Multiplying with Larger Numbers
Single Abacus Approach
Short Course
This is a short course (slide show below) on how to multiply any size numbers with a single digit number.
Multiplying with Larger Numbers
Setting up the Calculation
Again, let’s review how to set up a multiplication calculation. Remember, in this book, the first number of the multiplication calculation is the multiplicand. The second number is the multiplier.
First, set up the multiplicand. The multiplicand is set on the left most columns of the Cranmer abacus. Set the multiplicand, from left to right, starting in column 13.
Next, set up the multiplier. Count the number of digits in the multiplier and multiplicand. Then add the two numbers together and add 1 for the process of multiplication. This number is the column you should start to set the multiplier from left to right.
To calculate the product, we multiply each of the digits of both numbers. We start with the rightmost digit of the multiplier and multiply it to the leftmost digit of the multiplicand. The result is added number to the right of the multiplier. When all the digits of the multiplier and multiplicand have been multiplied, the result is called the final product.
Multiplying with Multiple Digit Multipliers
In this chapter, we will be working on calculations where the multiplicand is a single digit and the multiplier has several digits. Now, let’s look at the process of calculating the product with larger multipliers.
To start, multiply the rightmost digit of the multiplier and the leftmost digit of the multiplicand. Since the multiplicand is only 1 digit, the rightmost and leftmost digit is the same digit. Set the product in the two columns immediately to the right of the rightmost digit of the multiplier. This is called the first position. The result of the first multiplication is called a partial product. Clear the digit of the multiplicand that you just used.
Then multiply the new rightmost digit of the multiplier to the multiplicand. Add the product to the two columns immediately to the right of the rightmost digit of the multiplicand. The first position has shifted one column to the left.
Continue multiplying each digit of the multiplier and adding the product to the partial product after shifting the position one column to the left. Clear each digit of the multiplicand after each step. When you have completed multiplying each digit of both numbers and adding the product to the partial product, all the digits of the multiplier will be cleared. The result will be the final product.
Examples
Now, let’s look at some more examples of this process. In these examples, the multiplicand will be a single digit but multiplier can be as large as 9,999,999,999. Click on the link below to show the steps to calculate the answer.
Example: 8 times 98
Example: 9 times 37
Example: 6 times 149
Example: 7 times 943
Example: 4 times 2,556
Example: 3 times 73,145
Example: 8 times 253,748
Example: 7 times 1,396,573
Example: 6 times 274,109,790
Example: 9 times 1,158,879,215