)

2 less 3 , A 4 more, which means we take the first example and the multiplier 1 .

Let's write it down 1 to the quotient in place of the first point (in the hundreds place), and write the found product under the dividend:

Now we find the difference between the first incomplete dividend and the product of the found quotient and the divisor:

The resulting value is compared with the divisor. 15 more 2 , which means we have found the second incomplete dividend. To find the result of division 15 on 2 again remember the multiplication table 2 and find the greatest product that is less 15 :

2 × 7 = 14 (14< 15)

2 × 8 = 16 (16 > 15)

The required multiplier 7 , we write it as a quotient in place of the second point (in tens). We find the difference between the second incomplete dividend and the product of the found quotient and divisor:

We continue the division, why we find third incomplete dividend. We lower the next digit of the dividend:

We divide the incomplete dividend by 2, putting the resulting value in the category of units of the quotient. Let's check the correctness of the division:

2 × 7 = 14

We write the result of dividing the third incomplete dividend by the divisor into the quotient and find the difference:

We got the difference equal to zero, which means the division is done Right.

Let's complicate the problem and give another example:

1020 ÷ 5

Let's write our example in a column and define the first incomplete quotient:

The thousands place of the dividend is 1 , compare with the divisor:

1 < 5

We add the hundreds place to the incomplete dividend and compare:

10 > 5 – we have found an incomplete dividend.

We divide 10 on 5 , we get 2 , write the result into the quotient. The difference between the incomplete dividend and the result of multiplying the divisor and the found quotient.

10 – 10 = 0

0 we do not write, we omit the next digit of the dividend – the tens digit:

We compare the second incomplete dividend with the divisor.

2 < 5

We should add one more digit to the incomplete dividend; for this we put in the quotient, on the tens digit 0 :

20 ÷ 5 = 4

We write the answer in the category of units of the quotient and check: we write the product under the second incomplete dividend and calculate the difference. We get 0 , Means example solved correctly.

And 2 more rules for dividing into a column:

1. If the dividend and divisor have zeros in the low-order digits, then before dividing they can be reduced, for example:

As many zeros in the low-order digit of the dividend we remove, we remove the same number of zeros in the low-order digits of the divisor.

2. If there are zeros left in the dividend after division, then they should be transferred to the quotient:

So, let’s formulate the sequence of actions when dividing into a column.

1. Place the dividend on the left and the divisor on the right. We remember that we divide the dividend by isolating incomplete dividends bit by bit and dividing them sequentially by the divisor. The digits in the incomplete dividend are allocated from left to right from high to low.
2. If the dividend and divisor have zeros in the lower digits, then they can be reduced before dividing.
3. We determine the first incomplete divisor:

A) allocate the highest digit of the dividend into the incomplete divisor;

b) compare the incomplete dividend with the divisor; if the divisor is larger, then go to point (V), if less, then we have found an incomplete dividend and can move on to point 4 ;

V) add the next digit to the incomplete dividend and go to point (b).

1. We determine how many digits there will be in the quotient, and put as many dots in place of the quotient (under the divisor) as there will be digits in it. One point (one digit) for the entire first incomplete dividend and the remaining points (digits) are the same as the number of digits left in the dividend after selecting the incomplete dividend.
2. We divide the incomplete dividend by the divisor; to do this, we find a number that, when multiplied by the divisor, would result in a number either equal to or less than the incomplete dividend.
3. We write the found number in place of the next quotient digit (dot), and write the result of multiplying it by the divisor under the incomplete dividend and find their difference.
4. If the difference found is less than or equal to the incomplete dividend, then we have correctly divided the incomplete dividend by the divisor.
5. If there are still digits left in the dividend, then we continue division, otherwise we go to point 10 .
6. We lower the next digit of the dividend to the difference and get the next incomplete dividend:

a) compare the incomplete dividend with the divisor, if the divisor is greater, then go to point (b), if less, then we have found the incomplete dividend and can move on to point 4;

b) add the next digit of the dividend to the incomplete dividend, and write 0 in the place of the next digit (dot) in the quotient;

c) go to point (a).

10. If we performed division without a remainder and the last difference found is equal to 0 , then we did the division correctly.

We talked about dividing a multi-digit number by a single-digit number. In the case where the divider is larger, division is performed in the same way:

Column division(you can also find the name division corner) - standard procedure Varithmetic, designed to divide simple or complex multi-digit numbers by breakingdivided into a number of simpler steps. As with all division problems, one number, calleddivisible, is divided into another, calleddivider, producing a result calledprivate.

The column can be used to divide natural numbers without a remainder, as well as to divide natural numbers with the remainder.

Rules for writing when dividing by a column.

Let's start by studying the rules for writing the dividend, divisor, all intermediate calculations and results whendividing natural numbers in a column. Let’s say right away that writing long division isIt is most convenient on paper with a checkered line - this way there is less chance of straying from the desired row and column.

First, the dividend and the divisor are written in one line from left to right, after which between the writtennumbers represent a symbol of the form.

For example, if the dividend is 6105 and the divisor is 55, then their correct notation when dividing inthe column will be like this:

Look at the following diagram illustrating places to write dividend, divisor, quotient,remainder and intermediate calculations when dividing by a column:

From the above diagram it is clear that the required quotient (or incomplete quotient when divided with a remainder) will bewritten below the divisor under the horizontal bar. And intermediate calculations will be carried out belowdivisible, and you need to take care in advance about the availability of space on the page. In this case, one should be guidedrule: the greater the difference in the number of characters in the entries of the dividend and the divisor, the greaterspace will be required.

Division of a natural number by a single-digit natural number, column division algorithm.

How to do long division is best explained with an example.Calculate:

512:8=?

First, let's write down the dividend and divisor in a column. It will look like this:

We will write their quotient (result) under the divisor. For us this is number 8.

1. Define an incomplete quotient. First we look at the first digit on the left in the dividend notation.If the number defined by this figure is greater than the divisor, then in the next paragraph we have to workwith this number. If this number is less than the divisor, then we need to add the following to considerationon the left the figure in the notation of the dividend, and work further with the number determined by the two consideredin numbers. For convenience, we highlight in our notation the number with which we will work.

2. Take 5. The number 5 is less than 8, which means you need to take one more number from the dividend. 51 is greater than 8. So.this is an incomplete quotient. We put a dot in the quotient (under the corner of the divisor).

After 51 there is only one number 2. This means we add one more point to the result.

3. Now, remembering multiplication table by 8, find the product closest to 51 → 6 x 8 = 48→ write the number 6 into the quotient:

We write 48 under 51 (if we multiply 6 from the quotient by 8 from the divisor, we get 48).

Attention! When writing under an incomplete quotient, the rightmost digit of the incomplete quotient should be aboverightmost digit works.

4. Between 51 and 48 on the left we put “-” (minus). Subtract according to the rules of subtraction in column 48 and below the lineLet's write down the result.

However, if the result of the subtraction is zero, then it does not need to be written (unless the subtraction is inthis point is not the very last action that completely completes the division process column).

The remainder is 3. Let's compare the remainder with the divisor. 3 is less than 8.

Attention!If the remainder is greater than the divisor, then we made a mistake in the calculation and the product iscloser than the one we took.

5. Now, under the horizontal line to the right of the numbers located there (or to the right of the place where we do notbegan to write down zero) we write down the number located in the same column in the record of the dividend. If inThere are no numbers in the dividend entry in this column, then division by column ends here.

The number 32 is greater than 8. And again, using the multiplication table by 8, we find the nearest product → 8 x 4 = 32:

The remainder was zero. This means that the numbers are completely divided (without remainder). If after the lastsubtraction results in zero, and there are no more digits left, then this is the remainder. We add it to the quotient inparentheses (eg 64(2)).

Column division of multi-digit natural numbers.

Division by natural multi-digit number produced in the same way. At the same time, in the firstThe “intermediate” dividend includes so many high-order digits that it becomes larger than the divisor.

For example, 1976 divided by 26.

• The number 1 in the most significant digit is less than 26, so consider a number made up of two digits senior ranks - 19.
• The number 19 is also less than 26, so consider a number made up of the digits of the three highest digits - 197.
• The number 197 is greater than 26, divide 197 tens by 26: 197: 26 = 7 (15 tens left).
• Convert 15 tens to units, add 6 units from the units digit, we get 156.
• Divide 156 by 26 to get 6.

So 1976: 26 = 76.

If at some division step the “intermediate” dividend turns out to be less than the divisor, then in the quotient0 is written, and the number from this digit is transferred to the next, lower digit.

Division with decimal fraction in quotient.

Decimals online. Converting decimal fractions to fractions and ordinary fractions to decimals.

If the natural number is not divisible by a single digit natural number, you can continuebitwise division and get a decimal fraction in the quotient.

For example, divide 64 by 5.

• Divide 6 tens by 5, we get 1 ten and 1 ten as a remainder.
• We convert the remaining ten into units, add 4 from the ones category, and get 14.
• We divide 14 units by 5, we get 2 units and a remainder of 4 units.
• We convert 4 units to tenths, we get 40 tenths.
• Divide 40 tenths by 5 to get 8 tenths.

So 64:5 = 12.8

Thus, if, when dividing a natural number by a natural single-digit or multi-digit numberthe remainder is obtained, then you can put a comma in the quotient, convert the remainder into units of the following,smaller digit and continue dividing.