🎒 Field Trip Fraction Challenge

Utangamano School was planning an educational field trip for Grade 8 learners. The school wanted to expose learners to different learning environments that connect classroom knowledge to real-life experiences.

Each learner was to choose one place to visit based on their interests:

What fraction of the learners were to visit the historical site?

🔬
Science Museum
⅜ of all learners
👨‍🎓 👩‍🎓 👨‍🎓
🎨
Art Gallery
⅓ of remaining
👩‍🎓 👨‍🎓
🏛️
Historical Site
? (Rest)
👨‍🎓 👩‍🎓 👨‍🎓 👩‍🎓

💡 Step-by-Step Solution

1
Science Museum:
⅜ of all learners visit the science museum
2
Remaining after Science Museum:
1 - ⅜ = ⁸⁄₈ - ³⁄₈ = ⁵⁄₈ of learners remain
3
Art Gallery:
⅓ of remaining = ⅓ × ⁵⁄₈ = ⁵⁄₂₄ of all learners
4
Historical Site (Final Answer):
1 - ⅜ - ⁵⁄₂₄ = ?
Convert to common denominator: ²⁴⁄₂₄ - ⁹⁄₂₄ - ⁵⁄₂₄ = ¹⁰⁄₂₄ = ⁵⁄₁₂

Visual Fraction Model

⅜
Museum
⁵⁄₂₄
Gallery
?
Historical
Complete fraction bar representing all learners (1 whole)

Select the correct fraction of learners visiting the historical site:

👏
👏
👏
👏
👏
👏
👏
👏

📚 Understanding Fractions of Remainders

Key Concept: When finding a fraction "of remaining," multiply that fraction by what remains after previous selections.

Complete Calculation:

  1. Science Museum: ⅜ of all learners
  2. Remaining: 1 - ⅜ = ⁵⁄₈
  3. Art Gallery: ⅓ of ⁵⁄₈ = ⅓ × ⁵⁄₈ = ⁵⁄₂₄ of all learners
  4. Historical Site: 1 - ⅜ - ⁵⁄₂₄
  5. Find common denominator (24): ²⁴⁄₂₄ - ⁹⁄₂₄ - ⁵⁄₂₄ = ¹⁰⁄₂₄
  6. Simplify: ¹⁰⁄₂₄ = ⁵⁄₁₂ (divide by 2)

Answer: ⁵⁄₁₂ of the learners visit the historical site.