Problemas matemáticos e raciocínio lógico · Visual Fractions Area Models
Calculadora e visualizador interativo de frações
Visualizador interativo de frações e produto de frações por área: fatias e malha retangular
- No navegador
- Sem cadastro
- Dedução ao vivo
- Modo projetor
- Folha de exercícios A4
Janela de demonstração matemática● 60 FPS
Variáveis de controle do experimento
Deduções e métricas em tempo real
Fração simplificada
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Denominador comum
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Valor decimal
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Número misto
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Dedução de fórmulas em tempo real
Fórmula fundamental:
--Substituição de valores:
--Conclusão: --
Versão para o fundamental:🎮 Valor posicional dos decimais ↗
Exemplos clássicos e armadilhas de exame
Worked Problem
Problema: Calculate 3/4 + 2/5. Show common denominator steps and simplified mixed fraction.
Derivação passo a passo:
- 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.
Derivação passo a passo:
- 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.
Folha de investigação em aula e exercícios
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.
Perguntas frequentes e erros comuns
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).