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Chapter 8: Problem 90

Find each percent. See Sections 7.2 or 7.3. $$ 95 \% \text { of } 50 $$

Short Answer

Expert verified
95% of 50 is 47.5.

Step by step solution

01

Understand the problem

We are tasked to find 95% of 50. This means we need to calculate 95% as a fraction of 50.
02

Convert percentage to decimal

To convert a percentage to a decimal, divide by 100. For 95%, we have \( \frac{95}{100} = 0.95 \).
03

Multiply the decimal by the given number

Multiply the decimal form (0.95) by 50 to find 95% of 50. \[0.95 \times 50 = 47.5\]
04

Verify the calculation

Re-check the multiplication: \( 0.95 \times 50 = (0.95 \times 100) \times 0.5 = 95 \times 0.5 = 47.5 \), confirming that the calculation is correct.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fraction Conversion
Understanding how to convert percentages into fractions is a crucial mathematical skill. Percentages are essentially fractions out of 100. So, to convert a percentage into a fraction, you simply take the percentage number and place it over 100.
For instance, if we take 95%:
  • The percentage part, 95, becomes the numerator.
  • The number 100 (representing "per hundred") becomes the denominator.
  • Thus, 95% can be expressed as the fraction \(\frac{95}{100}\).
This fraction can further be simplified if necessary. But for calculations involving percentages directly, simplifying isn't always needed. Using fractions enables us to express percentages in a form that's compatible with other mathematical operations, particularly multiplication and division. This conversion is fundamental in solving problems involving percentages.
Decimal Multiplication
Decimal multiplication plays an important role when dealing with percentages. Once you've converted a percentage to a decimal, the next step is to multiply this by the referenced number to find the desired value.
Decimal conversion is straightforward:
  • Simply divide the percentage by 100. For instance, 95% becomes 0.95.
After conversion, it鈥檚 time to multiply the number. In our example, you multiply 0.95 by 50. This calculation can be broken down as follows:
  • Align the numbers from the right, treating them as whole numbers for the initial multiplication.
  • Multiply 95 by 50, which results in 4750. However, remember we treated the numbers as whole numbers.
  • Now, adjust for the decimal places. There are two decimal places (in 0.95), so the full product division by 100 gives 47.5.
Ultimately, by understanding decimal multiplication, you get precise results from percentage calculations.
Step-by-Step Solution
Breaking down problems into clear steps can aid understanding and prevent errors. Here's how you can solve a percentage problem step-by-step:
  • Step 1: Understand the Problem. Identify that you need to find a percentage of a number. Here, it's 95% of 50.
  • Step 2: Convert the Percentage to a Decimal. Turn the percentage into a decimal by dividing by 100. This makes 95% into 0.95.
  • Step 3: Perform the Multiplication. Multiply the decimal by the given number. Here, multiply 0.95 by 50 to get 47.5.
  • Step 4: Verify Your Results. Check calculations to confirm accuracy, ensuring that your process has been followed correctly and results match expected logic.
By learning and following these systematic steps, even those who struggle with mental math can accurately find percentages of numbers, reducing the chance for errors and increasing confidence in problem solving.

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