Problem 19 - Prealgebra

Question

Find the percent of each number mentally. $$150 \% \text { of } 54$$

Step-by-Step Solution

Answer

150% of 54 is 81.

Step 1: Understand the Problem

We need to find what 150% of 54 is. This means finding 150 out of 100 parts of the number 54.

Step 2: Find 100% of the Number

Since 100% of any number is the number itself, we find that 100% of 54 is simply 54.

Step 3: Find 50% of the Number

To find 50% of a number, we divide it by 2. So, 50% of 54 is \( 54 \div 2 = 27 \).

Step 4: Add the Percentages

Now, add the amounts from 100% and 50% to find 150% of the number. That is \( 54 + 27 = 81 \).

Key Concepts

Mental Math

When tackling percentage problems through mental math, it's crucial to understand the concept behind the numbers. Mental math allows us to swiftly compute percentage values without relying on calculators.
This exercise involves calculating 150% of 54. By breaking this down using mental math techniques, we can make the process seamless and less daunting.
A good mental tool to use is visualizing percentages in parts. Here, 150% can be imagined as 1.5 times the original number.

• First, recognize that 100% of a number is just the number itself.
• Then, find additional percentages, like 50%, by using simple arithmetic operations, such as division by 2 for 50%.

Finally, add these results to determine the larger percentage. By practicing these skills, students can train their brains to process numbers quicker, leading to more robust mental math abilities.

Step-by-Step Solutions

Solving percentage problems with a clear, step-by-step approach ensures accurate results. Following steps systematically can also enhance understanding. In this example, to find 150% of 54, each calculation step builds upon the last. First, identify that 100% of any number is the number itself—in this case, 54.
Then, determine 50% by halving the number. For 54, dividing by 2 gives us 27.
Next, simply add these two results together:

• 100% of 54 equals 54
• 50% of 54 equals 27
• Adding 54 and 27 gives us 81

Thus, 150% of 54 is 81. Completing these steps attentively not only confirms the accuracy but solidifies the approach for similar problems in the future.

Percentage Concepts

Understanding percentage concepts is fundamental to mastering related calculations. **Percentages** represent parts per hundred, serving as a way to express how a number compares to a whole (100%).
In this example, 150% means we are looking for not just the whole amount but an additional 50% on top of it. By grasping how percentages extend beyond 100%, we can compute 150% as 1.5 times the original amount. **Common conversions in percentages:**

• 100% is the full amount or the original number.
• 50% is half of the amount, dividing by 2.
• 200% would be twice the amount, multiplying by 2.

Such insights simplify complex percentage problems and are pivotal for both manual calculations and when leveraging mental math techniques. Recognizing these core ideas aids significantly in handling percentages across various contexts.