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dividend
divisor
DIVIDE WITH CIRCLE MODELS
SHOW COLOR
EXPLAIN
SHOW INPUT

# Instructions for Dividing Fractions Designer

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 3/4 by 2/3. The algorithm below the image shows how the quotient 2 5/8 results from multiplying the dividend 1 3/4 by the reciprocal (inverse) of 2/3.

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 2/3 will fit into the dividend 2 5/8 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 3/4 by 1 2/3, giving a quotient of 1 1/20. When you increase the divisor to 2 2/3 you will get the quotient .21/32. Here, you can see that when the divisor is larger than the dividend, the quotient is less than 1. The quotient picture shows 21/32 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.

Suggestions:

Start with a dividend of 2 1/4 and a divisor of 2/3. Notice how 3 3/8 divisor amounts fit into the dividend. Increase the dividend by 1 to get 2 1/4 divided by 1 2/3 giving a quotient of 1 7/20. Then increase the divisor to 2 2/3. This will result in a quotient smaller than one (27/32) , 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 2/3 and a divisor of 2 2/3. Notice that the divisor and dividend are the same size, resulting in a quotient of one. 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.

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 cover the dividend 1/2 by the divisor 2/3 only 3/4 of the divisor is needed to cover the dividend. If you cover 2/3 by 1/2 you will find it will take a whole 1/2 piece plus 1/3 of the 1/2 piece.

WINDOWS COMPUTERS

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.