# Long Division

๐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.

## 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: $93:3=$
Solution:

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 $9$ by the number $3$.
We'll record the result above the digit $9$ on the bar.
$9:3=3$

$3$ is the quotient.

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

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

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

We will get a remainder of $0$. 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: $31$

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

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

Now we will divide the digit located on the left $6$.
We will write the result above the bar, only the whole numbers.

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

Now let's find the remainder: multiply the result $1$ by the divisor $4$ and subtract as needed.

The remainder is $2$.
Let's bring down the next digit.
Now we have a completely new number $24$

We will divide $24$ by $4$.
$24 รท 4 = 6$
Write down the $6$ above the digit $4$ over the bar.
We will find the remainder by multiplying by the divisor and subtracting accordingly:

We got the remainder $0$.
Now let's move on to the third digit $4$.
We bring it down from above
and divide:
$4:4=1$
Let's write $1$ above the bar in the correct place.
The remainder is $0$.
We have completed the exercise and the result is $161$.

Note:
If we had received an exercise like this:

When dividing $4$ by $5$, it turns out that there are no whole numbers because $4$ is smaller than $5$.
Therefore, in a case like this, you would write $0$ over $4$, continue to find the remainder, and proceed in the same manner.
Bring down the number $9$ and so on.
The answer is $99$.

### Division by a Two-Digit Number

Look at the exercise $1436 \div 12=$
Solution:
We will write it down correctly.
We notice that the number $1$ is less than $12$, so we write a $0$ above the number $1$.
Let's find the remainder $14$.
Divide $14$ by $12$ and we get $1$.
Let's find the remainder and proceed in the same manner.
The answer is $119$ and the remainder is $8$.

## Ejemplos y ejercicios con soluciones de la divisiรณn larga

### Answer

$15$

### Answer

$8$

### Answer

$5$

### Answer

$2$

### Answer

$19$

Do you know what the answer is?
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