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Divide with Circle Models uses circles to demonstrate division of fractions.

You can input the divisor and dividend for a division of fractions example. The dividend or divisor each must be less than 6. The quotient must be less than 21.

If you want just a whole number for for the divisor or the dividend, type in 0 (zero) for a numerator. If you do not want a whole number, type in 0 (zero) for the whole number. Do not type in 0 for the denominator.

You are told that division by a number can be done by multiplying by the reciprocal. So the algorithm looks like this:

division algorithm

Another method would be to write the dividend and divisor over a common denominator (like fractions). You can then divide the numerators. For example:

Divide algorithm 2

This method makes it easier to see the relative sizes of the dividend and divisor.

You can then compare this with the image for the same example. Notice the dividend has 21 common denominator marks and the divisor has 8 common denominator marks giving 21/8 for the quotient.

On the left is a <SHOW COLOR> check box. Uncheck <SHOW COLOR> to turn off the quotient. This will allow the teacher to ask the student to demonstrate the size of the quotient.

The <EXPLAIN> check box will show the dividend, divisor, and quotient numerals. Uncheck <EXPLAIN> to turn the explanation off, allowing the teacher or student to demonstrate how the quotient is found.

Uncheck the <SHOW INPUT> button to make the dividend and divisor input boxes act the same as a password input box. This will allow you to ask your students the factors and and the product as pictured.


Start with a dividend of 2 1/4 and a divisor of 1/4. Notice how 9 divisor amounts fit into the dividend. Increase the dividend by 1/4 increments. For example, keep the dividend at 2 1/4 and change the divisor to 1/4, 1/2, 3/4, and continue with this pattern. See how quotient decreases as the divisor increases. You are finding how many divisor sections fit into the dividend.

You can also demonstrate how as the divisor decreases the quotient increases. Try a Dividend of 2 2/3 and a divisor of 2 2//3. Decrease the divisor by 1/3/ increments. For example, keep the dividend at 2 2/3 and change the divisor to 2 1/3, 2 0/3, 1 2/3, etc, and continue with this pattern. You will see the quotient increase.

Keep the divisor and the dividend the same. For example, divide 1 1/2 by 1 1/2. Notice how the divisor fits into the dividend once.

Notice that if the divisor is larger than the dividend, the quotient is less than one. Try 1 3/4 divided by 3 1/2. Notice that only half the divisor fits into the dividend.

Divide one(1) by 2/3. (Enter 1 for the whole number, 0 for the numerator and 1 for the denominator. Then enter 0 and 2/3 for the divisor. You will get 3/2 or 1 1/2 for the quotient. This shows that 1 divided by any fraction will give the reciprocal (inverse) of the fraction.

Think of the dividend as available pizza and the divisor as the amount of the available pizza that can fit into a take-out container. If there are 5 1/2 pizzas and the container can hold 3/4 pizza, you can fill 7 containers with one piece left over. The piece will fill 1/3 of a container, so you can fill 7 1/3 containers.

How do you explain what's really going on when you divide 1/2 by 2/3? This is hard to picture, but if you write both 1/2 and 2/3 over a common denominator (making them like fractions) you will have 3/6 divided by 4/6. This is easier to see because you can consider the numerators 3 and 4. So dividing 1/2 by 2/3 is the same as dividing 3 by 4, giving you 3/4. Tick marks are shown to show the common denominator.


You may copy the screen by pressing <Print Screen> on the keyboard. This copies the screen into Windows Clipboard™. The screen can then be pasted into Windows Paint™

or your favorite imaging program. Windows Paint™ will allow you to crop, print, or save the image.

Windows 7 users can use the Snipping Tool™ to capture any part of the screen you wish. These images can be edited and saved in PNG, GIF(recommended) or JPEG formats.