Dividing Multi-Digit Numbers

Long division works left to right, deciding how many fit at each place value in turn.

The leftover moves right

Whatever does not divide at one place becomes part of the next place along.

Zeros are not optional

If nothing fits at a place, write 0 there. Skipping it moves every later digit and wrecks the answer.

Check by multiplying

Multiply the answer by the divisor. It should give back the number you started with.

One place at a time

Long division works through the dividend from the left, one digit at a time: divide, multiply, subtract, bring down, repeat. Each cycle handles one place of the answer. Knowing the cycle by name makes it much easier to hold on to.

Estimating each digit

With a two-digit divisor you have to estimate how many times it fits, then check by multiplying. Round the divisor to make the guess easy. Guessing and adjusting is not a weakness of the method — it is the method.

Quotient digits belong in columns

Each digit of the answer sits above the digit you were dividing into. Misplacing one changes the answer by a factor of ten. Estimating the whole answer first — knowing it should have three digits, say — catches this immediately.

Carrying on past the point

When the dividend runs out and a remainder is left, add a decimal point and zeros and keep going: 7 ÷ 4 = 1.75. There is nothing special about the point — you are just moving into tenths, then hundredths.