Fraction Manipulatives
Work with two fraction boards, A and B. Click pieces to build up to three wholes, use the sign controls for negative amounts, and compare their areas or add them. An exact common denominator explains the result. No decimal rounding or remote calculation is used.
Key features
- Click or keyboard-activate pieces in three whole strips on each board
- Reslice to a new denominator only when the same area uses an integer number of pieces
- Copy A to B at B's piece size when an exact equivalent arrangement exists
- Explore equality, ordering and addition with signed common-denominator steps
- See mixed-number and negative results with a magnitude-area diagram
- Download strict versioned JSON or a bilingual SVG diagram
How to use
- Start from the 1/2 and 2/4 example or clear the boards. On each board, click an empty tile to fill through it or a filled tile to remove from it onward.
- Use the +1 and −1 controls or keyboard Enter/Space on a tile. Choose a positive or negative sign for each board.
- Choose a target denominator and select Reslice to preserve exact area. If the piece count would not be an integer, the board stays unchanged; use Clear and change to start a new amount.
- Select Equivalence, Sum or Compare. Read the common-denominator counts, reduced answer and visual area bars.
- Save the project as JSON or the current model as SVG. Import a valid version 1 JSON project to continue later.
Use cases
- Show why one half and two quarters occupy the same area
- Build one and a half wholes using three half-size pieces
- Explore how a negative amount cancels positive pieces in addition
- Compare unlike denominators without approximating decimal values
Frequently asked questions
Why can I not reslice 1/2 into thirds?
One half would require 1.5 third-size pieces. This tool permits only whole pieces and keeps the amount unchanged when the target denominator cannot represent the exact same area. Choose sixths instead, or clear the board to build a different amount.
What does clicking a piece do?
Each board is a contiguous stack of equal-size pieces. Clicking an empty tile fills all pieces through that position; clicking a filled tile removes that tile and every later piece. Each tile is a native button that also works with Tab and Enter or Space. The ±1 controls offer a simpler keyboard alternative.
How are negative fractions drawn?
The red fill shows the magnitude of a negative fraction; it is not negative physical area. The minus sign is applied in the exact arithmetic. When opposite signs are added, the common-size cancellation count is shown.
Can I make mixed numbers?
Yes. Each board has three whole strips. For example, three halves display as 3/2 and 1 1/2. Sums can reach six wholes in magnitude. Denominators are integers from 1 through 12; each board contains at most three wholes.
Is the area calculation rounded?
No. Piece counts and denominators are small integers; the least common multiple, signed sum, comparison and reduction use exact integer arithmetic. The colored preview bar is a visual representation, while the displayed fractions are authoritative.
What is saved and uploaded?
The boards and selected mode stay in this browser tab unless you download JSON. The JSON has no personal data or automatic save. SVG contains the current diagram. Nothing is submitted to a server by this tool; a damaged or unsupported JSON import does not replace the current boards.
Privacy
Board choices stay in this browser tab. JSON and SVG downloads remain on your device; there is no automatic save, account sync, or remote submission.
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