Terrence collected 3 7/10 pounds of newspaper for the recycling drive. Austen collected 4 4/5 times as much newspaper as Terrence. How many pounds of newspaper did Austen collect?

Write your answer as a fraction or as a whole or mixed number.

To solve the problem, we need to calculate how many pounds of newspaper Austen collected by multiplying the amount Terrence collected by 4 4/5.

First, let's express the mixed numbers as improper fractions:

- Terrence collected \(3 \frac{7}{10}\) pounds of newspaper.
  
  Convert to an improper fraction:
  \[
  3 \frac{7}{10} = \frac{3 \times 10 + 7}{10} = \frac{30 + 7}{10} = \frac{37}{10}
  \]

- Austen collected 4 4/5 times as much newspaper.

  Convert \(4 \frac{4}{5}\) to an improper fraction:
  \[
  4 \frac{4}{5} = \frac{4 \times 5 + 4}{5} = \frac{20 + 4}{5} = \frac{24}{5}
  \]

Now, multiply the amount Terrence collected by the fraction representing how much more Austen collected:

\[
\text{Austen's collection} = \frac{37}{10} \times \frac{24}{5}
\]

Multiply the numerators together and the denominators together:

\[
\frac{37 \times 24}{10 \times 5} = \frac{888}{50}
\]

To simplify the fraction:

1. Find the greatest common divisor (GCD) of 888 and 50.
   
   The GCD of 888 and 50 is 2.

2. Divide both the numerator and denominator by their GCD:

\[
\frac{888 \div 2}{50 \div 2} = \frac{444}{25}
\]

Since \(\frac{444}{25}\) is an improper fraction, we can convert it to a mixed number:

\[
\frac{444}{25} = 17 \frac{19}{25}
\]

So, Austen collected **17 \(\frac{19}{25}\)** pounds of newspaper.

Would you like further details on the steps, or do you have any other questions?

Here are 5 questions you might find interesting:
1. How do you simplify improper fractions in different scenarios?
2. What are some practical applications of mixed numbers in daily life?
3. Would you like to explore how to calculate the GCD for simplifying fractions?
4. Do you want to practice converting mixed numbers to improper fractions?
5. Are you curious about other methods to verify the result?

**Tip:** When multiplying fractions, always remember to multiply the numerators together and the denominators together, then simplify the resulting fraction if possible!

Explore how Austen collected 4 4/5 times more newspaper than Terrence in this math problem. Learn the step-by-step solution using fractions and multiplication. Suitable for Grades 5-6.

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