Click on the Application then Click Check Button and the Name of the Current Fraction Operation will Display.
After You Follow Directions to Set a Problem, Press Space Bar to Review Problem.

 
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BACK    DIVISION OF FRACTIONS    ADDITION OF FRACTIONS   LESSON EXAMPLES
CLICK ORIGAMI FACTIONS TO SEE PAPER FOLDING TECHNIQUES

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Step0: Left click check button to reset and begin next operation after Fractions.
Fractions
Step1: Left click a section of gold beads to set a denominator. Press Left Arrow Key  (PLA).
Step2: Left click a section of the displaced gold beads to set a numerator. Press Right Arrow Key (PRA). Note the fraction of gold beads is equal the colored fraction of the paper pie.
Fractions of a Whole
Step1: Left click a section of gold beads to set denominator. PLA.
Step2: Left click a brown bead in the diagonal column that is adjacent to the triangle of brown beads above the gold beads that remain against the right post. PLA. The displaced rectangle of brown beads is the whole and sets the factor that times the denominator produces the whole. Press down arrow for more steps!
Step3: Right click a section of gold beads from the displaced group to set the numerator. PRA. Note the number of dark rectangle slices of the paper pie, these equal the fraction of the whole and the number of brown beads in the rectangle above the displaced triangle. Note that the number of slices in the fraction of the whole over the total number of slices in the number pie makes a fraction equivalent to the initial fraction. 		 Multiplication of Fractions
Step1: Left click section of gold beads to set first denominator. PLA. Left click another section of the gold beads that remain against the right post to set second denominator. PLA. The adjacent rectangle of brown beads equals the solution denominator.
Step2: Left click a section of the gold beads of the second denominator to set its numerator. PLA.  Note the colored rows of the paper pie representing the second fraction, and the equal number of displaced columns from the rectangle, representing an equivalent part of the solution denominator.
Step3: Counting from right to left, Left click a section of the gold beads against the left post equal the numerator of the second fraction. PRA. The displaced columns of the rectangle remain to the left. 
 Step4. Left click another section of the gold beads against the left post to set the numerator of the first denominator. PRA. Note the colored columns of the paper pie representing the first fraction, and the equal number of displaced columns from the rectangle, representing an equivalent piece of the part of the solution denominator prevoiusly displaced. The number of beads in this piece equal the dark colored rectangular slices of the paper pie and the solution numerator. Press down arrow for more steps! The solution to the multiplication of fraction problem in terms of paper pies can be formulated as a piece of a part of the whole pie divided by or compared to the whole pie. In other words, the numerator is equal the slices in the dark colored piece of the colored rows or in the piece of the part of the whole pie and  the denominator is equal the slices in the whole pie. 
MULTIPLICATION    DIVISION
CLICK ORIGAMI FACTIONS TO SEE PAPER FOLDING TECHNIQUES
   
                        Lesson Development

Origami Fractions or paper folding is a great hands on way to introduce fractions and fraction operations. The paper folding techniques introduce the single digit primes (2, 3, 5, and 7) as the first four fundamental numbers of equal sections in which a piece of paper can be folded. See the folding fractions lesson example. These four primes can then lead students into the exploration of the Sieve of Erasthenes and the primes included within the numbers 1 to 100. 
See Origami Fraction to learn how the fraction operations and numerical rules can be derived from paper folding. I recommend students become familiar with fraction operations by folding paper before using the Pythabacus, so that first the area concept of multiplication and the comparison of areas to define fractions are well understood. See the multiplying fractions lesson example. Equivalent fractions are also easily produced and defined using paper folding techniques. See lesson example.
The four fraction operations, equivalent fractions, reducing (see my reducing page) and the introduction to primes can constitute a first year or fourth grade introduction to fractions. Working out the answers to fractions on the Pythabacus is a great way for students to demonstrate and hone the understanding of fractions and fraction operations through the the area concept of multiplication and the comparison of areas. 
Finding the GCD and LCM, as well as prime factoring, decimals and percents might constitute second year or fifth grade fraction related math lessons. See the addition and formulas lesson examples.

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BACK     FRACTIONS      FRACTION OF A WHOLE        MULTIPLICATION OF FRACTIONS    LESSON EXAMPLES
CLICK ORIGAMI FACTIONS TO SEE PAPER FOLDING TECHNIQUES

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Division of Fractions
Step1: Left click a section of gold beads to set first denominator. PLA. Left click another section of the gold beads that remain against the right post to set second denominator. PLA. The adjacent rectangle of brown beads equals the whole but not the solution denominator.
Step2: Left click a section of the gold beads of the second denominator to set its numerator. PLA. The second numerator appears flipped in the equivalent multiplication statement. Note the colored rows of the paper pie representing the second fraction. 
Step3: Counting from right to left,left click a section of the gold beads against the left post equal the numerator of the second fraction. PRA.
The displaced columns of the rectangle remaining to the left, represent an equivalent part of the whole and is the solution denominator. 
Step4. Left click another section of the gold beads against the left post to set the numerator of the first denominator. PRA. Note the colored columns of the paper pie representing the first fraction, and the equal number of displaced columns from the rectangle, representing an equivalent piece of the whole and not just a piece of the previously displaced part. The number of beads in this piece equal the colored rectangular slices of the columns of the paper pie and the solution numerator. The solution to the division of fraction problem in terms of paper pies can be formulated as a piece of the whole pie divided by or compared to a part of the whole pie. In other words, the numerator is equal the slices in a piece of or the colored columns of the whole pie and the denominator is equal the slices in a part of or the colored rows of the whole pie. 		 Addition of Fractions 
Step1: Left click a section of gold beads to set first denominator. PLA. Left 
click another section of the gold beads that remain against the right post to set second denominator. PLA. The adjacent rectangle of brown beads 
equals the whole, the equivalent and the solution denominators.
Step2: Left click a section of the gold beads of the second denominator to set its numerator. PLA. Note the colored rows of the paper pie representing the second fraction. 
Step3: Counting from right to left, left click a section of the gold beads against the left post equal the numerator of the second fraction. PRA.
The displaced columns of the rectangle remaining to the left, represent an equivalent part of the whole, and the equivalent numerator of the second
fraction. 
Step4. Left click another section of the gold beads against the left post to set the numerator of the first denominator. PRA. Note the colored columns of the paper pie representing the first fraction, and the equal number of displaced columns from the rectangle, representing an equivalent piece of the whole and the equivalent numerator of the first fraction. The number of beads in this piece equal the colored rectangular slices of the columns of the paper pie. The solution to the addition of fraction problem in terms of paper pies can be formulated as a piece  of the whole pie plus a part of the whole pie divided by or compared to the whole pie. In other words, the numerator is equal the slices in a piece of or the colored columns of the whole pie plus the slices in a part of or the colored rows of the whole pie and the denominator is equal the slices in the whole pie.