The following picture was made by Multiply with Circles Designer:

multiply fractions circle image

The parts of a multiplication example are the first factor, the second factor, and the product.

You will notice from the picture that there are 4 rows of circles, each row containing 1 1/4 circles.

When the program starts, you will be asked to identify the first factor, the number of circles in each row, or 1 1/4.

You will then be asked to identify the second factor. The second factor is the number of rows, or 4. The second factor in this program will always be 1, 2, 3, or 4. The program will not continue unless each factor is correctly identified. You will then be asked to identify the product.

You can see from the picture that there are 4 complete circles. The four partial circles can be combined to form 1 more complete circle for a total of 5 circles. The product, then, is 5.

To calculate the product first write each factor in fraction form as shown in the example above. Then multiply the numerators of each factor for the numerator of the product and the denominators of each factor for the denominator of the product. You may enter the product in fraction form or whole or mixed number form, so 20/4 or 5 are both acceptable.

. Follow the directions in the dialog box after pressing the <START> button. The <EXPLAIN> button may be pressed after you enter the second factor to see how to do the example.

After you enter the product you may press the <REPORT> button. The report will ask for your name but you may submit a code for your name. This report will give same results as on the dialog box. The report may be printed or e-mailed.

You may prefer to use a short-cut method known as canceling.To cancel, first write each factor in fraction form. Then think of a number that will divide evenly into any number in the numerator and also any number in the denominator. You can cancel if the number you divide by - the greatest common factor of the numbers - is larger than 1. In the example, 4 will divide into 4 in the denominator of the first factor and into the numerator of the second factor. After you divide by 4, cross off the original term and write the answer near the original term. Then multiply across by the new number instead of the original terms. Canceling will give you smaller numbers to multiply and will give you a product in lowest terms. 

How to Cancel will play a short animation that shows you this shortcut way to write a fraction in lowest terms.

Since the second factor in each example of MULTIPLY FRACTIONS is a whole number,  you may use another method to calculate the product as shown in the example below. Multiply the whole number part of 3 2/3 by the second factor 3 and then the fraction part of 3 2/3 by the second factor 3. Then add the two numbers for the product.

Written out, the example would look like this:

distributive property illustration

As you can see, you are distributing the factor 3 over the whole number and the fraction part of 3 2/3.