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CLASS VIII • PROPORTIONAL REASONING–2Smart Lab: Ratios, Maps, Pie Charts & Inverse Proportion

Proportional Reasoning–2

Explore map scales, multi-term ratios, dividing a whole in a ratio, pie chart angles, and direct versus inverse proportion through interactive labs.

Fact Sheet: The Big Ideas

Proportional relationship: related quantities change by the same factor. Example: idli batter 2 cups rice : 1 cup urad dal can be scaled to 6 : 3 or 4 : 2.
Map scale / RF: RF 1 : 60,00,000 means 1 cm on the map represents 60,00,000 cm = 60 km on the ground.
Multi-term ratios: Spice mix 8 : 4 : 2 : 1 can be scaled to 4 : 2 : 1 : 0.5 by multiplying every term by 1/2.
Inverse proportion: If one quantity increases and the other decreases by the same factor, the product stays constant. Speed × time = distance.
Direct
a : b :: c : d
Cross multiply
a × d = b × c
Inverse
x × y = k
Pie chart
whole = 360°

Formula Hub

Cross Multiplication

If a : b and c : d are proportional, then:

a × d = b × c

Map Distance

Actual distance = map distance × scale factor.

RF 1 : n means 1 cm → n cm.

Divide Whole in Ratio

For total x in ratio a : b : c:

x×a/(a+b+c), x×b/(a+b+c), x×c/(a+b+c)

Pie Chart Angle

Slice angle = value/total × 360°.

All slice angles add to 360°.

Direct Proportion

Quotient remains constant.

x/y = k

Inverse Proportion

Product remains constant.

x × y = k

Direct: x/y = k    |    Inverse: x × y = k    |    Pie angle = value/total × 360°

Interactive Lab: Mixed Reasoning Quiz

Score: 0Current Streak: 🔥 0Badge: Ratio Explorer


Activity Zone

🗺️ Map Scale Distance Calculator

RF 1 : 60,00,000 means 1 cm on the map represents 60 km. Enter a map distance.

Bengaluru
Chennai

🥣 Multi-Term Ratio Scaler

Scale a recipe, paint mix, concrete mix, or any multi-term ratio.

🥧 Pie Chart Angle Builder

Enter values and labels to generate slice angles and a quick pie preview.

🚰 Inverse Proportion Solver

Use x₁y₁ = x₂y₂. Example: workers × days, pumps × hours, speed × time.

Worksheet Generator

Generate practice questions on map scales, multi-term ratios, pie chart angles, direct proportion, and inverse proportion.



Real-World Use

Maps and atlases: Representative fractions convert map measurements into actual distances.
Construction: Concrete mixes divide cement, sand, and gravel in fixed ratios.
Data handling: Pie charts turn proportions into 360° angle slices.
Work and time: More workers or pumps usually reduce time if the rate per worker/pump stays the same.

🌍 Real-Life Case Generator

Teacher Tools

Learning Outcomes

  • Use cross multiplication to test proportional ratios.
  • Interpret representative fractions in maps.
  • Scale ratios with more than two terms.
  • Divide a whole quantity in a given multi-term ratio.
  • Convert data values to pie chart angles.
  • Distinguish direct and inverse proportion.

Classroom Prompts

  • Why is map distance not always the same as road distance?
  • What assumptions make worker-time problems inverse proportion?
  • How can a pie chart be checked for accuracy?

Exit Tickets

  • Divide 80 ml of paint in the ratio 2 : 3 : 5.
  • Find the pie angle for 15 out of 60 students.
  • Explain why 2 pumps in 18 hours becomes 4 pumps in 9 hours.