Twelve Is What Percent Of 60

Understanding percentages is a fundamental skill in mathematics and everyday life. Whether you're calculating discounts, figuring out tips, or analyzing data, knowing how to work with percentages is essential. In this article, we'll break down the process of finding what percentage one number is of another, using the specific example of determining what percentage twelve is of sixty. By the end, you'll have a clear understanding of the steps involved and be able to apply this knowledge to various real-world scenarios.

What is Percentage?

Percentage, derived from the Latin per centum meaning "out of one hundred," is a way of expressing a number as a fraction of 100. It's a dimensionless number, meaning it doesn't have any units attached to it. We use the percent symbol, %, to indicate that a number is a percentage. For instance, 50% represents 50 out of 100, or one-half.

Percentages are used extensively in various fields, including:

• Finance: Calculating interest rates, investment returns, and profit margins.
• Retail: Determining discounts, sales tax, and markup prices.
• Statistics: Representing proportions, survey results, and data analysis.
• Education: Grading tests, calculating averages, and comparing scores.

Understanding percentages is crucial for making informed decisions in these areas. Now, let's dive into the process of calculating what percentage twelve is of sixty.

Calculating Percentage: The Formula

To find what percentage one number (the part) is of another number (the whole), we use the following formula:

Percentage = (Part / Whole) × 100

In our case:

• Part: 12
• Whole: 60

So, we need to find what percentage 12 is of 60. Let's apply the formula step by step.

Step-by-Step Calculation

1. Identify the Part and the Whole: The problem states "twelve is what percent of 60." Here, 12 is the part we are interested in, and 60 is the whole to which we are comparing it.
2. Set up the Fraction: Write the part over the whole as a fraction. In this case, it's 12/60.
3. Simplify the Fraction (Optional): Simplifying the fraction can make the calculation easier. 12/60 can be simplified by dividing both the numerator (12) and the denominator (60) by their greatest common divisor, which is 12.
   • 12 ÷ 12 = 1
   • 60 ÷ 12 = 5
   • So, the simplified fraction is 1/5.
4. Convert the Fraction to a Decimal: Divide the numerator by the denominator to convert the fraction to a decimal.
   • 1 ÷ 5 = 0.2
5. Multiply by 100: Multiply the decimal by 100 to convert it to a percentage.
   • 0. 2 × 100 = 20
6. Add the Percent Symbol: Finally, add the percent symbol (%) to the result to indicate that it is a percentage.
   • 20%

Therefore, twelve is 20% of sixty.

Alternative Method: Using Proportion

Another way to solve this problem is by setting up a proportion. A proportion is an equation stating that two ratios are equal. In this case, we can set up the proportion as follows:

12/60 = x/100

Here, x represents the percentage we are trying to find. To solve for x, we can cross-multiply:

• 12 × 100 = 60 × x
• 1200 = 60x

Now, divide both sides by 60 to isolate x:

• x = 1200 / 60
• x = 20

So, twelve is 20% of sixty.

Real-World Examples and Applications

Understanding how to calculate percentages is valuable in many real-world scenarios. Let's explore a few examples:

1. Discounts: Suppose a store is offering a 12% discount on an item that originally costs $60. To find the discount amount, you calculate 12% of $60.

   • Discount = (12 / 100) × $60
   • Discount = 0.12 × $60
   • Discount = $7.20

   So, the item is discounted by $7.20, and the new price is $60 - $7.20 = $52.80.

2. Test Scores: If you score 12 out of 60 on a test, your percentage score is calculated as:

   • Percentage = (12 / 60) × 100
   • Percentage = 0.2 × 100
   • Percentage = 20%

   This means you scored 20% on the test.

3. Sales Tax: If you buy an item for $12 and the sales tax is 6%, you can calculate the tax amount as:

   • Tax = (6 / 100) × $12
   • Tax = 0.06 × $12
   • Tax = $0.72

   So, the sales tax is $0.72, and the total cost is $12 + $0.72 = $12.72.

4. Budgeting: If you allocate $12 out of a total budget of $60 for entertainment, the percentage of your budget allocated to entertainment is:

   • Percentage = (12 / 60) × 100
   • Percentage = 0.2 × 100
   • Percentage = 20%

   This means you are spending 20% of your budget on entertainment.

Common Mistakes to Avoid

When calculating percentages, it's essential to avoid common mistakes that can lead to incorrect results. Here are a few to watch out for:

1. Incorrectly Identifying the Part and the Whole: Ensure you correctly identify which number is the part and which is the whole. The part is the number you are comparing to the whole, and the whole is the total or reference number. Confusing these can lead to significant errors.

2. Forgetting to Multiply by 100: After dividing the part by the whole, remember to multiply the result by 100 to convert it to a percentage. Forgetting this step will give you a decimal, not a percentage.

3. Rounding Errors: When dealing with decimals, rounding too early can affect the accuracy of your final percentage. It's best to keep as many decimal places as possible during the calculation and round only at the end.

4. Misunderstanding Percentage Increase or Decrease: When calculating percentage increase or decrease, make sure to use the original value as the denominator. The formula is:

   • Percentage Change = ((New Value - Original Value) / Original Value) × 100

   Using the wrong denominator will give you an incorrect percentage change.

5. Not Double-Checking Your Work: Always double-check your calculations to ensure accuracy. A small mistake can lead to a significant difference in the final result.

Advanced Percentage Problems

Once you've mastered the basics, you can tackle more complex percentage problems. Here are a few examples:

1. Finding the Whole When the Percentage and Part Are Known: If you know that 20% of a number is 12, you can find the number (the whole) by rearranging the formula:

   • Percentage = (Part / Whole) × 100
   • 20 = (12 / Whole) × 100
   • Whole = (12 × 100) / 20
   • Whole = 1200 / 20
   • Whole = 60

   So, the number is 60.

2. Calculating Consecutive Percentages: If an item is discounted by 20% and then an additional 10%, you can't simply add the percentages together. Instead, calculate each discount sequentially:

   • Original Price: $100
   • First Discount (20%): $100 - (0.20 × $100) = $80
   • Second Discount (10%): $80 - (0.10 × $80) = $72

   The final price is $72, which is not the same as a 30% discount (which would be $70).

3. Percentage Composition: In chemistry, percentage composition refers to the percentage by mass of each element in a compound. To calculate this, you divide the mass of each element by the total mass of the compound and multiply by 100.

   For example, in water (H2O), the molar mass of hydrogen is approximately 2 g/mol, and the molar mass of oxygen is approximately 16 g/mol. The total molar mass of water is 18 g/mol.

   • Percentage of Hydrogen = (2 / 18) × 100 ≈ 11.11%
   • Percentage of Oxygen = (16 / 18) × 100 ≈ 88.89%

Practical Tips for Everyday Use

To make calculating percentages easier in your daily life, consider the following tips:

1. Memorize Common Percentage Conversions: Knowing common percentage-to-fraction conversions can speed up calculations. For example:

   • 10% = 1/10
   • 20% = 1/5
   • 25% = 1/4
   • 50% = 1/2
   • 75% = 3/4

2. Use Mental Math: Practice mental math techniques to estimate percentages quickly. For example, to find 10% of a number, simply move the decimal point one place to the left. To find 5%, divide 10% by 2.

3. Utilize Calculators and Apps: When dealing with complex or precise calculations, don't hesitate to use a calculator or a percentage calculator app on your smartphone. These tools can save time and reduce the risk of errors.

4. Break Down Problems: Break down complex percentage problems into smaller, more manageable steps. This can make the calculations less daunting and easier to understand.

5. Relate Percentages to Real-World Scenarios: Connect percentages to real-world situations to reinforce your understanding. Think about discounts, tips, taxes, and other everyday scenarios where percentages are used.

Conclusion

Calculating what percentage one number is of another is a fundamental skill with numerous applications in everyday life. By understanding the basic formula, practicing step-by-step calculations, and avoiding common mistakes, you can confidently tackle a wide range of percentage problems. Remember to identify the part and the whole correctly, convert fractions to decimals accurately, and double-check your work. With practice, you'll become proficient in using percentages in various contexts, from finance and retail to statistics and education. So, next time you need to calculate a discount, analyze data, or understand a proportion, you'll be well-equipped to handle it with ease. In the case of twelve is what percent of sixty, the answer is 20%. Keep practicing and applying these skills to enhance your mathematical proficiency and problem-solving abilities.