Problem 33 - Prealgebra

Question

What number is \(56 \%\) of \(85 ?\) ( lesson \(6-8\) )

Step-by-Step Solution

Answer

56% of 85 is 47.6.

Step 1: Understanding the Problem

We need to find what number is 56% of 85. This means we have to calculate the number that represents 56% of the total 85.

Step 2: Convert Percentage to Decimal

To find a percentage of a number, we first convert the percentage into a decimal. We do this by dividing the percentage by 100. So, we convert 56% into a decimal by computing \( \frac{56}{100} \).

Step 3: Calculate the Decimal Value

Perform the division: \( \frac{56}{100} = 0.56 \). Now, we have converted 56% to the decimal 0.56.

Step 4: Multiply by the Total Value

To find 56% of 85, multiply the decimal 0.56 by 85. This step calculates \( 0.56 \times 85 \).

Step 5: Perform the Multiplication

Calculate the product: \( 0.56 \times 85 = 47.6 \).

Step 6: Conclude with the Result

The solution to the problem is that 56% of 85 is 47.6.

Key Concepts

Converting Percentages to Decimals

Converting percentages to decimals is a fundamental skill in mathematics that can make percentage calculations much simpler. When we look at a percentage, what we are really seeing is a fraction out of 100. For example, 56% can be thought of as 56 out of 100. To convert a percentage to a decimal, you take the percentage value and divide it by 100. This is because a percentage is simply a number divided by 100. This tiny trick transforms a percentage into a usable decimal for further calculations. Here's how you do it:

• Take your percentage number, for example, 56%.
• Divide by 100: \( \frac{56}{100} \).
• This gives you the decimal 0.56.

After converting 56% into 0.56, you're now ready to use this decimal in additional operations like multiplication to find percentages of a number.

Basic Multiplication

Once you have a decimal, like 0.56 from the percentage conversion, you can now use basic multiplication to find a percentage of a number. Multiplication is one of the core operations in math—it's essentially repeated addition. In our example, we are calculating what 56% of 85 is. After converting 56% to 0.56, we perform the multiplication:

• Take the decimal: 0.56.
• Multiply by the number you want the percentage of: 85.
• So the operation is \( 0.56 \times 85 \).

This means you are essentially adding 85, 0.56 times. Performing this multiplication gives you 47.6, which is 56% of 85. Multiplication in this context helps you scale a number by your desired percentage.

Problem-Solving Steps

Solving problems using percentages involves a sequence of structured steps that make the process straightforward. Let's break down the steps we used in our example problem where we found 56% of 85:

• **Understand the Problem:** Know what you are being asked. Here, "What number is 56% of 85?" implies finding a portion of 85.
• **Convert the Percentage:** Change 56% to a decimal, which is easier to handle mathematically. That gives you 0.56.
• **Multiply:** Use the decimal to compute the part of the total by multiplying it with 85.
• **Calculate the Result:** Perform the multiplication to find the requested value, which is 47.6 in this case.
• **Verify and Conclude:** Always double-check your results to ensure accuracy, and then conclude by stating the problem's solution.

Following these steps ensures you effectively and correctly resolve percentage problems every time.