60 Of 90 Is What Number

60 out of 90: Understanding Percentages, Fractions, and Ratios

Knowing how to calculate percentages is a fundamental skill applicable across numerous areas of life, from academic studies and professional work to everyday scenarios like shopping and budgeting. This article delves into the question "60 out of 90 is what number?" and explores the various mathematical approaches to solve it, highlighting the underlying concepts of percentages, fractions, and ratios. We will also look at practical applications and demonstrate different methods for calculating similar problems.

Understanding the Problem: 60 out of 90

The question "60 out of 90 is what number?" essentially asks us to express the relationship between 60 and 90 as a percentage, fraction, or decimal. This represents a part-to-whole relationship, where 60 is the part and 90 is the whole. We can use several methods to find the solution.

Method 1: Using Fractions

The simplest approach involves expressing the relationship as a fraction: 60/90. This fraction represents 60 parts out of a total of 90 parts. To simplify this fraction, we find the greatest common divisor (GCD) of 60 and 90, which is 30. Dividing both the numerator (60) and the denominator (90) by 30, we get:

60/90 = 2/3

This simplified fraction, 2/3, represents the same proportion as 60/90. It tells us that 60 is two-thirds of 90.

Method 2: Converting the Fraction to a Decimal

To convert the fraction 2/3 into a decimal, we divide the numerator (2) by the denominator (3):

2 ÷ 3 ≈ 0.6667

This decimal, approximately 0.6667, represents the decimal equivalent of the fraction 2/3. Note that this is a recurring decimal, meaning the "6" repeats infinitely. For most practical purposes, rounding to a sufficient number of decimal places (like four in this case) is acceptable.

Method 3: Converting the Decimal to a Percentage

To express the decimal 0.6667 as a percentage, we multiply it by 100:

0.6667 x 100 ≈ 66.67%

Therefore, 60 out of 90 is approximately 66.67%.

Method 4: Direct Percentage Calculation

We can also directly calculate the percentage using the formula:

(Part / Whole) x 100%

Substituting the values from our problem:

(60 / 90) x 100% = 0.6667 x 100% ≈ 66.67%

This method yields the same result as the previous methods, confirming that 60 out of 90 is approximately 66.67%.

Understanding Ratios

The relationship between 60 and 90 can also be expressed as a ratio: 60:90. Similar to fractions, ratios express the proportional relationship between two or more numbers. Just like the fraction, this ratio can be simplified by dividing both numbers by their GCD (30):

60:90 = 2:3

This simplified ratio, 2:3, tells us that for every 2 units of one quantity, there are 3 units of another.

Practical Applications

Understanding these calculations has many real-world applications:

• Academic Performance: If a student answers 60 out of 90 questions correctly on a test, their score is approximately 66.67%.
• Sales and Marketing: If a company sells 60 units out of a total stock of 90 units, their sales represent 66.67% of their inventory.
• Financial Analysis: If a business has a profit of $60,000 on a total revenue of $90,000, the profit margin is 66.67%.
• Survey Results: If 60 out of 90 respondents answered "yes" to a survey question, 66.67% of respondents answered affirmatively.

Solving Similar Problems

The methods described above can be applied to solve similar problems. For instance, let's consider:

Problem: 35 out of 70 is what number?

Solution:

1. Fraction: 35/70 = 1/2
2. Decimal: 1 ÷ 2 = 0.5
3. Percentage: 0.5 x 100% = 50%

Therefore, 35 out of 70 is 50%.

Problem: What is 40% of 120?

Solution:

1. Convert Percentage to Decimal: 40% = 0.4
2. Multiply: 0.4 x 120 = 48

Therefore, 40% of 120 is 48.

Conclusion: Mastering Percentages, Fractions, and Ratios

This article has comprehensively addressed the question "60 out of 90 is what number?" We explored different methods of calculation, emphasizing the importance of understanding percentages, fractions, and ratios. Mastering these concepts is crucial for navigating various aspects of life, from simple everyday tasks to complex professional scenarios. The ability to quickly and accurately calculate proportions not only improves problem-solving skills but also contributes to better decision-making in various contexts. Remember to practice these techniques regularly to build proficiency and confidence in handling numerical problems efficiently. Understanding these fundamental mathematical concepts lays the foundation for more advanced mathematical and analytical skills. By employing the methods explained here, you can confidently tackle similar percentage, fraction, and ratio problems with ease and accuracy. Continue practicing, and you'll soon become adept at effortlessly solving these types of calculations.