What will be the simplest form of the ratio 3 hours: 1 day?

### Concept & Unit Homogeneity in Ratios To form a valid mathematical ratio, both quantities must be expressed in the exact same units. You cannot compare hours directly to days without conversion. $$ \text{Ratio} = \frac{\text{Quantity 1}}{\text{Quantity 2}} \text{ (after equating units)} $$ ### Step-by-Step Solution * **Given:** $3$ hours and $1$ day. * **Convert units:** Since $1$ day contains $24$ hours, convert "1 day" into hours to match the other quantity. $1 \text{ day} = 24 \text{ hours}$ * **Set up the ratio:** $\text{Ratio} = 3 \text{ hours} : 24 \text{ hours}$ * **Simplify:** Divide both sides by their highest common factor, which is $3$. $\frac{3}{3} : \frac{24}{3}$ $1 : 8$ ### Exam Strategy & Shortcut Whenever comparing disparate time units (hours to days, minutes to hours), immediately convert the larger unit into the smaller unit. Knowing $1$ day $= 24$ hours makes this a mental math problem: $3/24 = 1/8$. ### Common Pitfall Creating the ratio without converting units first (yielding $3:1$), which compares completely different scales of time and leads to an incorrect answer. ### Final Answer Therefore, the correct answer is **$1 : 8$**.