# How to Do Long Division with a Remainder

## What Is Long Division with a Remainder?

Long division is a method for dividing numbers.

Long division is used for dividing numbers that have many digits.

Sometimes a number will not divide exactly into another: there will be a remainder.

## A Real Example of How to Do Long Division

Doing long division, when there will be a remainder, is easy.

### Question

Divide the numbers below.

### Step-by-Step:

# 1

Identify the number being *divided* (called the dividend) and the number you are *dividing by* (called the divisor).

# 2

Write the dividend inside the *long division bracket* and the divisor outside to its left:

# 3

Divide the first digit of the dividend (1) by the divisor (6). Do not count remainders.

1 ÷ 6 = 0

6 goes into 1 **0** times.

# 4

Write the answer (0) above the long division bracket.

# 5

Multiply the answer from **Step 3** (0) with the divisor (6).

0 × 6 = 0

Write the answer underneath the digit divided into:

# 6

Subtract the bottom number (0) from the top number (1).

1 − 0 = 1

# 7

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

# 8

Divide this number (14) by the divisor (6). Do not count remainders.

14 ÷ 6 = 2 ~~ r 2 ~~

6 goes into 14 **2** times.

# 9

Write the answer (2) above the long division bracket.

# 10

Multiply the answer from **Step 8** (2) with the divisor (6).

2 × 6 = 12

Write the answer underneath the number divided into:

# 11

Subtract the bottom number (12) from the top number (14).

14 − 12 = 2

# 12

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

# 13

Divide this number (20) by the divisor (6). Do not count remainders.

20 ÷ 6 = 3 ~~ r 2 ~~

6 goes into 20 **3** times.

# 14

Write the answer (3) above the long division bracket.

# 15

Multiply the answer from **Step 13** (3) with the divisor (6).

3 × 6 = 18

Write the answer underneath the number divided into:

# 16

Subtract the bottom number (18) from the top number (20).

20 − 18 = 2

There are no more digits to bring down.

# 17

The number above the long division bracket is the *quotient*. The number at the bottom is the *remainder*.

# 18

Write the answer as **23** (the quotient), **r** (for remainder) **2** (the remainder).

### Answer:

The solution to 140 ÷ 6 is 23 r 2.