Question

Hunter answered 48 questions correctly out of a total of 54 questions. What percent of the total questions did Hunter answer correctly?

Short answer

Answer: Hunter answered approximately 88.89% of the total questions correctly.

Step-by-step solution

Identify the numbers in the problem

In this exercise, we are given that Hunter answered 48 questions correctly out of a total of 54 questions. So correct answers = 48, and total questions = 54.

Calculate the fraction of correct answers

To find the fraction of correct answers, divide the number of correct answers (48) by the total number of questions (54). This can be written as: Fraction of correct answers = correct answers / total questions

Calculate the percentage of correct answers

To convert the fraction of correct answers to a percentage, multiply the fraction by 100: Percentage of correct answers = Fraction of correct answers × 100

Plug in the numbers and solve

Now, we can plug in the numbers in the formula derived in step 3: Percentage of correct answers = (48 / 54) × 100 Evaluate the expression within the parentheses first: Percentage of correct answers = (0.88888...) × 100 Finally, multiply the result by 100: Percentage of correct answers ≈ 88.89% Hence, Hunter answered about 88.89% of the total questions correctly.

Key concepts

Calculating Percentages

Understanding how to calculate percentages is crucial not only in mathematics but also in everyday life, such as figuring out discounts during shopping or determining the right tip at a restaurant. Percentages represent a part of a whole expressed out of a total of 100. To calculate the percentage of correct answers, as in the case of Hunter's quiz, we start by comparing the number of correct answers to the total number of questions.

Using a simple formula: \( \text{Percentage of Correct Answers} = \frac{\text{Number of Correct Answers}}{\text{Total Questions}} \times 100 \), the idea is to see what portion the number of correct answers is of the total. Multiplying this fraction by 100 translates it into a percentage, which is often easier to understand and communicate. For instance, knowing you got 88.89% on a test is more intuitive than saying you got 48 out of 54 answers correct.

Fraction to Percentage Conversion

Converting fractions to percentages is a fundamental skill that transforms a part-to-whole relationship into a more universally understood form. To convert a fraction, you simply multiply it by 100. This process transforms the denominator from whatever it was initially to 100, which defines a percentage.

For example, if Hunter has a fraction representing correct answers as \( \frac{48}{54} \), the conversion to a percentage involves the operation \( \frac{48}{54} \times 100 \). It’s important to simplify the fraction if possible before multiplying by 100, as it will make the multiplication step simpler and the result more immediate.

Mathematics Problem Solving

Mathematical problem solving involves a step-by-step approach to tackle mathematical challenges effectively. As demonstrated with Hunter's quiz, we began by identifying the essential elements of the problem: the number of correct answers and the total number of questions. Then, we expressed the performance as a fraction before translating it into a percentage.

Each step is taken methodically, ensuring accuracy and comprehension. When presented with mathematical problems, always look for key information, figure out what you need to find, and determine the relationship between the known and unknown. Solving Hunter's problem required division, multiplication, and understanding of how fractions relate to percentages—a blend of skills that are often utilized in various mathematical problem-solving scenarios.