# Middle Computation

## 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).

## 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.

## 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.

## Multiplication (2 by 1 digit)

Times tables are great for multiplying one-digit (and select two-digit) numbers. But, once we get into larger numbers, it's important to understand how multiplication works when numbers have multiple digits.  We typically use a number of algorithms for doing multiplication -- namely we multiply all digits of multipliers by all digits of multiplicands.  The processes become automatic, but it's very helpful for students to understand why we have to multiply each digit by each each digit.

## Multiplication (Times tables)

**Note: A huge part of learning times tables is practice.  Scroll down for a blank times table chartworksheets (40 and 100 problem sets), times table sprints (for competitive practice), and times table tesselations (for artistic practice).**

Multiplication is the process of adding groups, multiple times.  It's a streamlined and faster way to add, if you need to add the same number repeatedly.

$4+4+4+4+4=5 \times 4$

## Subtraction (with regrouping, 3+ digits)

Once students learn how to subtract with regrouping, they can apply those skills to numbers of any size!  For more on regrouping (how and why it works), see lesson on Subtraction (with Regrouping, 2-1 and 2-2 digits).

The first step in subtracting multi-digit numbers is setting the problem up vertically, making sure that the place values are lined up (ones to ones, tens to tens, etc).