Some multiplications look hard until you change them into an easier one with the same answer. The doubling and halving multiplication trick does exactly that: you halve one number, double the other, and the answer does not change. It turns 18 × 5 into 9 × 10, and 16 × 25 into 4 × 100. This guide explains why it works, shows you how to use it for ×5 and ×25, covers what to do with odd numbers, and ends with a five-minute practice plan.
Picture a rectangle made of squares, 4 squares wide and 16 squares long. It holds 4 × 16 squares. Now cut it in half across its width and put the two halves end to end. The new rectangle is 2 squares wide and 32 squares long. You have not added or removed a single square, so the area is the same. Do it once more and you get a strip 1 square wide and 64 squares long.
That is the whole reason the trick works. Halving one side of a rectangle and doubling the other side keeps its area. Teachers often show this with arrays of dots or with area models; the Kentucky Center for Mathematics presents doubling and halving this way for students in grades 3 and 4.
It is worth saying clearly: this is not magic, and it is not a rule you must always follow. It is a strategy you choose when it makes the sum friendlier. The aim is to reach a number like 10 or 100, because multiplying by those is easy.
Five is half of ten. So multiplying by 5 is the same as multiplying by 10 and then halving. There are two ways to use this.
Put a zero on the end of 18 to get 180, then halve it.
If the other number is even, halve it and double the 5 into a 10:
Both routes give the same answer. Route 2 is usually quicker in your head, because halving a small number is easier than halving a big one. Komodo Math uses 34 × 5 as its example of the half and double method too.
Twenty-five is a quarter of 100. Double 25 and you get 50; double again and you get 100. So for ×25, you double the 25 twice and halve the other number twice.
Here 8 was halved twice, to 4 and then to 2, while 25 was doubled twice, to 50 and then to 100. More examples:
A quick check: halving a number twice is the same as dividing it by 4. So for ×25 you can simply ask, "How many fours are in this number?" There are 4 fours in 16, so 16 × 25 is 4 hundreds.
If the number does not split into fours neatly, multiply by 100 first and then divide by 4:
Dividing by 4 is just halving twice: half of 3600 is 1800, and half of 1800 is 900.
Halving an odd number gives a half, such as 3.5, which makes the sum harder, not easier. You have two choices.
For example, 7 is odd, so do not halve it. Work out 7 × 10 and halve that:
The same idea works with 25. Fifteen cannot be halved neatly, so multiply by 100 first:
Some multiplications have nothing to halve or double into a friendly number. Take 13 × 7. Both numbers are odd, and neither one is close to 5, 10, 25 or 100. Halving and doubling only makes it messier. For a sum like this, split it into parts instead: 10 × 7 = 70 and 3 × 7 = 21, and 70 + 21 = 91. A good mental maths learner knows several strategies and picks the right one, which is what our Multiply in Minutes guide is about.
The trick pays off when one number is a 5 or ends in 5 or 0, and the other number is even. Watch out for these trigger numbers: 5, 15, 25, 35, 45, 50 and 250. When you see one of them next to an even number, think "halve and double".
The first two examples also appear in a Magoosh lesson for adult test-takers, which shows how useful the idea stays long after primary school.
Strategies stick when you use them a little every day. Here is a short routine.
The trick relies on knowing your basic facts, so keep those sharp with the 10-question Times Tables mode. If they still feel shaky, start with our guide on how to learn times tables fast.
Tip for parents and teachers: after each problem, ask the child, "Which number did you halve, and why?" Explaining the choice matters more than speed. It shows they are choosing a strategy, not following a recipe. Children who like doubles may also enjoy the near doubles strategy for addition, and those who want more shortcuts can explore Vedic maths multiplication tricks.
It is a mental maths strategy where you halve one number in a multiplication and double the other. The answer stays the same, but the new sum is often easier, such as turning 34 × 5 into 17 × 10.
Think of the multiplication as a rectangle. Cutting it in half and putting the halves end to end makes it half as wide and twice as long, but it still has the same number of squares inside, so the area (the answer) does not change.
Multiply by 10 and then halve, so 18 × 5 is half of 180, which is 90. Or, if the other number is even, halve it first and multiply by 10: 84 × 5 = 42 × 10 = 420.
Halve the other number twice and double 25 twice to make 100. For example, 24 × 25 = 6 × 100 = 600. If the number does not divide by 4 neatly, multiply by 100 and then divide by 4.
Halve the other number instead if it is even, or use the ×10 or ×100 route and halve at the end. For example, 7 × 5 is half of 70, which is 35.
Skip it when neither number halves or doubles into something friendly, such as 13 × 7. Split the sum into tens and ones instead, or use a times-table fact you already know.
It is a real strategy based on how multiplication works, not a trick that only works by luck. It works every time, and the skill is knowing when it makes a sum easier.