Questions: Modeling Real Life A class makes a paper chain that is 5 7/12 feet long. The class adds another 3 5/6 feet to the chain. About how long is the chain now?

Modeling Real Life A class makes a paper chain that is 5 7/12 feet long. The class adds another 3 5/6 feet to the chain. About how long is the chain now?

Transcript text: Modeling Real Life A class makes a paper chain that is $5 \frac{7}{12}$ feet long. The class adds another $3 \frac{5}{6}$ feet to the chain. About how long is the chain now?

Solution

Solution Steps

Step 1: Convert Mixed Numbers to Improper Fractions

Convert $ 5 \frac{7}{12} $ to an improper fraction: \[ 5 \frac{7}{12} = \frac{5 \times 12 + 7}{12} = \frac{67}{12} \]

Convert $ 3 \frac{5}{6} $ to an improper fraction: \[ 3 \frac{5}{6} = \frac{3 \times 6 + 5}{6} = \frac{23}{6} \]

Step 2: Find a Common Denominator

The denominators are 12 and 6. The least common denominator (LCD) is 12. Convert $ \frac{23}{6} $ to a fraction with denominator 12: \[ \frac{23}{6} = \frac{23 \times 2}{6 \times 2} = \frac{46}{12} \]

Step 3: Add the Fractions

Add the two fractions: \[ \frac{67}{12} + \frac{46}{12} = \frac{67 + 46}{12} = \frac{113}{12} \]

Step 4: Convert the Result Back to a Mixed Number

Convert $ \frac{113}{12} $ back to a mixed number: \[ \frac{113}{12} = 9 \frac{5}{12} \]