Fractions
Double Abacus Approach
The Double Abacus (Double-A) Approach
The Double Abacus approach simplifies adding subtracting, multiplying and dividing fractions by separating the two parts of each fraction. The top number of the fraction (numerator) is set in the top abacus. The bottom number (denominator) is set in the bottom abacus. numbers being divided to the bottom abacus. The links below will walk you through the each of the steps to develop your skill using this approach to add, subtract, multiply and divide fractions.
Fraction Basics
Fractions and all of the arithmetic operations that use fractions are based on a few basic concepts:
First, let's learn/review the concept and definition of a fraction. The What is a Fraction section answers this question in more detail.
Next, let's learn/review the general rule for working with fractions which is: "Smaller is better". So, in the Reducing Fractions section, we will show you how to reduce a fraction to its "simplest terms".
Then, to add or subtract fractions, the denominator (lower number) needs to the same. In the Lowest Common Denominator section, we will show you how to find the common number.
A short course (slide show) is also included that summarizes both concepts.
Click on the Basic Fractions link to access this information.
Adding Fractions
The key principle of adding two fractions is that the denominator of both fractions needs to be the same. If the denominator of both fractions is the same, then we don’t need to calculate a new denominator. But, if the denominators are different, we must be able to convert both fractions to a new denominator. In other words, we need to add “apples to apples”. Otherwise, any sum of the two fractions won’t make any sense. Click on the link to learn the steps to Add Fractions.
Subtracting Fractions
The steps we will use to subtract fractions are very similar to the steps we used to add fractions. Click on the Subtracting Fractions link to learn these steps. The denominators need to be the same so we will need to find the lowest common denominator.
Multiplying Fractions
Multiplying fractions uses a few steps from the addition and subtraction process we just learn but also adds a few steps. Both fractions need to be reduced but the denominators don't need to be the same. There is also an additional step to cancel common factors before the numerators and denominators are multiplied. Click on the Multiplying Fractions link to learn these steps.
Dividing Fractions
The final operation is dividing fractions. The process of dividing fraction is almost the same as the process used to multiply fraction. The only difference is that an additional step is added. Click on the Dividing Fractions link to learn the steps.
Simplified Abacus Fractions Text
You can obtain the full text of this material by clicking on the link, Simplified Abacus Fractions.