Mental division

Mental division is not a single method. It is a small set of habits, and knowing which to reach for is most of the skill.

Split the dividend into friendly parts

Any dividend can be broken into pieces that the divisor goes into cleanly. Divide each piece and add the results.

Halve instead of dividing by 4 or 8

Dividing by four is halving twice. Dividing by eight is halving three times. Most people halve far more reliably than they divide.

Read a multiplication fact backwards

7 x 8 = 56 also says 56 / 8 = 7. A student who knows their multiplication facts already knows the matching division facts, and pausing to convert is what makes division feel slower than it needs to be.

Use place value on multiples of ten

Check by multiplying

Every division has a multiplication that undoes it, and checking mentally is far quicker than redoing the division. If 368 / 8 = 46, then 46 x 8 must give 368. Working that back out takes a couple of seconds and catches a halving that went wrong.

Remainders in your head

When the division does not come out exactly, find the nearest multiple of the divisor below the dividend and subtract.

What the remainder should become depends on the question. Fourteen buses hold everyone except two people, so fifteen buses are needed. Fourteen full boxes are packed and two items are left over. The arithmetic is the same and the answers differ.

Common mistakes

Splitting into parts the divisor does not divide

Breaking 144 into 100 + 44 for a division by six gives two awkward pieces. Choose parts that are multiples of the divisor.

Scaling only one number

In 4,200 / 70, dividing both by ten keeps the quotient the same. Dividing only the top by ten changes the answer.

Check yourself