Problem 49 - Prealgebra

Question

The table shows the number of sports films created with different themes. Which theme occurs \(\frac{5}{12}\) as many times as boxing? $$\begin{array}{|l|c|}\hline \text { Surnume } & \text { Eluus } \\\\\hline \text { Boxing } & 204 \\\\\hline \text { Horse Racing } & 139 \\\\\hline \text { Football } & 123 \\\\\hline \text { Baseball } & 85 \\\\\hline\end{array}$$

Step-by-Step Solution

Answer

Baseball occurs \(\frac{5}{12}\) as many times as Boxing.

Step 1: Identify the Theme Count

From the table, we see the number of films for each theme: Boxing has 204, Horse Racing has 139, Football has 123, and Baseball has 85.

Step 2: Calculate Fraction of Boxing Count

We need to find which theme has \(\frac{5}{12}\) of the number of Boxing films. First, calculate \(\frac{5}{12} \, \text{of} \, 204\) using the formula: \[\frac{5}{12} \times 204 = \frac{5 \times 204}{12}\]

Step 3: Simplify the Calculation

Start simplifying the product and the divisor:\[\frac{5 \times 204}{12} = \frac{1020}{12}\]Divide 1020 by 12 to find the exact number.

Step 4: Division Result

Dividing 1020 by 12, we perform the calculation \(1020 \div 12 = 85\). So, the target number among the themes is 85.

Step 5: Identify Matching Theme

Finally, compare the calculated number, 85, with the film counts for each theme in the table. From the table, Baseball has 85 films.

Key Concepts

Fractions in Mathematics

Fractions are an essential building block in mathematics. They help us to express parts of a whole as well as ratios between numbers. In this exercise, the fraction \(\frac{5}{12}\) tells us how much of the boxing film count we're interested in finding. To use a fraction, you usually multiply it by another number to find a part or portion.
Here's how it works with our example:

• Multiply the boxing film count of 204 by the fraction \(\frac{5}{12}\).
• When you multiply, treat the fraction as a division: first multiply the numerator (5) by 204.
• Then divide the result by the denominator (12).
• This tells us how many films for another theme are needed to represent \(\frac{5}{12}\) of boxing films.

This example demonstrates how fractions convert counts to meaningful comparisons relative to other numbers.

Sports-Themed Math Problems

Sports-themed math problems are a fun way to apply math concepts to real-world scenarios. They engage students by relating mathematical concepts to sports, a topic many find exciting.
In the exercise, we used a sports-related scenario to solve a fraction problem. We were asked to determine which sports theme's film count represents \(\frac{5}{12}\) of the boxing theme's film count. By involving a relatable story like sports films, it can make the mathematics seem more tangible.

• Problems with sports themes often include counting and comparing different sports.
• This makes it easier to visualize and understand the mathematical operations.
• It helps to see how mathematical computations relate to real-world quantities, like the number of films.

Sports-themed math problems not only make learning fun but also demonstrate real-world applications of math.

Math Word Problems

Math word problems help translate mathematical equations and operations into everyday language. This shows how math is used in daily life to solve problems or make comparisons, much like the exercise provided.
Our exercise was a word problem framed within the context of counting sports films. By describing a situation using words, students were required to convert this information into a mathematical operation. Here’s what happens:

• You start with a real-world question: what theme occurs \(\frac{5}{12}\) as many times as boxing?
• Identify the necessary math operation to find the answer, in this case, multiplication followed by division.
• This type of problem-solving builds logical reasoning skills as you must decipher how the narrative translates to numbers and operations.

Math word problems often mimic everyday situations, enabling students to see the practical side of math, encouraging better understanding and retention.