Long Division

🏆Practice long division

Long Division

We'll go step by step, dividing one digit at each step. We'll start with the digit on the left, write down the division result above the drawn line, and look for the remainder.

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Long Division

Notation Mode

We'll draw a division bar
Inside the bar, we'll write the dividend (the number we want to divide).
To its left, we'll write the divisor (the number by which we want to divide).
Above the bar, we'll write the quotient (the result of the division).
In each step, we will divide one digit. We start with the leftmost digit, write the result (whole numbers only) above the bar, and look for the remainder by multiplying this number by the divisor.
We write the result of the multiplication below the number we just divided and subtract to find the remainder.
We bring down the next digit from above to continue dividing.
We divide in the same way, find the remainder.
When there are no more digits to bring down, it means we have finished the exercise.
The digit that we cannot divide is the remainder or residue.


Division of a Two-Digit Number by a Single-Digit Number

Take a look at the following exercise: 93:3=93:3=
Solution:

Division of a two-digit number by a one-digit number

We will set it up this way:
Write the dividend inside the bar. To its left, write the divisor.
Above the bar, we will write the quotient.
Pay attention: What matters to us in this exercise are the quotient and the remainder.
First, we will divide the first digit 99 by the number 33.
We'll record the result above the digit 99 on the bar.
9:3=39:3=3

33 is the quotient.

2 - Division of a two-digit number by a one-digit number

Remember that we said we're also interested in the remainder?
To find it, we'll multiply the 33 (the result we obtained) by 33 (the divisor).
Record the result below the 99.
3×3=93 × 3=9

Now, we subtract 99 from 99 and we get the remainder.
99=09-9=0
We obtained a remainder of 00

Now let's move on to the second digit 33.
We bring it down from the top and divide the number again.
3:3=13:3=1
The quotient is 11, so we will write it above the digit 33 on the bar.
Let's see what the remainder is:
Multiply the quotient by the divisor, it will give us
1×3=31×3=3
Write 33 below 33 and subtract.

3 - Division of a two-digit number by a one-digit number

We will get a remainder of 00. There is no remainder, and we don't have any more digits to bring down, which means we are finished.
The quotient is what remains written above the bar: 3131

4 - Division of a two-digit number by a one-digit number


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Division of a Three-Digit Number by a One-Digit Number

Look at the following exercise: 
644:4=644:4=
Solution:
We will write it out correctly.

1 - Division of a three-digit number by a one-digit number

Now we will divide the digit located on the left 66.
We will write the result above the bar, only the whole numbers.

6:4=16:4=1
Plus the remainder.
Let's write 11 above the bar on top of the number 66.

2 - Division of a three-digit number by a one-digit number

Now let's find the remainder: multiply the result 11 by the divisor 44 and subtract as needed.

The remainder is 22.
Let's bring down the next digit.
Now we have a completely new number 2424

3 - Division of a three-digit number by a single-digit number

We will divide 2424 by 44.
24÷4=624 ÷ 4 = 6
Write down the 66 above the digit 44 over the bar.
We will find the remainder by multiplying by the divisor and subtracting accordingly:

4 - Division of a three-digit number by a single-digit number

We got the remainder 00.
Now let's move on to the third digit 44.
We bring it down from above
and divide:
4:4=14:4=1
Let's write 11 above the bar in the correct place.
The remainder is 00.
We have completed the exercise and the result is 161161.

Step 5 -Dividing a three-digit number by a one-digit number


Note:
If we had received an exercise like this:

Dividing 4 by 5

When dividing 44 by 55, it turns out that there are no whole numbers because 44 is smaller than 55.
Therefore, in a case like this, you would write 00 over 44, continue to find the remainder, and proceed in the same manner.
Bring down the number 99 and so on.
The answer is 9999.

2 - When dividing 4 by 5


Division by a Two-Digit Number

Look at the exercise 1436÷12=1436 \div 12=
Solution:
We will write it down correctly.
We notice that the number 11 is less than 1212, so we write a 00 above the number 11.
Let's find the remainder 1414.
Divide 1414 by 1212 and we get 11.
Let's find the remainder and proceed in the same manner.
The answer is 119119 and the remainder is 88.

Division by a two-digit number


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