Question

Mrs. Webster surveyed her class of 20 students. She asked each student to identify his or her favorite sport out of a list of five sports. Each student could only choose one sport and everyone participated. The results of the survey are shown in the chart. $$ \begin{array}{|l|l|} \hline \text { Football } & 8 \\ \hline \text { Basketball } & 5 \\ \hline \text { Baseball } & 4 \\ \hline \text { Soccer } & 2 \\ \hline \text { Hockey } & 1 \\ \hline \end{array} $$ What is the ratio of football fans to soccer fans? Write your answer in the box.

Short answer

The ratio is 4:1.

Step-by-step solution

Understand the problem

Identify that you need to find the ratio of students who prefer football to those who prefer soccer. Use the data from the given chart.

Extract relevant data

From the chart: - Number of students who prefer football: 8- Number of students who prefer soccer: 2

Set up the ratio

Express the ratio of football fans to soccer fans as \(\frac{\text{Number of Football Fans}}{\text{Number of Soccer Fans}}\). Plug in the numbers obtained from the chart: \(\frac{8}{2}\)

Simplify the ratio

Simplify the fraction \(\frac{8}{2}\) by dividing the numerator and the denominator by their greatest common divisor (GCD), which is 2. \(\frac{8 \div 2}{2 \div 2} = \frac{4}{1}\)

Key concepts

Survey Data Analysis

To solve ratio problems, you first need to analyze the data given in the survey. In this case, Mrs. Webster surveyed her class of 20 students to determine their favorite sport among five options. Each student chose a favorite, and the results were tallied in a chart.
To analyze survey data:

• Identify the question or problem: Here, we want to find the ratio of football fans to soccer fans.
• Extract the relevant numbers: From the chart, we know 8 students prefer football and 2 prefer soccer.
• Convert this data into a format useful for answering the question: This means setting up a ratio using these numbers.

Good survey data analysis is the foundation for solving ratio problems. Pay close attention to each part of the data.

Fractions Simplification

Simplifying fractions is crucial in solving ratio problems. In the exercise, we express the ratio of football fans to soccer fans as \(\frac{8}{2}\).
To simplify this fraction:

• Find the greatest common divisor (GCD) of the numerator and the denominator, which is 2 in this case.
• Divide both the numerator and the denominator by the GCD: \(\frac{8 \, \text{div} \, 2}{2 \, \text{div} \, 2}\).
• This leaves us with \(\frac{4}{1}\), which simplifies to just 4.

Simplifying fractions makes your final answer cleaner and easier to understand. It’s an essential skill in math and can be applied to a wide range of problems.

Ratios in Math

Ratios are used in math to compare two quantities. They can tell you how much of one thing there is compared to another.
Here's how to work with ratios:

• Set up the ratio by placing the two numbers in relation to each other: \(\frac{8}{2}\).
• Simplify the ratio to make it easier to understand: Simplified, \(\frac{8}{2}\) becomes 4, meaning there are 4 football fans for every soccer fan.
• Use ratios to compare different quantities: Ratios go beyond simple fractions; they can compare parts of a whole or show different relationships in data.
• Apply ratios to real-life situations: Understanding ratios can help you in everyday life, from cooking to budgeting.

Ratios help us make sense of data and can often give a clearer picture of a situation by comparing parts of the data set directly.