4. Chinese MethodLets use this example: 24 x 13
2
4
3
1
First draw a set of lines to represent
24. Then draw a set of lines to
represent 13 that run perpendicular
to the lines that represent 24.
Next separate the diagram into
sections where the right corner is
section 1, the top and bottom corners
make up section 2 and the left corner
is section 3.
5. Chinese Method
Next you count up the number of
Intersections starting from the right
most section.
If the number is greater that 9, we drop
the ones value and carry the tens to the
next section.
We do this until we complete all sections
to get our answer
7. AdditionalQuestions for the Chinese Method
What if there is a 0 place value? What if there are different amount
of digits?
30 x 12
Set up the problem as normal, but
draw a dotted line to represent a
place value of 0.
Set up your diagram by moving
from top to bottom and left to
right with highest value
321 x 23
9. Egyptian Method
1 13
2 26
4 52
8 104
16 208
24 x 13
1. Create 2 columns with the
first column having a list of
binary numbers
2. And the second where you
start with one of the factors
then double it in the following
rows
3. Next we look at the first
column and add up the
numbers to get 24 4. Then we take the
corresponding numbers in the
second column and find their
sum to get our answer
104
+ 208
312
10. 1 20 n 20 x n
2 21 2n 21 x n
4 22 4n 22 x n
8 23 8n 23 x n
16 24 16n 24 x n
m x n
Egyptian Method Explanation
Add up the first column accordingly to equal m. Then take the corresponding values in
the third column and find their sum to get your answer
Column 1 represents
binary numbers
Column 2 represents the
power of 2 that corresponds
to the binary in column 1
Column 3 represents the
doubling n values
Column 4 represents the
power of 2 that corresponds
to the doubling values in
column 3
11. Egyptian Method Explanation
How the distributive law applies
24 x 13
= (8+16) x 13
= (8x13) + (16x13)
= (23x13) + (24x13)
= 104 + 208
= 312
Rewrite the problem as a sum of powers of 2
12. What’s So Special About Powers of Two?
Definition of even and odd numbers helps explain why
powers of two are so useful. Every even number can be
represented by 2k and odd number can be 2k+1 (or -1).
So when you use powers of 2, you will always be
able to represent any number whether it is odd or even.
14. Lattice Method
1. Draw a grid that has as many rows and columns as the digits
in the numbers you are multiplying with diagonal lines through
each box.
2. Line up the digits of the
two numbers you are
multiplying with the boxes.
3. Multiply the corresponding numbers for
each box. The upper triangle is the tens and the
lower is the ones value.
4. Add the numbers
along the diagonals.
Carry double-digit
numbers to the next
diagonal sum.
15. Lattice Method Explanation
Similar to the previous methods, the
lattice method follows the same idea of
the distributive law.
Students find very helpful since it breaks
down the steps for traditional
multiplication.
When you use this method you are essentially
computing the following distributive law:
(10x20)+(3x20)+ (10x4)+(3x4)
200+60+40+12
312
16. Additional Benefits of Lattice Method
1. Follow the same steps as before
until the grid is filled.
Multiplying Decimals
2. Drag the decimal points from each side
along the horizontal and vertical lines until they intersect.
3. Drag the decimal point down the
corresponding diagonal line and place
in the answer.
