To determine how many whole friendship bracelets Bryan can make, we first need to convert the total length of leather cord from a mixed number to an improper fraction.
Bryan has \(5 + \frac{2}{3}\) feet of cord. We can convert this to an improper fraction:
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Convert the whole number to a fraction:
- The whole number 5 can be written as \(\frac{5 \cdot 3}{3} = \frac{15}{3}\).
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Add the fractional part: \[ 5 + \frac{2}{3} = \frac{15}{3} + \frac{2}{3} = \frac{15 + 2}{3} = \frac{17}{3} \] So, Bryan has \(\frac{17}{3}\) feet of leather cord.
Next, we need to find out how many bracelets he can make if each one requires \(\frac{1}{2}\) foot of cord.
To find the number of bracelets, we divide the total amount of cord by the length needed for each bracelet:
\[ \text{Number of bracelets} = \frac{\frac{17}{3}}{\frac{1}{2}} \]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \text{Number of bracelets} = \frac{17}{3} \cdot \frac{2}{1} = \frac{17 \cdot 2}{3 \cdot 1} = \frac{34}{3} \]
Now, we can convert \(\frac{34}{3}\) into a mixed number to find out how many whole bracelets that is:
\[ 34 \div 3 = 11 \quad \text{(with a remainder of 1)} \] This means: \[ \frac{34}{3} = 11 \frac{1}{3} \]
Thus, Bryan can make 11 whole bracelets with \(\frac{17}{3}\) feet of leather cord.
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