Multiplying only with Single Digits

Short Course 

This is a short course (slide show) on how to multiply only with single digits.  Just click on the link above to start the show. 

Multiplying only Single Digits

In the Basic Multiplication page you learned that every multiplication problem involves 2 numbers: the multiplicand and the multiplier. The result of the multiplication is called the product. As we said earlier, the first number will be the multiplicand and the second number will be the multiplier. .

Entering the Multiplicand

First, let’s enter the multiplicand (that is the first of the two numbers in your multiplication calculation). Starting in the left most column of your Cranmer abacus (column 13), enter the number from left to right. If the multiplicand is only 1 digit, enter it in column 13.

Entering the Multiplier

Next, we will enter the multiplier (the second number in your multiplication calculation). We will enter this number on the right side of the Cranmer abacus but only after we leave some columns empty so that we can begin to record the partial product. So how do we determine where to start entering the multiplier? 

• First, count the number of digits in the multiplier and multiplicand

• Now, add the two numbers together and add 1 for the process of multiplication. This is the column you should start to enter the multiplicand, from left to right.

• If both the multiplier and multiplicand are single digits, add 1 for the process of multiplication giving 3.

• Then enter the single digit for the multiplier in column 3.

Now you have entered all the digits of the multiplier. But before you can begin to multiply, you must understand one additional concept about where to enter the product.

Entering the Product

The two columns immediately to the right of the multiplicand are called the first position. This is a very important concept. In this book, the multiplication of any two digits is always a two digit number. For example, 2 times 2 = 04. The zero (0) is entered immediately to the right of the multiplicand and the digit 2 would be entered in the next column to the right.

In this example, 2 times 2 = 04, the multiplicand, 2, is entered in column 13. The multiplier, 2, would be set in column 3 (1 digit in the multiplier + 1 digit in the multiplicand + 1 for the process of multiplication).  So, we have two columns empty for the product. Since we already know that the product is 04, we enter 0 in column 2 (nothing is entered) and 4 is entered in column 1. The last step is to clear the digit of the multiplier that we just used. The product is the number on the right side of the Cranmer abacus.

Calculating the Product

Once you understand where the multiplier, the multiplicand and the product are located in the Cranmer abacus, you can easily calculate a multiplication problem by following these steps:

• First, enter the multiplicand

• ·Determine which column to begin entering the multiplier. Add the number of digits in the multiplier to the number of digits in the multiplicand and add 1 for the process of multiplication.

• Then enter the multiplier.

• ·Calculate the product by multiplying each digit of the multiplier times each digit of the multiplicand. Start the process with the right most digit of the multiplier and multiply it by each digit in the multiplicand. Add the 2 digit product of each multiplication to partial product moving from left to right. When you have completed all the multiplications for 1 digit of the multiplier, clear that digit from the multiplier.  

• When all the numbers in the multiplier have been cleared, the number in the right of the abacus is the final product.

In our examples, both the multiplicand and multiplier are single digits. Even though you already know the result of the calculation, these examples will show you how to correctly setup the calculation and arrive at the correct product. The asterisk (*) is used instead writing the work times in each multiplication example. For example, 4 times 3 is written as 4 * 3. 

Examples

Now, let’s look at some more examples of this process. In these examples, the multiplicand and the multiplier will be a single digit.  Click on the link to show the steps to calculate the answer. 

• Example: 4 times 3

• Example: 6 times 5

• Example: 8 times 7

• Example: 6 times 9

Build Your Skill

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