## 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.

## Multiplication (by 3+ digits)

We discuss the algorithm for multiplying multi-digit numbers in detail in the lesson Multiplication (2x2 digits).  Once you start working with longer numbers, the process continues:

## Multiplication (2 by 2 digits)

The algorithm for multiplying a two-digit number by a one digit number is pretty simple: you multiply the one-digit number by both digits of the second number.  And, if you keep things lined up, your tens digit ends up in the tens column and your ones digit lands in the ones column, and your answer turns out perfect.