Fraction Builder Game
Build an exact rational value by choosing equal parts and shading proper, improper or equivalent fractions.
Math puzzle challenges
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Instructions, device progress and accessibility
Choose Practice or UTC Daily mode and select a difficulty. Use keyboard, touch, Tab, and Enter with the controls. Wrong checks reduce score; Hint and Undo mark assisted rounds. There is no required sign-in, and results remain on this device.
Local progress is checked when play begins.
Fraction Builder — Rules, Examples and Help
Build an exact rational value by choosing equal parts and shading proper, improper or equivalent fractions.
How to play Fraction Builder
First look at the target fraction shown above the drawing. The top number counts how many equal parts are needed; the bottom number specifies the number of equal parts in one whole. Choose a partition size from the menu, then shade sections by touching them or using the plus and minus buttons. Each horizontal bar represents one whole, so the drawing can represent a value larger than one. Tap Check answer when the shaded portions show the same rational number as the target.
How equivalence works
A partition of a whole into four pieces with three pieces shaded has value 3/4. If each of those pieces is divided into two equal pieces, there are eight pieces and six are shaded: 6/8. Those pictures represent the same amount. The checker cross-multiplies the numerator and denominator, so an equivalent model can pass even if it does not use the original denominator. For example, 6/8 equals 3/4 because 6 × 4 equals 8 × 3.
Improper fractions and whole bars
An improper fraction has more shaded parts than one full bar can hold. To build 7/4, shade one complete four-part bar and three more parts in the next bar. You are representing 1 and 3/4 wholes, not seven independent wholes. On harder levels, the answer may extend into a third bar. Every bar always has the same denominator. The number of subdivisions is an important part of the model, not merely a visual decoration.
Tips for solving quickly
Begin by checking whether your partition matches the target denominator. If it does, the required shaded-part count is usually the target numerator. When using another denominator, scale numerator and denominator by the same multiplier. Do not count the blue bars as separate numerator values. They are collections of equal parts. If the board is incomplete, Undo restores a previous step and Hint can demonstrate one correct equivalent drawing.
Common questions
Can I select equivalent fractions? Yes, any legal partition and shading count that represent the target exactly will pass. Is this an estimating game? No. Fractions are compared by exact integer arithmetic. Does a picture larger than one whole count? Yes, when the target is improper. Are Daily and Practice identical? Both use the same mathematical rules; Daily repeats one fixed challenge for that date and difficulty.