Problemas matemáticos y razonamiento · Visual Fractions Area Models
Calculadora y visualizador interactivo de fracciones
Visualizador interactivo de fracciones y multiplicación de áreas: porciones de pizza y cuadrículas
- Cálculo en cliente
- Sin registro
- Derivación en vivo
- Modo proyector
- Hoja de trabajo A4
Ventana de demostración matemática● 60 FPS
Variables de control del experimento
Derivaciones y métricas en tiempo real
Fracción simplificada
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Denominador común
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Valor decimal
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Número mixto
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Derivación de fórmulas en tiempo real
Fórmula básica:
--Sustitución de valores:
--Conclusión: --
Versión para primaria:🎮 Valor posicional de los decimales ↗
Ejemplos clásicos y análisis de errores en exámenes
Worked Problem
Problema: Calculate 3/4 + 2/5. Show common denominator steps and simplified mixed fraction.
Derivación paso a paso:
- LCM(4, 5) = 20. 3/4 = 15/20, 2/5 = 8/20. Sum = 15/20 + 8/20 = 23/20 = 1 3/20.
Worked Problem
Problema: Explain why 2/3 * 4/5 = 8/15 using an area grid model.
Derivación paso a paso:
- Unit square partitioned into 3 rows and 5 columns (15 tiles). Shading 2 rows and 4 columns creates an 8-tile overlap out of 15, yielding 8/15.
Hoja de indagación en clase y tareas
Q1. Variant 1: Ming eats 3/8 pizza, sister eats 1/4 pizza. What fraction eaten? What fraction remains?
Answer Key: 1/4 = 2/8. Total eaten = 3/8 + 2/8 = 5/8. Remaining = 1 - 5/8 = 3/8.
Q2. Variant 2: From a 6m rope, compare cutting 2/3 meter vs cutting 2/3 of its length. What remains?
Answer Key: Cutting 2/3 meter leaves 6 - 2/3 = 5 1/3 m. Cutting 2/3 of length leaves 6 * (1 - 2/3) = 2m.
Q3. Variant 3: Calculate 5/6 / 2/3 and explain why we invert and multiply.
Answer Key: 5/6 * 3/2 = 15/12 = 5/4 = 1 1/4. Dividing by 2/3 means dividing by 2 then multiplying by 3, which is multiplying by 3/2.
Preguntas frecuentes y errores conceptuales
Why can't we add numerators and denominators directly in fraction addition?
Because denominators define slice unit size! 1/2 and 1/3 are different sized blocks; you cannot sum counts until sliced to uniform size (common denominator).
What is fraction simplification (reduction)? Why does value stay constant?
Dividing numerator and denominator by their greatest common factor. Grouping multiple small tiles into fewer equivalent large blocks leaves total value invariant.
Distinguish proper, improper, and mixed fractions.
Proper: numerator < denominator (< 1). Improper: numerator ≥ denominator (≥ 1). Mixed: whole number + proper fraction (e.g. 1 2/3).
Why does dividing by a fraction equal multiplying by its reciprocal?
Multiply top and bottom of complex fraction [A] / [2/3] by 3/2: denominator becomes (2/3)*(3/2) = 1, leaving A * (3/2).