Welcome to an example that will show the relationship between
stick multiplication. Also called Mayan multiplication or Japanese multiplication,
and partial products. We'll first find the product of fourteen and thirty-seven
using stick multiplication. And to keep things organized
we'll let a green stick equal ten, and a blue stick
equal one. So for fourteen, because fourteen is equal to
ten plus four, we'll model fourteen with one green stick,
and four blue sticks.
So that's ten, eleven, twelve,
thirteen and fourteen. Now we'll model thirty seven.
And since thirty seven is equal to thirty plus seven,
we'll model thirty seven with
three green sticks, and seven blue sticks,
in a different direction. So here we have
ten, twenty, thirty.
Then we need seven blue sticks. So one,
two, three, four,
five, six and seven.
The intersection points represent our product.
Which intersection point of two greens
represents ten time ten or one hundred. So notice here we have
one, two three hundreds or three hundred. Each intersection point of a green and a blue
represent ten times one or ten. So notice here we have one,
two, three, four, five, six, seven tens or seventy.
And here we have
one, two, three, four, five, six,
seven, eight, nine, ten, eleven twelve tens,
or one hundred twenty. And then finally,
each intersection point of two blues represents one times one, or one.
So we have one, two, three, four, five, six, seven,
eight, nine, ten, eleven, twelve, thirteen, fourteen,
fifteen, sixteen, seventeen, eighteen, nineteen, twenty,
twenty-one, twenty-two, twenty-three, twenty-four, twenty-five, twenty-six, twenty-seven, and twenty-eight.
So using our stick multiplication,
fourteen times thirty-seven is equal to three hundred,
plus seventy, plus one hundred twenty,
plus twenty-eight, which equals five hundred
eighteen. So fourteen times thirty-seven
equals five hundred eighteen. When performing stick multiplication, these values here
do represent the partial products of our product.
One way to show this would be to write fourteen
as ten plus four, and write thirty-seven as thirty,
plus seven. And now to find this product we'd perform
repeated distribution. Meaning we'd first distribute the ten.
So notice that ten times thirty is equal to three hundred,
which we see here in our stick multiplication.
And then we'd have ten
times seven which is seventy.
so we'd have plus seventy, which we see here in our stick multiplication.
And now we would distribute the four, so we'd have four times thirty or one hundred twenty.
Which again we see here in our stick our stick multiplication.
And hen finally, we have plus
four times seven which is twenty-eight. So,
plus twenty-eight gives us our final partial product,
which we see here in this stick multiplication,
giving us our product of five hundred eighteen.
So not only does stick multiplication
give us a nice visual for multiplication,
it also demonstrates the partial products of a given product.
I hope you found this helpful.