Ratio and Proportion
Maharashtra Board · Class 9 · Mathematics
Quick revision notes for Ratio and Proportion — Maharashtra Board Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Basic Concepts and Definitions
- Ratio compares two or more quantities of the same type
- Ratio is expressed as a:b or a/b where b ≠ 0
- Ratios are unitless and must be in the same units before comparison
Direct and Inverse Proportion
- In direct proportion, as one quantity increases, the other increases proportionally
- In inverse proportion, as one quantity increases, the other decreases proportionally
- Direct proportion: x/y = k (constant ratio)
Properties of Equal Ratios
- Five main properties: Invertendo, Alternando, Componendo, Dividendo, Componendo-Dividendo
- These properties help solve complex ratio problems efficiently
- Each property transforms equal ratios in a specific way
Theorem of Equal Ratios
- If a/b = c/d, then a/b = c/d = (a+c)/(b+d)
- Can be extended to multiple ratios
- Extremely useful in solving problems with multiple variables
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