When faced with mathematical problems or scenarios, we often encounter fractions or ratios that can lead to confusion if not properly understood. One such example is calculating "60 of 90." Let's dive into this concept, break it down step by step, and explore its practical applications.

## What Does "60 of 90" Mean?

The phrase "60 of 90" essentially refers to a fraction where 60 is a part of 90. This can be translated mathematically as:

[ \frac{60}{90} ]

To simplify this fraction, we look for the greatest common divisor (GCD) of the numerator and denominator.

## Step-by-Step Simplification

**Identify the GCD**: The GCD of 60 and 90 is 30.**Divide both by the GCD**: [ \frac{60 \div 30}{90 \div 30} = \frac{2}{3} ]

Thus, **60 of 90 simplifies to ( \frac{2}{3} )**.

## Calculating the Percentage

Another common way to express "60 of 90" is by calculating it as a percentage. To find the percentage, use the formula:

[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 ]

Using our numbers: [ \text{Percentage} = \left( \frac{60}{90} \right) \times 100 ]

Calculating this gives us: [ \text{Percentage} = \left( \frac{2}{3} \right) \times 100 = 66.67% ]

So, **60 of 90 equals approximately 66.67%**.

## Practical Applications

Understanding "60 of 90" can be useful in numerous real-life scenarios:

### 1. Academic Grading

Suppose a student scores 60 out of 90 points on a test. Knowing the percentage (66.67%) helps both the student and educator evaluate performance and areas needing improvement.

### 2. Project Management

In project management, if 60 tasks are completed out of a total of 90, the completion rate (66.67%) is crucial for understanding project progress and ensuring deadlines are met.

### 3. Budgeting

When allocating a budget, if 60 units of budgeted expenses have been used out of a total of 90 units, it shows that about two-thirds of the budget is consumed, prompting a review of spending.

## Conclusion

In summary, "60 of 90" simplifies to ( \frac{2}{3} ) or approximately 66.67%. Understanding how to interpret such ratios is valuable in various aspects of everyday life, from education to finance. By grasping these mathematical concepts, individuals can make more informed decisions.

### Further Learning

For those interested in deepening their understanding of fractions and percentages, consider exploring topics like:

- The concept of ratios in various contexts
- How percentages affect budgeting and financial planning
- The importance of data interpretation in business decisions

In mathematics, understanding how to translate numbers into meaningful insights is a key skill that benefits both personal and professional development.

This content is inspired by the discussions found on BrainlY where learners engage in problem-solving and collaborative learning. Always remember to verify the information and practice calculations to enhance your understanding!