# Division (whole numbers)

## Long Division-With Remainders (multi-digit divisors)

Once students master the process of long division, longer problem just have more steps and require stronger multiplication skills.  The process is exactly the same.

To review the long division process (and acronyms for remembering the steps), see the lesson on Long Division with remainders (1 digit divisor).

Just like with one digit-divisors, we typically use the "house method" to do long division with multi-digit divisors.  Remember, the "house method" reverses the divisor and dividend

## Long Division-With Remainders (1-digit Divisor)

Division (once you get past the division facts that are just the inverse of times tables) is the most complicated whole number operation -- mostly because doing long division requires multiplication and subtraction.  Students who have not learned their times tables or mastered subtraction with borrowing will struggle with long division.

The trickiest part of long division is keeping numbers and place values oriented properly (when you divide into a number you must divide the divisor into each digit of the dividend).

## Long Division-No Remainders (multi-digit divisors)

Once students master the process of long division, longer problem just have more steps and require stronger multiplication skills.  The process is exactly the same.

To review the long division process (and acronyms for remembering the steps), see the lesson on Long Division with no remainders (1 digit divisor).

Just like with one digit-divisors, we typically use the "house method" to do long division with multi-digit divisors.  Remember, the "house method" reverses the divisor and dividend

## Long Division- No Remainders (1-digit Divisor)

Division (once you get past the division facts that are just the inverse of times tables) is the most complicated whole number operation -- mostly because doing long division requires multiplication and subtraction.  Students who have not learned their times tables or mastered subtraction with borrowing will struggle with long division.

The trickiest part of long division is keeping numbers and place values oriented properly (when you divide into a number you must divide the divisor into each digit of the dividend).

## Divisibility Rules

Division, especially of long numbers, can be tedious.  Even when students know all of their times tables and division facts, figuring out if a number is divisible by a certain number can take some time.

Here are some tricks!

0: When working with rational numbers, you cannot divide by 0.  A number divided by 0 is undefined.

1: All numbers are divisible by 1.  Any number divided by 1 is itself.

## Division Facts

Division facts are the opposite of times tables.  For some students, the process of learning the times tables automatically means that they know the division facts.  Other students need to learn the division facts more explicitly. Knowing division facts makes long division much easier. It's worth it for students to learn these facts.