Long division
A number is far too big for any times-table fact. How do you divide it, by one digit or by two, a piece at a time?
Where you are 4 inside
What this area is about
Long division splits one big division of whole numbers into a few small ones. It works from the biggest place down, trades whatever is left into the next place, and records the quotient one digit at a time, with a remainder when the division does not come out even.
How these fit together
First methods. Partial quotients takes away easy multiples of the divisor, such as 100 or 10 groups at once, and adds up how many groups were taken. Dividing by a single digit shares hundreds, tens and ones in turn, trading what is left into the next smaller place.
The algorithm. The standard long division algorithm is partial quotients with no choosing: divide, multiply, subtract and bring down, one quotient digit in each place.
A harder divisor. Dividing by a two-digit number keeps the same layout, but each quotient digit is now a guess, made by rounding the divisor, and then tested.
A path through it
Partial quotients first, since dividing by a single digit refers back to it; then dividing by a single digit; then the standard algorithm; then two-digit divisors. All of it rests on multi-digit multiplication.
Finish here and you can divide a decimal by a whole number, turn a fraction into a decimal, and later carry the same steps over to polynomial long division.