Proportional Reasoning-2

Map scales, three-part ratios, pie charts, and inverse proportion, where one quantity goes up as the other goes down.

Key ideas

A scale of 1 : 250 means 1 cm on the plan is 250 cm (2.5 m) in real life.
A three-part ratio a : b : c shares a total into a + b + c equal parts.
In a pie chart each part gets an angle in proportion to its size; the angles add to 360°.
Direct proportion: both go up together (more items, more cost). Inverse proportion: one goes up as the other goes down (more workers, fewer days).
In inverse proportion the product stays the same.

Scale	real length = plan length × scale number
Pie chart angle	part ÷ total × 360°
Inverse proportion	x₁ × y₁ = x₂ × y₂
Units	100 cm = 1 m; 1000 m = 1 km

Treating an inverse proportion as direct (doubling the workers does not double the days).
Forgetting to convert centimetres to metres after using the scale.
Using the total of the ratio as 100 instead of a + b + c.

A plan of a room has a scale of 1 : 250. On the plan the room is 8 cm by 10 cm. Find its real length, breadth and floor area.

Working: 8 × 250 = 2000 cm; 10 × 250 = 2500 cm

Answer: 20 m by 25 m; 500 m²