Problem 20 - Prealgebra

Question

Find the percent of each number mentally. $$125 \% \text { of } 300$$

Step-by-Step Solution

Answer

125% of 300 is 375.

Step 1: Convert Percent to Decimal

To find 125% of a number, first convert the percentage to a decimal. A percentage is essentially a number out of 100, so divide 125 by 100 to convert it. \[ 125\% = \frac{125}{100} = 1.25 \]

Step 2: Multiply by the Number

Now that we have converted the percent to a decimal, multiply the decimal by the number you want to find 125% of, which is 300. \[ 1.25 \times 300 \]

Step 3: Calculate the Product

Perform the multiplication from Step 2. \[ 1.25 \times 300 = 375 \]

Step 4: Conclusion

The result of the multiplication is the answer to the problem. Therefore, 125% of 300 is 375.

Key Concepts

Mental Math for Percentages

Mental math is a valuable skill, especially when working with percentages. When you see a percentage problem, try breaking it into simpler parts. Instead of being intimidated by 125%, think of it as 100% plus 25%.
This approach can simplify your calculation:

• First, solve 100% of the number. In this case, 100% of 300 is simply 300.
• Then, find 25% of 300, which is a quarter of 300. This gives you 75.
• Finally, add those two results together: 300 + 75 = 375.

By visualizing percentages as parts of a whole, mental math becomes much more manageable and helps in quick calculations.

Understanding Math Conversions

Math conversions, especially percentages to decimals, are essential in solving various mathematical problems. Converting percentages to decimals involves a simple operation: divide by 100. This is because percentages are based on the idea of 'per hundred'.

In our example, converting 125% to a decimal:

• Divide 125 by 100, which becomes 1.25.

This decimal form becomes extremely handy, allowing you to perform further calculations easily. Understanding these basics of conversion is foundational to efficiently tackling percentage problems, making math less complex and more intuitive.

Simplifying Multiplication Tasks

Multiplication is a core arithmetic skill, and simplifying it makes solving math problems faster and easier. When multiplying by decimals, breaking down the decimal can simplify the operation. For example, when you multiply a number by 1.25:

• Understand it as multiplying by 1 (which keeps the number the same) and then adding 25% of it. This is similar to our mental math breakdown: 300 times 1 is 300, and adding 0.25 times 300 gives another 75, which sums up to 375.

This strategy can help you understand multiplication of decimals without having to rely solely on calculators, elevating your problem-solving skills with practice.

Building Problem Solving Skills

Problem solving in mathematics is like navigating through a maze. It involves understanding the problem, finding creative routes to a solution, and applying the right techniques correctly. Tackling percentage problems like this one involves:

• Decoding the problem by recognizing it involves a percentage.
• Deciding if mental math or step-by-step written methods suit your style better.
• Converting percentages to decimals to streamline calculations.
• Breaking the task into manageable chunks if needed, like simplifying multiplication.

Developing these problem-solving skills not only enhances your math ability but also boosts confidence in approaching various other mathematical tasks.