Learning the Abacus  @Kutztown University

Introduction

This is the introduction (slide show) to the Learning the Abacus Class at Kutztown University. 

Beginner Abacus 

The Beginners Abacus (sometimes called the 3 Way Abacus) can be used to introduce a student to simple counting with beads.  The abacus has 3 columns with 9 beads in each column.  The student can use the abacus to learn to add and subtract small numbers.  This abacus is not recommended for students who can learn and remember the multiplication and division tables.  

Double Abacus Approach

The Double Abacus approach simplifies the process of multiplying, and dividing numbers as well as calculating fractions.  This process uses the multiplication and division tables and separates the two numbers being used to either the top or bottom abacus.  The result is set in the remaining abacus.  Below are the slide shows for multiplying, dividing and calculating fractions. 

Multiplication

The Double Abacus approach simplifies the multiplication process by separating the two numbers being multiplied to the top abacus.  Then the product is calculated in the bottom abacus from left to right.   This allows for multiplying larger numbers (6 digits) with larger products.  The slide show below is a short course in multiplying numbers using this approach. 

Division

The Double Abacus approach simplifies the division process by separating the two numbers being divided to the bottom abacus.  Then the result (quotient) is calculated in the top abacus from left to right.   This allows for dividing larger numbers (6 digits) with larger quotients.  The slide show below is a short course in dividing numbers using this approach. 

Decimals

Multiplying and dividing decimals is simplified using the Double Abacus approach.  The slide show below is a short course in multiplying and dividing decimals using this approach.

Fractions

Learning to add, subtract, multiply and divide fractions is simplified using the Double Abacus approach.  The numerator (top number)  is set in the top abacus and the denominator (bottom number) is set in the bottom abacus.  Then the resulting fraction is calculated using both abaci. The slide show below is a short course in adding, subtracting, multiplying and dividing fractions using this approach.

Single Abacus Approach

Many students use a Single Abacus to multiply and divide 2 numbers or add, subtract, multiply and divide fractions using the multiplication or division tables.   The numbers in the calculation and the result are entered in special positions  on the abacus.  The slide shows below show the processes for performing these calculations.  

Multiplication

Multiplying 2 numbers using a Single Abacus involves setting the first number (multiplicand) on the left side of the abacus and the second number (multiplier) to the right of the first number.  Several columns on the right edge of the abacus are used to calculate the product.  The slide show below is a short course in multiplying 2 numbers.  

Division

Dividing 2 numbers using a Single Abacus involves setting the first number (divisor) on the left side of the abacus and the second number (dividend) on the right edge of the abacus.  The result (quotient) is set between the divisor and dividend during the calculation.  The slide show below is a short course in dividing 2 numbers.  

Fractions

Adding, subtracting, multiplying and dividing fractions using a Single abacus involves setting the numbers in the fraction is special columns.  The final result is calculated using these positions.  The slide show below is a short course in adding, subtracting, multiplying and dividing fractions using this approach.