How do you divide by 5 in your head?
Double the number, then divide the result by 10. For 35 ÷ 5, double 35 to get 70. Divide 70 by 10 and the answer is 7.
Imagine five friends splitting a €35 picnic bill equally. Each pays €7. Nothing needs writing down, and nobody has to open the calculator. With an €85 bill, the same two steps give 170, then €17 each.
It sounds slightly backwards: make the number bigger to make the division easier. Here is why that is allowed.
Why does doubling help?
Picture 35 wooden counters packed into groups of five. You have seven groups. Now make an identical copy of every counter, keeping each copy in the same group.
The total doubles to 70. Every group doubles to ten. But the number of groups stays seven. Counting groups of ten in 70 gives the same answer as counting groups of five in 35.
That is the idea behind the equivalent fractions property: multiplying the top and bottom by the same nonzero number keeps the value unchanged. Here, 35/5 = 70/10. We choose doubling because it turns five into a friendly ten.
A bigger bill, the same two steps
Try 125 ÷ 5. First, double 125: 250. Then divide by ten: 25.
Dividing by ten makes each digit worth one tenth as much: 250 becomes 25, while 46 becomes 4.6. If place value feels slippery, the guide to decimals takes it slowly.
There is a handy check: multiply your answer by five. Does it bring you back to the original number? Here, 25 × 5 = 125. A quick check is often more useful than doing the same calculation twice.
What if the answer is not a whole number?
The shortcut still works. For 23 ÷ 5, double 23 to get 46, then divide by ten: 4.6. A €23 bill shared between five people is €4.60 each.
Be careful with the tempting instruction “drop the last digit”. Dropping the 6 from 46 would give 4, which is wrong. You are dividing by ten, not deleting part of the number.
Context matters, too. Share 23 whole sweets between five people without cutting any, and each gets four, with three left over. Money can be split into cents; whole sweets may need a remainder. Both answers describe the same division in different ways.
One to try before you go
A five-pack of notebooks costs €12.50. What does one notebook cost?
Show me the two steps
Double 12.50 to get 25. Divide 25 by ten: €2.50. Check it with five lots of €2.50: €12.50.
You do not need a new trick for every number. If 50 ÷ 5 already feels obvious, use what you know. Keep this shortcut for the numbers that make you pause, and continue the mental maths course at your own pace.