# How to Do Long Division With Decimals (Mathematics Lesson)

# 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.

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.

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:##### Interactive Test

**show**

##### Note

# 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.

##### Top Tip

# 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.