Revision Notes for Class 8 Maths Chapter 10: Proportional Reasoning 2

Condensed revision notes for Class 8 Maths Chapter 10: Proportional Reasoning 2 – Ganita Prakash. These Class 8 Mathematics Chapter 10 notes are ideal for quick revision just before exams.

• Dividing a whole in a given ratio: each part’s share = (that part’s ratio number ÷ sum of all ratio numbers) × total quantity.
• Similar vs congruent: shapes with sides in the same ratio are similar (same shape), but only congruent if also the same actual size.
• Triangle inequality: a triangle can be constructed only if the sum of any two sides exceeds the third side.
• Pie chart angle for a category = (category count ÷ total count) × 360°. All angles in a pie chart always sum to 360°.
• Direct proportion: x/y = constant (both quantities increase or decrease together in the same ratio).
• Inverse proportion: x × y = constant (as one quantity increases, the other decreases proportionally). Test: check that x₁y₁ = x₂y₂ = x₃y₃… for every pair.
• Common inverse-proportion situations: number of workers vs. days to finish a job; number of taps vs. time to fill a tank; speed vs. time for a fixed distance; number of machines vs. days for a fixed output.
• Common direct-proportion situations: quantity bought vs. price paid (at a fixed rate); number of pages vs. time to read (at a fixed reading speed).
• Combined work rates: add individual rates (1/time for each) to find the combined rate; total time = 1 ÷ combined rate.
• Rule of thumb: always check with the product test (xy = constant) before assuming a relationship is inverse — don’t just guess from the wording.

More on this chapter: Solutions | Extra Questions | Class 8 Maths Book | Formulas Handbook

Written by Satish

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