Multiplying by Doubling

Doubling is a superpower

You already know that doubling means making twice as much — see Doubling and Halving if you need a reminder. What many people do not realise is that doubling is a multiplication strategy in its own right. By doubling again and again, you can multiply by 2, 4, 8 and even 16 without memorising those tables — and you can do it with big numbers, in your head.

Doubling and the powers of 2

Here is the key insight. The numbers 2, 4, 8 and 16 are all built by doubling:

• × 2 = double once
• × 4 = double twice (because 4 = 2 × 2)
• × 8 = double three times (because 8 = 2 × 2 × 2)
• × 16 = double four times (because 16 = 2 × 2 × 2 × 2)

So to multiply by one of these, you just keep doubling.

Building a doubling chain

Start with any number and write its doubling chain. Each new number is double the one before.

Example — start with 7:

Multiply 7 by	Doublings	Result
2	double once	14
4	double twice	28
8	double 3 times	56
16	double 4 times	112

So 7 × 8 = 56 and even 7 × 16 = 112, all from one chain of doublings: 7 → 14 → 28 → 56 → 112.

Worked example: multiply by 4

Work out 23 × 4 by doubling.

1. Double 23: 23 + 23 = 46.
2. Double 46: 46 + 46 = 92.
3. So 23 × 4 = 92.

Two quick doubles handle a multiplication that might otherwise need written working.

Worked example: multiply by 8

Work out 14 × 8 by doubling.

1. Double 14 → 28.
2. Double 28 → 56.
3. Double 56 → 112.
4. So 14 × 8 = 112.

Three doublings, no times table for 8 required.

The double-and-halve trick

Here is a second, clever use of doubling. In any multiplication, you can double one number and halve the other, and the answer stays exactly the same. This lets you swap a hard product for an easy one.

Why does it work? Doubling multiplies the product by 2, and halving divides it by 2 — those two changes cancel out, leaving the answer unchanged.

Example — 16 × 5:

1. Halve 16 → 8. Double 5 → 10.
2. Now you have 8 × 10 = 80.
3. So 16 × 5 = 80, found the easy way.

You can even repeat it. For 8 × 25: double-and-halve to 4 × 50 = 200, or again to 2 × 100 = 200. Same answer, easier each step.

Hard product	Double and halve	Easy product	Answer
16 × 5	halve 16, double 5	8 × 10	80
14 × 50	halve 14, double 50	7 × 100	700
6 × 35	double 6, halve...	use 3 × 70	210
18 × 5	halve 18, double 5	9 × 10	90

(For 6 × 35, halving 35 is awkward, so instead double 35 and halve 6: 3 × 70 = 210. Pick whichever direction gives whole numbers.)

When doubling shines

Doubling is at its best when:

• you are multiplying by 2, 4, 8 or 16, or
• one number in the product is even, so the double-and-halve trick gives whole numbers.

For odd-by-odd products like 7 × 9, doubling helps less — there a split strategy or known fact is quicker.

A practice activity

Make a doubling staircase. Pick a starting number, say 9. Write it at the bottom step, then keep doubling up the staircase: 9, 18, 36, 72, 144. Now you can instantly read off 9 × 2, 9 × 4, 9 × 8 and 9 × 16.

Then try the double-and-halve trick on these: 12 × 5, 25 × 8, 14 × 5. (Answers: 6 × 10 = 60; double-and-halve twice to 100 × 1... easier: 25 × 8 = halve 8 double 25 → 50 × 4 = 200; 7 × 10 = 70.)

Where this leads

Doubling underpins the 4 and 8 Times Tables and feeds straight into Mental Math Strategies. It is also the seed of an idea you meet much later: powers of 2 and how computers count. A skill this simple, reaching this far, is well worth practising.