Super Awesome Math

Long Division Worksheets

Long division practice · Grades 3–4

Long division practice from 3-digit by 1-digit up to 5-digit by 2-digit problems, printed on a notebook grid with the frame drawn and empty squares for the working. The frame can be written the English way (divisor outside the bracket, quotient above the overbar) or the continental way (divisor top right, quotient beneath it), and problems can divide exactly or leave a remainder. For step-by-step practice, start with 3-digit by 1-digit problems that divide exactly, move to 4-digit by 2-digit once divide, multiply, subtract and bring down are automatic, and turn remainders on last. Every set is randomly generated, and an optional answer key gives each quotient and remainder.

Skills: long division, remainders, place value, estimation. Format: printable, randomized on every load.

Sheets are randomized, free to print, and carry no answer key on purpose – why Super Awesome Math works this way.

How to do it

Long division works one digit at a time, left to right, repeating the same four steps – divide, multiply, subtract, bring down – until the digits of the dividend run out.

  1. Look at the first digit of the dividend. If the divisor does not fit into it, take the first two digits instead. In 864 ÷ 6, the 8 is enough: 6 fits into 8 once.
  2. Divide: write how many times the divisor fits above the digit you are working on, on the quotient line. Write the 1 above the 8, not anywhere else – the column it sits in is what gives it its place value.
  3. Multiply the divisor by that figure and write the product underneath: 1 × 6 = 6, written under the 8.
  4. Subtract to find what is left over: 8 − 6 = 2. The remainder at this step must be smaller than the divisor; if it is not, the figure in the quotient was too small.
  5. Bring down the next digit of the dividend beside the remainder, making 26, and start again from the divide step. Repeat until every digit has been brought down.
  6. When there are no digits left, whatever remains is the remainder. 864 ÷ 6 leaves nothing, so the answer is exactly 144.

Where it goes wrong

  • Losing the columns. A quotient figure written one place to the left or right changes the answer by a factor of ten, which is why the sheets are printed on a grid with one digit per square.
  • Forgetting the zero. If the divisor does not fit into the digit you brought down, a 0 still goes in the quotient before bringing down the next one – skipping it is the single most common mistake.
  • A remainder as big as the divisor. That always means the previous figure was too small, not that the problem is unusual.

Frequently asked questions
When do children learn long division?
Long division normally arrives at the end of grade 3 or in grade 4, after multiplication facts and subtraction are secure. Each step divides, multiplies, subtracts and brings down, so weakness in any of those shows up quickly.
What is the difference between the two notations?
The bracket form puts the divisor to the left of the dividend with the quotient on an overbar above; the corner form puts the divisor to the top right with the quotient beneath it. They are the same method written differently, and which one a child sees depends on the country they are taught in.
Should I allow remainders?
Start with problems that divide exactly, so the method itself is the only new thing. Turn remainders on once the four steps are automatic, because a leftover forces a child to check that it really is smaller than the divisor.
Do these long division worksheets come with an answer key?
Yes. Tick Print an answer key and the answers print with the sheet: every quotient, with any remainder written after an r (as in 144 r3). Each sheet also carries a set number – the same number with the same settings always deals the same problems, so a sheet and its key can be printed again later.
Can I print 4-digit by 2-digit long division with no remainders?
Yes. Choose the 4 ÷ 2 digits preset and leave Allow remainders off, and every problem divides exactly. To build up to it, work through the presets in order: 3 ÷ 1 introduces the four steps, 4 ÷ 1 makes them longer, 4 ÷ 2 adds estimating with a two-digit divisor, and 5 ÷ 2 is the longest.

Settings
  • Preset: 3-digit by 1-digit, 4-digit by 1-digit, 4-digit by 2-digit or 5-digit by 2-digit
  • Notation: bracket or corner frame
  • Columns: number of problem columns per page
  • Allow remainders instead of exact division
  • Print an answer key

Example problems
  • 864 ÷ 6 = □
  • 3172 ÷ 4 = □
  • 4164 ÷ 12 = □
  • 31752 ÷ 42 = □

More Arithmetic

By grade