Parent guide · 5 min read
Dividing decimals for kids: moving the point the same way in both numbers
Dividing by a decimal is the point where many children stop trusting their own working. The rule they are given, "move the decimal point", sounds like a trick, and it is easy to move it in one number and not the other. This guide explains why the rule works, so it stops being a trick, and then goes through the examples that cause most of the errors.
Try this tonight
4 things you can do at home
Say it as a question about groups
Read 7.2 ÷ 0.4 as "how many 0.4s fit into 7.2?" Putting it in words makes it a counting question rather than a rule, and it makes a wrong answer such as 1.8 or 180 look odd straight away.
Estimate before calculating
Round to friendly numbers: 7.2 is about 7 and 0.4 is about half a unit, so the answer should be around 14 to 18. When the final working gives 1.8, the estimate shows something is off by a factor of 10.
Make the divisor whole, and move both points
The divisor 0.4 needs one move to become 4. Do the same one move on 7.2, to get 72. Draw an arrow on each number, so it is obvious that both moved by the same amount.
Divide, then put the point straight above
Work out 72 ÷ 4 = 18. If the number being divided still has a decimal point after moving, write the point in the answer straight above where it sits, and then divide as normal.
Why moving both points does not change the answer
Dividing is the same as comparing two amounts, and comparing is not changed by scaling both amounts equally. 7.2 ÷ 0.4 asks how many 0.4s are in 7.2. Ten times as much on both sides, 72 and 4, asks the same question: how many 4s are in 72. The answer is 18 either way.
This is also the same reason that 6 ÷ 3 and 60 ÷ 30 are equal. A child who sees the pair as "the same fraction, written differently" has understood the idea rather than learned a rule.
A worked example: when the divisor has more places
Take 3.6 ÷ 0.09. The divisor has two decimal places, so move both points two places: 3.6 becomes 360 (add a zero to fill the gap) and 0.09 becomes 9. Now 360 ÷ 9 = 40.
The common error is moving the divisor two places but the other number only once, giving 36 ÷ 9 = 4. The estimate catches it: 0.09 is about a tenth, and there are about ten tenths in every whole, so 3.6 holds about 36 or more of them, which is closer to 40 than to 4.
A worked example: a whole-number divisor
When the divisor is already a whole number, as in 4.5 ÷ 3, nothing needs to move. Divide as normal and keep the point straight above: 4.5 ÷ 3 = 1.5. Similarly 1.2 ÷ 5 = 0.24, because 12 tenths shared between 5 is 2.4 tenths, which is 0.24 as a decimal.
A child who has moved the point here without need has created extra work. A quick question to ask is "is the number I am dividing by already whole?" If yes, the only job is placing the point correctly in the answer.
The belief that division always makes numbers smaller
With whole numbers, dividing makes the answer smaller, so children expect this always to hold. Dividing by a number less than 1 breaks that: 6 ÷ 0.5 = 12, because there are 12 halves in 6. The answer is bigger than the number you started with.
The "how many fit?" reading makes this natural. It is worth saying out loud when it comes up, since a child who believes the old rule will "correct" a right answer into a wrong one.
Signs it’s time for outside help
When home help has done what it can
- Moves the decimal point in the divisor but not in the other number.
- Cannot say what 7.2 ÷ 0.4 is asking in words.
- Gets an answer a factor of 10 too big or too small and does not notice.
- Believes that dividing must always give a smaller number.
- Loses the point when the answer needs a zero, such as 0.24.
- Is fine with whole-number long division but stalls once a decimal appears.
Questions parents ask
FAQ
What grade do children learn to divide decimals?
In the US Common Core, dividing decimals to hundredths is introduced in Grade 5 (ages 10–11), and fluent division of multi-digit decimals follows in Grade 6. Other curricula, including the Australian Curriculum, cover it across the upper primary years.
Do I have to move the point in both numbers?
Yes, by the same number of places. That keeps the answer the same. Moving it in only one number changes the question.
Why do I add zeros sometimes?
When the divisor has more decimal places than the other number, there are not enough digits to move past. Adding zeros after the last decimal digit does not change the value, so 3.6 can be written as 3.60 and then 360.
Should my child use a calculator to check?
It is a fine check once the working is done by hand. The estimate is the more useful habit, because it works in a test where the calculator may not be allowed.
Further reading
Classes that fit
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