Divide with circle models

Learn or teach by designing your own divide visual fractions examples. All examples are modeled with circles.



With Divide With Circle Models Designer you can design fractions examples using circle models.

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.

The default example above pictures with circle models the division of 1 34 by 23 . The algorithm below the image shows how the quotient 2 58 results from multiplying the dividend 1 34 by the reciprocal (inverse) of 23.

When dividing, you are asking how much of the divisor or how many divisors fit into the dividend. In the above example the divisor is smaller than the dividend. This image shows that the divisor 23 will fit into the dividend 2 58 times. The quotient picture changes from dark blue to light blue each time the divisor fits into the dividend. The small mark on the right of each quotient circle shows where the fraction starts to be drawn on the circle..

To help understand the picture, keep increasing the divisor by one. So the next picture will show the division of 1 34 by 1 23, giving a quotient of 1 120. When you increase the divisor to 2 23 you will get the quotient 2132. Here, you can see that when the divisor is larger than the dividend, the quotient is less than 1. The quotient picture shows 2132 of the divisor fits into the divident..

Uncheck the <EXPLAIN> check box to turn off the answer and the explanation. You can ask your learners to complete the number sentence.

Uncheck the <SHOW INPUT> check box to make the input dialog boxes work like a password input boxes, hiding the numbers you input. This will uncheck the <EXPLAIN> check box. With <EXPLAIN> and <SHOW INPUT> unchecked you can ask your learners to write a number sentence that explains the picture.

With <EXPLAIN> and <SHOW COLOR> unchecked you can ask your learners to complete the picture by shading the circles.


Start with a dividend of 2 14 and a divisor of 23. Notice how 3 38 divisor amounts fit into the dividend. Increase the divisor by 1 to get 2 14 divided by 1 23 giving a quotient of 1 720. Then increase the divisor to 2 23. This will result in a quotient smaller than one (2732) , showing that the quotient is smaller than one when the divisor is larger than the dividend.

You can also demonstrate how as the divisor decreases the quotient increases. Try a Dividend of 2 23 and a divisor of 2 23. Notice that the divisor and dividend are the same size, resulting in a quotient of one. Decrease the divisor by 13 increments. For example, keep the dividend at 2 23 and change the divisor to 2 13, 2 03, 1 23, etc, and continue with this pattern. You will see the quotient increase.

Try 1 34 divided by 3 12. Notice that only half the divisor fits into the dividend.

Divide one(1) by 23. (Enter 1 for the whole number, 0 for the numerator and 1 for the denominator. Then enter 0 and 23 for the divisor. You will get 32 or 1 12 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 12 pizzas and the container can hold 34 pizza, you can fill 7 containers with one piece left over. The piece will fill 13 of a container, so you can fill 7 13 containers.

How do you explain what's really going on when you divide 12 by 23? This is hard to picture, but if you cover the dividend 12 by the divisor 23 only 3/4 of the divisor is needed to cover the dividend. If you cover 23 by 12 you will find it will take a whole 12 piece plus 13 of the 12 piece.


Windows users can select any part of the screen by right clicking and selecting "Take a screenshot". Adjust to fit mage you want. This copies the selection into Windows Clipboard™. The screen can then be pasted into Windows Paint™ or your favorite imaging program. Or you can select "Download" which will put the image into your files "Download" folder.


To take a screen shot with the Ipad first press the Sleep/Wake button at the top right of the Ipad. While holding the Sleek/Wake button press and release the round Home button at the bottom of the screen. You should see a photo of the screen by going to the Home page and pressing the Photos icon.