Problem 64 - Algebra 1

Question

Kareem Abdul-Jabbar scored \(38,387\) points and grabbed \(17,440\) rebounds in 1560 National Basketball Association games. How many points did he average per game? How many rebounds did he average per game? (Round your answers to the nearest tenth.) ) Source: NBA

Step-by-Step Solution

Answer

Kareem Abdul-Jabbar averaged approximately \(\frac{38,387}{1560} = 24.6\) points per game and \(\frac{17,440}{1560} = 11.2\) rebounds per game.

Step 1: Identify the Total Points and Total Games

Identify the total amount of points which is stated as \(38,387\) points and the total number of games which is \(1560\) National Basketball Association games

Step 2: Calculate Average Points Per Game

Calculate the average by dividing the total points by total games which is \(\frac{38,387}{1560}\). Use a calculator to get the result and remember to round to the nearest tenth.

Step 3: Identify Total Rebounds

Next, identify the total number of rebounds, which is stated as \(17,440\) rebounds.

Step 4: Calculate Average Rebounds Per Game

Divide the total number of rebounds by the total number of games, so \(\frac{17,440}{1560}\). Use a calculator to get the result, and again, remember to round to the nearest tenth.

Key Concepts

Calculating Averages

Understanding how to calculate averages is essential for interpreting data in various contexts, from sports statistics to exam scores. An average, also known as the mean, is found by dividing the sum of a set of numbers by the quantity of numbers in the set.

For instance, take the example of Kareem Abdul-Jabbar's impressive basketball career. To find his average points per game, we start by identifying the total number of points he scored, which is 38,387. We then divide this by the total number of games he played, which is 1,560. The formula we use is:
\[\begin{equation} \text{Average Points Per Game} = \frac{\text{Total Points}}{\text{Total Games}} \.\end{equation}\]
Similarly, to calculate his average rebounds per game, we divide the total number of rebounds, 17,440, by the same number of games:
\[\begin{equation} \text{Average Rebounds Per Game} = \frac{\text{Total Rebounds}}{\text{Total Games}} \.\end{equation}\]
Averages provide a simple yet powerful way to gauge performance over time, offering a single value that summarizes multiple individual events.

Division in Algebra

Division is one of the fundamental operations in algebra, and it plays a crucial role in calculating averages. Understanding how to divide in algebra is about breaking down a quantity into equal parts.

In the context of our basketball example, when we calculate averages, we are dividing the total points and rebounds by the number of games. This is represented algebraically as a fraction or ratio. For Abdul-Jabbar's points, we represent it as:
\[\begin{equation} \frac{38,387}{1560} \.\end{equation}\]
This operation distributes the total points evenly across all the games played. It's important to recognize that division in algebra follows the same rules as arithmetic division, but it can also involve variables and more complex expressions. When performing division, especially with large numbers, a calculator is invaluable for ensuring accuracy.

Rounding Numbers

After calculating averages, it's often necessary to round numbers to make them simpler to understand and use. Rounding is the process of adjusting numerical values to a specified degree of accuracy. When rounding to the nearest tenth, as the basketball exercise suggests, we look at the digit in the hundredths place.

If the hundredths digit is 5 or greater, we round the tenth's place up. Otherwise, we leave it as is. Here's what this looks like for Abdul-Jabbar's averages:

\[\begin{equation} \text{Points Per Game} \textrm{Original number}: 24.\textrm{6076...} \textrm{Rounded number}: 24.6 \.\end{equation}\]
\[\begin{equation} \text{Rebounds Per Game} \textrm{Original number}: 11.\textrm{1794...} \textrm{Rounded number}: 11.2 \.\end{equation}\]
Rounding is not only about simplicity; it also helps in reporting statistics in a consistent and standardized manner.