Multiplication
Single-Abacus Approach
The Single Abacus (Single-A) Approach
The Single Abacus approach is used by many students to multiply 2 numbers. In this approach, the first number (called the multiplicand) is entered in the left side of the abacus. The second number (the multiplier) is entered in the columns to the right of the first number leaving some columns empty on the right side to begin entering the result (product). Click on the links below to learn more details about this approach.
Basic Multiplication
Multiplication is a shortcut method for adding the same number many (or multiple) times. Instead of repeating the addition process, you can say multiply a number (called the multiplicand) by how many times you want to add it (this number is called the multiplier). The resulting number is called the product. For example, to add the number 1, 3 times (1 + 1 + 1) results in the number 3. Using multiplication, we say: 1 (multiplicand) times 3 (multiplier) is 3 (product). If we add the number 2, 3 times (2 + 2 + 2), the result is 6. Using a multiplication shortcut, we say 2 times 3 is 6. The Basic Multiplication document reviews the basic multiplication concepts in more detail.
Multiplying only Single Digits
The first step in learning multiplication is to multiply only with single digits. Click on the link to get started.
Multiplying with Single Digit Numbers
Now that you have reviewed the basics of multiplication (in the previous section), you are ready to multiply larger numbers (multiplicands) by single digit numbers (multipliers). This section introduces how to use a technique (using two-digit positions) to enter the partial product and continue to add to the partial sum as we multiply the multiplier and each digit of the multiplicand. Click on the link, Multiplying with Single Digits to multiply larger numbers with a single digit number.
Multiplying with Larger Numbers
In this section, we will discuss multiplying a large number (multiplier) and single digit (multiplicand). We will continue to develop the technique (using two-digit positions) to enter the partial product and continue to add to it as multiply each digit of the multiplier. Click on the link, Multiplying with Larger Numbers, to continue learning single abacus multiplication.
Multiplying with Any Size Numbers
In this section, we put it all together. Both the multiplicand and multiplier can be more than 1 digit in length. Click on the link, Multiplying with Any Size Numbers, to understand how to multiply any size numbers.
Multiplying Decimals
When we added and subtracted decimal numbers using the Cranmer abacus, we determined the unit point with the help of the unit marks. This keeps all the numbers in the calculation in the correct columns. However, when we multiply decimal numbers, we don’t need to keep the numbers in columns.
In this section, you will learn a technique for multiplying decimal numbers that uses the technique we used in the previous sections with a few steps added . Click on the link, Multiplying Decimals, to learn a simple method for multiplying decimal numbers.
Abacus Multiplication Textbook
You can obtain the full textbook of this material by clicking on the link, Abacus Multiplication.