Multiplying on fingers

Many of us, even as adults, sometimes resort to adding or subtracting on our fingers. They provide a convenient way of counting, being in base ten, and while finger-counting tends to be discouraged in school, it works – and fingers are always available.

However, not everyone knows that it’s also possible to multiply on our fingers. Multiplying on fingers is not as easy as adding or subtracting with the fingers, and you do need first of all to know in your head how to multiply low numbers by 2, 3, 4 and 5. But most children (and adults) who have difficulties with multiplication have the worst problems with the 6, 7 or 8 times table. These are the ones that can be done on the fingers.

It’s a bit complicated to remember what to do, and takes a little practice to become familiar with the technique. Some children would find it more trouble than it’s worth. However a child who learns kinaesthetically and has difficulty remembering anything by rote would probably grasp this quickly. So do try this with your children, even if it seems highly complex from an adult point of view.

Here’s what you do:

Hold your hands horizontally in front of you, with your elbows sticking out, palms facing down, tips of middle fingers touching. (That’s the hardest part to describe in text!)

Mentally (or with marker pen, if you like) number the thumbs as 6, index fingers as 7, middle fingers 8, ring fingers 9, little fingers 10. You have to define the thumbs as honourary fingers for the purposes of this ‘manual calculator’.

To do any multiplication, from 6×6 through to 9×9, touch two fingers together which represent the numbers you want to multiply. For instance, for 7×8, touch index finger of one hand to middle finger of the other.

Finger multiplication

The two touching fingers and all the ones nearer to you than the ones touching are the ‘tens’ group. In the 7×8 example you have five: both thumbs, both index fingers and one middle finger are in that group, so the answer contains 5 tens.

The remaining number of fingers on each hand – in this case 3 on one hand and 2 on the other – must be multiplied together to give the ‘units’ of the answer. 3×2 = 6.

The answer to 7×8 is five tens and six units, 50+6 = 56.

It sounds horrendous, but some children love it and it really works.

Problem with multiplying on fingers

Sometimes the ‘units’ add up to more than 10, in which case the ten must be ‘carried’ and added onto the other tens. For instance, if you multiply 6×7, you will have 3 tens (2 thumbs and one finger), with 3 and 4 fingers respectively remaining, and 3×4 is 12. So either add 12 to 30 and don’t worry about it being units, or carry the 10 mentally and add 40 to 2 – either way you get 42.

It works for every multiplication from 6×6 to 10×10 (not that you’d want such a complex method for multiplying by 10 – if you think you do, try reading the page on multiplication tricks).

For more articles about teaching basic maths without workbooks or drill, see:

More complex multiplication
Introducing place value
Algebra for six-year-olds
Prime numbers and factors

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