Multiplying with Single Digit 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 numbers with Single Digits
Setting up the Calculation
Let’s review how to set up a multiplication calculation. Remember, 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.
Multiplying with Single Digit Multipliers
Now, let’s look at the process of calculating the product. In this chapter, we will be working on calculations where the multiplier is a single digit and the multiplicand has several digits.
The process for determining the final product involves calculation many partial products. The partial product is calculated by multiplying one digit from the multiplier times each digit of the multiplicand. When each digit is multiplied, the product is a two digit number (remember that 2 * 2 = 04). This two digit number is added the number to the right of the multiplier. As we multiply each two digit pair of numbers, we apply them in two column groups called positions. Each position is determined by shifting one column to the right. First position (of the partial product) is the two columns immediately to the right of the rightmost digit of the multiplier. If you put your finger on the second column of the first position, it will mark the beginning of the second position. The product of the next digit pair will start in this column and use the column to its right. Again, move your finger to right one more column (in the partial product). This is the beginning of Third position. This continues until all the columns to the right of the multiplier are used by for the partial product.
Think back to your pencil and paper (or literary Braille) days and how you learned to multiply. You entered the two numbers one above the other. Then you multiplied each digit in the first number by each digit of the second number starting with the rightmost digit of the second number. The product of each digit pair was entered below the second number, shifting to the right one digit and adding the product. The process of using positions that we are using is very similar to the old process only you are shifting from left to right rather than right to left in the old process.
Let’s apply this process to some multiplication calculations where the multiplicand is a larger number (more than 1 digit) and the multiplier is a single digit. To calculate the product, we multiply each of the digits of both numbers. The result is added number to the right of the multiplier.
To start, multiply the rightmost digit of the multiplier and the leftmost digit of the multiplicand. Since the multiplier is only one 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, first position.
Now, 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. For example, if the product of the first two digits was added in columns 3 and 2, then the product of the next two digits would be added in columns 2 and 1. In this example, columns 3 and 2 would be called first position and columns 2 and 1 would be called second position. The partial product is completed when all digits of the multiplicand have been multiplied by the digit in the multiplier. Then, clear this digit of the multiplier. Since there are no more digits in the multiplier, your partial product becomes the final product.
Examples
Now, let’s look at some more examples of this process. In these examples, the multiplicand will be as large as 99,999 but the multiplier will always be a single digit. Click on the link to show the steps to calculate the answer.
Example: 85 times 5
Example: 119 times 7
Example: 681 times 5
Example: 2,573 times 8
Example: 3,527 times 2
Example: 5,417 times 3
Example: 53,245 times 5
Example: 64,041 times 9
Example: 82,789 times 6
Example: 93,447 times 4