What is the ratio of 18 minutes to one hour, expressed in simplest fractional form?

Introduction / Context:
Ratio questions are very common in aptitude tests because they check your understanding of proportional comparison between quantities with the same units. Here, you are given 18 minutes and one hour, and you need to express the ratio of these times in simplest fractional form. This is a foundational concept that appears in time and work, speed, and percentage questions as well.

Given Data / Assumptions:

• First quantity: 18 minutes.
• Second quantity: 1 hour.
• We know that 1 hour equals 60 minutes.
• We must express the ratio 18 minutes : 60 minutes and simplify it.

Concept / Approach:
When forming a ratio, both quantities must be in the same unit. After converting, the ratio a : b can often be simplified by dividing both terms by their greatest common divisor. Once converted and simplified, the ratio can be written either as a : b or as a fraction a / b. For time, using minutes for both values makes the comparison straightforward.

Step-by-Step Solution:
Step 1: Convert one hour to minutes. One hour equals 60 minutes. Step 2: Now write the ratio in terms of minutes: 18 minutes : 60 minutes. Step 3: To simplify, divide both numbers by their greatest common divisor. The greatest common divisor of 18 and 60 is 6. Step 4: Divide both terms by 6: 18 / 6 = 3 and 60 / 6 = 10. Step 5: So the simplified ratio is 3 : 10. Step 6: Expressing this as a fraction gives 3/10.

Verification / Alternative check:
You can also convert 18 minutes to a fraction of an hour directly. Since 60 minutes is one hour, 18 minutes is 18 / 60 hours. Simplifying this fraction, divide numerator and denominator by 6 to get 3 / 10 hours. This confirms again that the ratio of 18 minutes to one hour is 3/10, because you are essentially comparing 0.3 hours to 1 hour.

Why Other Options Are Wrong:
1/5: This equals 0.2, which is less than 18 / 60 = 0.3, so it understates the fraction of an hour.
3/4: This equals 0.75 hours, much larger than 18 minutes and therefore incorrect.
1/7: This is about 0.1428, which is too small compared with 0.3.
2/5: This is 0.4, which is greater than the true value of 0.3 for 18 minutes out of an hour.

Common Pitfalls:
A frequent mistake is to forget to convert hours into minutes or vice versa before forming the ratio. Some learners keep the units mixed, which can lead to meaningless comparisons. Others simplify 18 : 60 incorrectly by dividing by the wrong common factor or by skipping the simplification step altogether. Always ensure that units are consistent and that the numbers are reduced to simplest form.

Final Answer:
The ratio of 18 minutes to one hour is 3/10.