Question

A basketball player made 9 out of 40 free throws last season. What percent of the free throws did she make? (A) \(0.225 \%\) (B) \(4.4 \%\) (C) \(22.5 \%\) (D) \(44.4 \%\)

Short answer

C) 22.5%

Step-by-step solution

Calculating the Ratio of Made Free Throws

First, determine the fraction of successful free throws by dividing the number of made free throws by the total attempts. The basketball player made 9 free throws out of 40 attempts. This can be expressed as the fraction \( \frac{9}{40} \).

Converting the Fraction to a Decimal

To convert the fraction \( \frac{9}{40} \) into a decimal, divide 9 by 40. Performing the division, we have \( 9 \div 40 = 0.225 \).

Converting the Decimal to a Percentage

To convert the decimal \(0.225\) to a percentage, multiply the decimal by 100. This gives \(0.225 \times 100 = 22.5\). Therefore, the percentage of successful free throws is \(22.5\%\).

Selecting the Correct Answer Choice

Now, compare the calculated percentage (22.5%) with the provided options. The option that matches our calculation is (C) \(22.5\%\).

Key concepts

Understanding Fractions

In mathematics, fractions are a way to express parts of a whole number. They consist of two numbers: a numerator (the top number) and a denominator (the bottom number). Think of a fraction as describing how many parts out of a total you are focusing on. For example, in the problem given, the fraction \( \frac{9}{40} \) tells us that 9 successful free throws were made out of 40 attempts.

• The numerator is 9, indicating the number of successful actions.
• The denominator is 40, representing the total number of attempts.

By understanding the relationship between the numerator and denominator, you can grasp how fractions represent part-to-whole relationships in various problems.

Converting Fractions to Decimals

To solve problems that involve percentages, it's often necessary to convert fractions into decimals. This conversion is straightforward: simply divide the numerator by the denominator.

Using the example from the exercise, you need to convert \( \frac{9}{40} \) into a decimal. Here's how:

• Divide 9 by 40, which equals 0.225.

Now you have the decimal equivalent of the fraction. This decimal helps to simplify calculations when you're moving towards finding percentages or comparing values.

Applying Mathematics Problem Solving

Problem-solving in mathematics involves a systematic approach to finding the solution, especially when dealing with calculations like percentages. The key steps include identifying what is being asked, performing the necessary calculations, and verifying the results.

For the given problem of determining what percentage of free throws were made, you followed a clear pattern:

• Determine the fraction: What part of the whole does 9 successful attempts out of 40 represent.
• Convert the fraction to a decimal: Transition from \( \frac{9}{40} \) to 0.225 through division.
• Convert the decimal to a percentage: Multiply 0.225 by 100 to get 22.5%.

The final step of problem solving is to check your answer against possible options, ensuring accuracy. Here, 22.5% matches option (C) in the exercise question. This systematic approach helps you build confidence and skill in tackling a wide range of mathematical challenges.