Ratio and Proportion Cheat Sheet

Key Definitions

• Ratio: A relationship between two quantities expressed as a fraction (e.g., 3:4).

• Proportion: An equation stating that two ratios are equal (e.g., \( \frac{a}{b} = \frac{c}{d} \)).

Important Concepts

Types of Ratios

• Direct Ratio: Compares two quantities directly.

• Inverse Ratio: Compares two quantities inversely (e.g., if A is to B, then B is to A).

Proportionality

• If \( a:b = c:d \), then \( a \times d = b \times c \).

Key Formulas

• a: First term of the first ratio

• b: Second term of the first ratio

• c: First term of the second ratio

• d: Second term of the second ratio

Cross Multiplication: a d = b c

Common Mistakes to Avoid

Common Mistake: Mixing up the terms in a ratio (e.g., writing \( a:b \) as \( b:a \)).

Memory Tricks

Tip: "RATIO" — Relation, Abstract, Two quantities, Interchangeable, Otherwise, think proportionally.

Key Diagrams

       a
       |
       |  b
       |
-------|------- 
       |
       |  c
       |
       d