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Four Multiplication Methods You Might Not Have Learned in School

There are many different ways to the answer.

When we learn how to multiply, we learn to split the equation into parts. First, we find the product using the ones place value. Then we move to the tens, followed by the hundreds. Finally, we sum everything up and arrive at our answer. This method works great, but it’s not always the most efficient. Here are a few other methods that can speed up the process.

In these examples, I am using 2 and 3 digit numbers. These methods also work with larger numbers.

Photo by Lucas van Oort on Unsplash
Photo by Lucas van Oort on Unsplash

The Lattice Method

Draw a grid and split each square with a diagonal line. Write one number along the top, and the other along the right-hand side, with one digit per column or row.

586 x 45 =

586 x 45: 586 on top, 45 on the right
586 x 45: 586 on top, 45 on the right

In each cell, multiply the row by the column. Split the product into a tens place value, and a ones place value. Write the tens digit above the diagonal line and the ones digit below the diagonal line.

5 x 4 = 20. Put the two above the line, zero below the line
5 x 4 = 20. Put the two above the line, zero below the line
Completed Grid
Completed Grid

Now, look at the grid by diagonals. Sum the digits across the diagonals. If the sum is greater than nine, carry the tens place value into the next column.

Sum across the blue and white diagonals
Sum across the blue and white diagonals
586 x 45
-> 2, (2+0+3), (5+4+2+2), (0+3+4), 0
-> 2, 5, 13, 7, 0
-> 2, 6, 3, 7, 0
= 26370

Finally, write out the sum over the diagonals as digits, and you’ll have your answer.

586 x 45 = 26,370

Photo by Photoholgic on Unsplash
Photo by Photoholgic on Unsplash

The Line Method

This method works incredibly well for 2- and 3-digit numbers when the digits are small. It can get a bit messy when you have many intersecting lines.

Draw a series of parallel lines representing each digit of the first number. The lines should be roughly at a 45-degree angle and have a gap between each digit.

For this example, we’ll work with 223 x 52

223 represented by lines
223 represented by lines

The hundreds place value is two; the two top lines represent it. The next two lines represent the tens, and the final three lines represent the ones place value.

Next, we draw the second number we are multiplying by. We do this by drawing a new set of parallel lines that cross the first set.

223 (orange) x 52 (blue)
223 (orange) x 52 (blue)

This time the lower set of lines represent five tens, and the upper two lines represent the ones. Note the higher place value lines are always to the left.

Now we draw dots where the lines intersect.

Dots at intersection points
Dots at intersection points

Next, we group the dots by position along the x-axis. Each group of dots represents a digit in our final answer. We sum the dots in each group. If the sum is greater than nine, carry the ten’s value into the next column.

Each group of dots represents a digit. Sum the dots
Each group of dots represents a digit. Sum the dots

Write out the combined sum of the groups as the answer.

223 x 52
-> 10 ,(4 + 10) ,(4 + 15) , 6   # sum the dots
-> 10, 14, 19, 6                # 14 and 19 are greater than nine
-> 10+1, 4+1, 9, 6              # carry the 1 from 14 and 19
-> 11596

223 x 52 = 11,596

Photo by Ryan Schram on Unsplash
Photo by Ryan Schram on Unsplash

The Criss-Cross Method

In this method, you move across the equation right to left. In the first step, we multiply the ones by the ones. Next, we move into the tens column and multiply tens by ones and ones by tens and sum up these two calculations. We continue to move across the equation. The overall pattern looks like this.

Criss-cross pattern
Criss-cross pattern

Yikes, that looks complex. It makes more sense when we look at it step by step.

The process is symmetrical. We only have one calculation at the edges (ones x ones or hundreds x hundreds). In the middle, we have three calculations.

The trickiest part is making sure that you carry the correct place value into the next column.

125 x 648
-> 6, 16, 46, 36, 40
-> 6+1, 6+4, 6+3, 6+4, 0
-> 7, 10, 9, 10, 0
-> 7+1, 0, 9+1, 0, 0
-> 8, 0+1, 0, 0, 0 
= 81000

125 x 648 = 81,000

Photo by Zachary Kadolph on Unsplash
Photo by Zachary Kadolph on Unsplash

The Slide Method

This method is almost magical. You start by doing the opposite of what you’d expect – reverse the digits of one of the multipliers.

This reversed number acts as a window. It moves across the equation one place value at a time.

424 x 83 =

Start with the window as far to the left as possible. The ones place value of the window should be under the other multiplier’s largest place value. Multiply these numbers together

Step 1: 83 reversed becomes 38. Multiply 4 x 8
Step 1: 83 reversed becomes 38. Multiply 4 x 8

Slide the window one place value to the right. Multiply both columns and sum the products.

Step 2: Slide to the right, multiply and sum the columns.
Step 2: Slide to the right, multiply and sum the columns.

Continue moving the window to the right.

Step 3: Slide, multiply, sum.
Step 3: Slide, multiply, sum.

Until the largest place value of the window is under the ones place value of the multiplier.

Group the sums from each step together. Move the appropriate place values to the next column.

424 x 83
-> reverse 83 -> 38 
-> 32, 28, 38, 12 # column sums
-> 32+2, 8+3, 8+1, 2
-> 34, 11, 9, 2
= 35192

424 x 83 = 35,192

Happy Multiplying!


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