# What Is Long Division?

Long division is a method for dividing numbers.

It is possible to use long division to divide into a decimal, divide by a decimal, and both together.

# How to Divide Into a Decimal

Long division can be used when the dividend is a decimal.

Question: What is the answer to the division below?:

• Identify the dividend and the divisor:

• Write the dividend and divisor as follows:

• Divide the first digit of the dividend (8) by the divisor (4), and write the whole number answer above the line. (Note: do not count remainders.)
8 ÷ 4 = 2.

• Multiply the answer from the previous operation (2) with the divisor (4). Write the result underneath the number divided into.
2 × 4 = 8.

• Subtract the bottom number from the top number.
8 - 8 = 0.

• The decimal point has been reached.

Place a decimal point in the answer, directly above the decimal point in the dividend.

• With the decimal point dealt with, long division carries on as normal.

Bring down the next digit of the dividend (4).

• Divide this number (4) by the divisor (4), and write the whole number answer above the line. (Note: do not count remainders.)
4 ÷ 4 = 1.

There are no more digits to bring down.

The solution to 8.4 ÷ 4 is 2.1.

# How To Divide By a Decimal

Long division can be used when the divisor is a decimal.

Question: What is the answer to the division below?:

• Identify the dividend and the divisor.

• Count how many digits there are after the decimal point in the divisor.
There is 1 digit after the decimal point:

• To do the division, we want the divisor to be a whole number. Move the decimal point to the right as many places to make it a whole number.

There was 1 digit after the decimal place, so move the decimal point 1 place to the right:

To keep the division the same, move the decimal point the same number of places to the right in the dividend.

Move the decimal place in the dividend 1 place to the right:

The division has become:

• Write the dividend and divisor as follows:

• Divide the first digit of the dividend (4) by the divisor (2), and write the whole number answer above the line. (Note: do not count remainders.)
4 ÷ 2 = 2.

• Multiply the answer from the previous operation (2) the divisor (2). Write the result underneath the number divided into.
2 × 2 = 4.

• Subtract the bottom number from the top number.
4 - 4 = 0.

• Bring down the next digit of the dividend (0).

• Divide this number (0) by the divisor (2), and write the whole number answer above the line. (Note: do not count remainders.)
0 ÷ 2 = 0.

All the digits have been brought down.

The solution to 4 ÷ 0.2 is 20.

# How To Divide When Both Numbers Are Decimals

The slider below shows an example of how to do long division, when both dividend and divisor are decimals:
show

# PARTS OF A DIVISION

• The number you divide is the dividend.

• The number you divide by is the divisor.

• The result of the division is the quotient.

# DIVISION AS THE OPPOSITE OF MULTIPLICATION

Division is the opposite, or inverse, of multiplication.

If:

then:

and:

If two factors multiply to a product, then the product divides by one factor to the other factor.

# DIVIDING INTO A DECIMAL

Dividing into a decimal is much like normal long division - just put a decimal point in the answer directly above the decimal point within the dividend.

# ZEROES AFTER THE DECIMAL POINT

In long division, digits of the dividend often have to be bought down.

Remember that after the last digit after a decimal point, there are endless number of 0s:

It may be that one of these 0s will have to be bought down in a long division.