Division worksheets

What this worksheet is for

Division is the operation where random generation fails most obviously: pick two numbers and the answer is almost never whole. This generator works the other way round. It draws the answer you want pupils to reach and the divisor, then multiplies them to produce the dividend — so every problem divides exactly, unless you ask for remainders, in which case the remainder is drawn to be smaller than the divisor and the arithmetic still closes. Choose the size of the quotient and the divisor and the same page covers everything from simple facts to long division.

Who it suits

Grade 3 to Grade 6, ages eight to twelve. A one-digit divisor with a two-digit quotient is the standard Grade 3 to 4 exercise; remainders arrive in Grade 4; a two-digit divisor is Grade 5 and 6 work and needs the long division layout.

How to use the settings

Set the divisor size first, then the quotient. Leave remainders off while the class is learning the method, and turn them on once dividing is secure — a remainder is a separate idea and it is worth meeting it on its own page. Choose column form for long division: it prints the bracket and leaves the space above it for the answer, which the in a row layout cannot do. Large working space is usually right for long division and unnecessary for facts.

What goes wrong

The commonest error in long division is dropping a place: the pupil brings down the next digit but writes the answer digit one column too far left, so the quotient comes out ten times too big. Missing zeros in the quotient cause the same symptom. With remainders, the usual fault is a remainder larger than the divisor, which means the pupil stopped subtracting one step early — worth pointing out as a check they can run themselves.

Questions

Do the problems always divide exactly?

Yes, unless you turn remainders on. The generator builds each problem from the quotient and the divisor rather than drawing a dividend and hoping, so there is no page where half the answers are decimals nobody expected.

How are remainders written in the key?

As the quotient, then the letter r, then the remainder — 47 r3. That is the convention pupils meet first, before fractions and decimals are introduced as alternatives.

What is the difference between the two layouts?

In a row prints the problem on one line with a space for the answer. Column form prints the long division bracket with the dividend inside it and room above for the quotient, which is what the written method needs.

Can I make the divisors easier without changing anything else?

Set the divisor to one digit and raise the digits in the quotient. That keeps the arithmetic in each step inside the times tables while still producing a long division that takes several steps.