GUIDE深度 · Deep dive
Simplifying and Solving Ratios
Simplify a ratio by dividing both terms by the GCD; solve a proportion by cross-multiplying: a:b=c:d means ad=bc. Make units consistent first.
Simplify
12:18 -> 2:3 (divide by 6).
Both terms should be integers.
Solve
x:3=4:6 -> 6x=12 -> x=2.
Cross-multiply, then solve the linear equation.
Keep the same order on both sides; swapping b and c is the most common cross-multiplication mistake.
FAQ
Is a ratio a fraction?
Same value, but a ratio emphasizes the relationship between terms.
Different units?
Convert to the same unit first.