Reducing Fractions

Just as multiplication is a shortcut method for adding the same number many (or multiple) times, division shows us how many times a number can be subtracted. Instead of repeating the subtraction process, you can say divide a number (called the dividend) by a second number (called the divisor). The result (called the quotient) is how many times you can subtract the divisor from the dividend. The process of division will continuously reduce the dividend until you are left with zero (0) or a number smaller than the divisor (called the remainder).

For example, how many times can we subtract the number 3 (divisor) from 12 (dividend)? If we subtract 3 once, our dividend is reduced to 9 (first subtraction). Subtracting 3 again results in the number 6 (second subtraction). We continue subtracting 3 from 6, resulting in 3 (third subtraction). Since we have only 3 remaining, we can only subtract 3, one more time (fourth subtraction). So, the total number of subtractions is 4 with no remainder. Using the division shortcut, we say 12 divided by 3 is 4 (with no remainder).  The number 12 was reduced to 0 by removing 3 four (4) times.  

Check out the Division Fundamentals document to review the basic multiplication concepts in more detail. 

Lowest Common Denominator

The first step in learning multiplication is to divide with single digits.  

Adding and Subtracting Fractions

Next, lets build on this basic technique and divide a single digit number into a larger number.   

Multiplying and Dividing Fractions

In this section, we will divide larger numbers into larger numbers using the same techniques from the Long Division section.   

Dividing Fractions

Finally, let's divide decimal numbers.  Just as we did with multiplication, we will remove the decimal point, complete the division and then re-add the decimal point in the correct location.    

Simplified Abacus Fractions Text

You can obtain the full text of this material by clicking on the link, Simplified Abacus Division.  

Subtracting Fractions

To divide larger numbers with 2 digit divisors, we introduce the concepts of a higher divisor, a lower quotient and upward adjustment.  While this sounds complicated, once you understand the concepts, the process of dividing two numbers will become much easier.