Multiplying with Any Size Numbers

Short Course 

This is a short course (slide show below) on how to multiply any size numbers.  

Multiplying with Any Size Numbers

Setting up the Calculation

The multiplication calculation is set up exactly the same as in the previous multiplication chapters.

First, set up the multiplicand. The multiplicand is the first of the two numbers in the multiplication calculation and 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.

The result of multiplication calculation is called the product. It is calculated by multiplying the digits of the multiplicand times the digits of the multiplier. 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 Larger Numbers

The process for calculating the final product involves both of the multiplication methods in the previous chapters. This is the process in more detail:

• First, we multiply the rightmost digit of the multiplier and the leftmost digit of the multiplicand. Set the product in the two columns immediately to the right of the rightmost digit of the multiplier, first position.

• Then, we multiply the same digit of the multiplier to next digit of the multiplicand. Add this product to the partial product after shifting 1 column to the right. The partial product is completed when all digits of the multiplicand have been multiplied by the digit in the multiplier. Lastly, clear this digit in the multiplier. A new digit will be used to multiply each digit in the multiplicand. This means that the new first position of the partial product 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. 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

In these examples, since both the multiplier and the multiplicand have more than 1 digit, the number of digits in the multiplicand will limit the size of the multiplier. If the multiplicand has 4 digits, then the multiplier can only have 4 digits. If the multiplicand is smaller, then the multiplier can be a larger number. 

• Example: 61 times 84

• Example: 36 times 49

• Example: 25 times 204

• Example: 73 times 943

• Example: 257 times 324

• Example: 493 times 483

• Example: 807 times 149

• Example: 7,288 times 448

• Example: 1,629 times 786

• Example: 6,540 times 1,704

• Example: 4,695 times 4,817

• Example: 9,738 times 8,448

Build Your Skill

Now you are ready to try some calculations on your own. Click on problems and their solutions to test your skill.