To find the price of 16 pears, we start by computing the expression given:
\[ \frac{1}{3} \cdot \frac{6}{16} \]
Calculating this expression step-by-step:
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Multiply the numerators: \[ 1 \cdot 6 = 6 \]
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Multiply the denominators: \[ 3 \cdot 16 = 48 \]
So, we have:
\[ \frac{6}{48} \]
Now we can simplify \(\frac{6}{48}\):
\[ \frac{6 \div 6}{48 \div 6} = \frac{1}{8} \]
Now we know that the price per pear is \(\frac{1}{8}\) of the price of 6 pears. Since 6 pears cost $3, we find the cost of one pear:
\[ \text{Price per pear} = \frac{3}{6} = \frac{1}{2} \]
To find the cost of 16 pears:
\[ \text{Total cost for 16 pears} = 16 \cdot \frac{1}{2} = 8 \]
To summarize, the equivalent values for \(\frac{1}{3} \cdot \frac{6}{16}\) are:
- \(\frac{1}{8}\) (the simplified form)
- \(\frac{6}{48}\) (the multiplication result before simplification)
Hence, the cost of 16 pears is $8.