A CBS News poll conducted January 5, 2017, among a nationwide random sample of **1204** adults, asked those adults about their party affiliation (Democrat, Republican or none) and their opinion of how the US economy was changing ("getting better," "getting worse" or "about the same"). The results are shown in the table below.


 
better

same

worse

Republican

160

170

125

Democrat

44

161

194

none

145

90

115

Use the two-way table above, please answer the following questions. **Please enter your answers as reduced fractions.**

What fraction of all survey respondents identified themselves as Democrats?   

What fraction of all survey respondents thought the economy was getting worse?   

What fraction of the Democrats thought the economy was getting worse?   

Among all survey respondents who thought the economy was getting worse, what fraction were Democrats?   

What fraction of all survey respondents were Democrats and thought the economy was getting worse?   

Let's break down the problem step by step using the data provided.

### Data Recap

\[
\begin{array}{|c|c|c|c|}
\hline
\textbf{Group} & \textbf{Better} & \textbf{Same} & \textbf{Worse} \\
\hline
\textbf{Republican} & 160 & 170 & 125 \\
\hline
\textbf{Democrat} & 44 & 161 & 194 \\
\hline
\textbf{None} & 145 & 90 & 115 \\
\hline
\end{array}
\]

### Total Number of Respondents

First, let's calculate the total number of respondents:

\[
\text{Total respondents} = 160 + 170 + 125 + 44 + 161 + 194 + 145 + 90 + 115 = 1204
\]

This matches the information provided.

### Question 1: Fraction of All Respondents Who Identified as Democrats

To find this, we sum the number of Democrats across all three opinions:

\[
\text{Total Democrats} = 44 + 161 + 194 = 399
\]

So, the fraction of all respondents who identified as Democrats is:

\[
\frac{399}{1204}
\]

This fraction is already in its reduced form.

### Question 2: Fraction of All Respondents Who Thought the Economy Was Getting Worse

To find this, we sum the number of respondents who thought the economy was getting worse:

\[
\text{Total worse} = 125 + 194 + 115 = 434
\]

So, the fraction of all respondents who thought the economy was getting worse is:

\[
\frac{434}{1204}
\]

This fraction can be reduced.

### Question 3: Fraction of Democrats Who Thought the Economy Was Getting Worse

This is the number of Democrats who thought the economy was getting worse, divided by the total number of Democrats:

\[
\frac{194}{399}
\]

This fraction is already in its reduced form.

### Question 4: Fraction of Those Who Thought the Economy Was Getting Worse That Were Democrats

This is the number of Democrats who thought the economy was getting worse, divided by the total number of respondents who thought the economy was getting worse:

\[
\frac{194}{434}
\]

This fraction can also be reduced.

### Question 5: Fraction of All Respondents Who Were Democrats and Thought the Economy Was Getting Worse

This is the number of Democrats who thought the economy was getting worse, divided by the total number of respondents:

\[
\frac{194}{1204}
\]

This fraction can be reduced.

### Final Calculation
Let’s now compute and reduce the necessary fractions where applicable.Here are the answers to each of the questions as reduced fractions:

1. **Fraction of all survey respondents identified as Democrats:** \(\frac{57}{172}\)
2. **Fraction of all survey respondents who thought the economy was getting worse:** \(\frac{31}{86}\)
3. **Fraction of the Democrats who thought the economy was getting worse:** \(\frac{194}{399}\) (already in reduced form)
4. **Fraction of those who thought the economy was getting worse that were Democrats:** \(\frac{97}{217}\)
5. **Fraction of all survey respondents who were Democrats and thought the economy was getting worse:** \(\frac{97}{602}\)

Would you like any further explanation, or do you have any other questions?

Here are 5 related questions for further exploration:
1. What fraction of Republicans thought the economy was getting better?
2. Among those who thought the economy was getting better, what fraction were Republicans?
3. What is the total number of respondents who thought the economy was getting better or staying the same?
4. How does the fraction of Republicans who thought the economy was getting worse compare to that of Democrats?
5. What percentage of respondents identified as neither Democrat nor Republican?

**Tip:** Always remember to reduce fractions to their simplest form to make them easier to interpret and compare.

Explore the analysis of a CBS News poll conducted among 1204 adults, focusing on fraction calculations regarding party affiliation and opinions on the US economy. Learn how to determine fractions of respondents who identified as Democrats, thought the economy was getting worse, and more.

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